Randomized Equivalence Study Evaluating the Efficacy of Two Commercial Internal Teat Sealants in Dairy Cows: Impact on Quarter-Level Dry Period IMI Dynamics
Sam Rowe (samrowe101@gmail.com)
September 1st, 2019
Download all datasets HERE
library(knitr)
#Windows
knitr::opts_knit$set(root.dir = "C:/Users/rowe0122/Dropbox/R backup/Lockout - R/LOCKOUT")
knitr::opts_chunk$set(echo=TRUE, warning=FALSE, message=FALSE)
#Mac
#knitr::opts_knit$set(root.dir = "~/Dropbox/R backup/Lockout - R/LOCKOUT")
Evaluate Data
Show first 10 rows of dataset
load(file="lockqtrdat.Rdata")
library(dplyr)
lockqtr = lockqtr %>%
mutate(Tx = recode(lockqtr$Tx,
"0" = "Orbeseal", "1" = "Lockout"))
Desc1 <- lockqtr %>% subset(select=c(FARMID,Cow,QTR,Tx,Age,Parity,IMIDO,SCCDO,MYDO,DIMDO,CM1,PeakSCC,DPlength,PCSampDIM,IMIPC,Cure,NewIMI))
head(lockqtr, n=10)
Inspect Data
library(summarytools)
#opts_chunk$set(comment = NA, prompt = FALSE, cache = FALSE, results = 'asis')
print(summarytools::dfSummary(lockqtr, valid.col=FALSE,graph.magnif=1,varnumbers=F,style="grid",graph.col = F))## Data Frame Summary
##
## Dimensions: 3175 x 24
## Duplicates: 0
##
## +-------------+---------------------------------+---------------------+----------+
## | Variable | Stats / Values | Freqs (% of Valid) | Missing |
## +=============+=================================+=====================+==========+
## | Cow | Mean (sd) : 9.4 (1.3) | 811 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 6.3 < 10.1 < 11.2 | | |
## | | IQR (CV) : 2.1 (0.1) | | |
## +-------------+---------------------------------+---------------------+----------+
## | QTR | 1. LF | 785 (24.7%) | 0 |
## | [factor] | 2. LR | 798 (25.1%) | (0%) |
## | | 3. RF | 796 (25.1%) | |
## | | 4. RR | 796 (25.1%) | |
## +-------------+---------------------------------+---------------------+----------+
## | FARMID | Mean (sd) : 3 (1.3) | 1 : 695 (21.9%) | 0 |
## | [numeric] | min < med < max: | 2 : 298 ( 9.4%) | (0%) |
## | | 1 < 3 < 5 | 3 : 1125 (35.4%) | |
## | | IQR (CV) : 2 (0.5) | 4 : 551 (17.3%) | |
## | | | 5 : 506 (15.9%) | |
## +-------------+---------------------------------+---------------------+----------+
## | Enrolldate | min : 2018-06-26 | 17 distinct values | 0 |
## | [Date] | med : 2018-07-31 | | (0%) |
## | | max : 2018-08-22 | | |
## | | range : 1m 27d | | |
## +-------------+---------------------------------+---------------------+----------+
## | Tx | 1. Orbeseal | 1580 (49.8%) | 0 |
## | [factor] | 2. Lockout | 1595 (50.2%) | (0%) |
## +-------------+---------------------------------+---------------------+----------+
## | Age | Mean (sd) : 46 (15.4) | 561 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 17 < 43.9 < 117 | | |
## | | IQR (CV) : 23.1 (0.3) | | |
## +-------------+---------------------------------+---------------------+----------+
## | Parity | 1. 1 | 1348 (42.5%) | 0 |
## | [factor] | 2. 2 | 927 (29.2%) | (0%) |
## | | 3. 3 | 584 (18.4%) | |
## | | 4. 4 | 316 (10.0%) | |
## +-------------+---------------------------------+---------------------+----------+
## | Calv1Date | min : 2016-02-08 | 208 distinct values | 0 |
## | [Date] | med : 2017-09-19 | | (0%) |
## | | max : 2017-12-01 | | |
## | | range : 1y 9m 23d | | |
## +-------------+---------------------------------+---------------------+----------+
## | MYDO | Mean (sd) : 25.4 (9) | 92 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 1.8 < 25.9 < 49 | | |
## | | IQR (CV) : 14.1 (0.4) | | |
## +-------------+---------------------------------+---------------------+----------+
## | DIMDO | Mean (sd) : 330 (65.5) | 195 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 256 < 307 < 869 | | |
## | | IQR (CV) : 62 (0.2) | | |
## +-------------+---------------------------------+---------------------+----------+
## | SCCDO | Mean (sd) : 4.6 (1.2) | 330 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 0 < 4.6 < 8.9 | | |
## | | IQR (CV) : 1.5 (0.3) | | |
## +-------------+---------------------------------+---------------------+----------+
## | PeakSCC | Mean (sd) : 5.7 (1.2) | 536 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 3 < 5.6 < 9.2 | | |
## | | IQR (CV) : 1.6 (0.2) | | |
## +-------------+---------------------------------+---------------------+----------+
## | CM1 | 1. 0 | 2384 (75.1%) | 0 |
## | [factor] | 2. 1 | 791 (24.9%) | (0%) |
## +-------------+---------------------------------+---------------------+----------+
## | Calv2Date | min : 2018-07-27 | 91 distinct values | 0 |
## | [Date] | med : 2018-09-24 | | (0%) |
## | | max : 2018-11-01 | | |
## | | range : 3m 5d | | |
## +-------------+---------------------------------+---------------------+----------+
## | DPlength | Mean (sd) : 54.9 (8.7) | 50 distinct values | 0 |
## | [numeric] | min < med < max: | | (0%) |
## | | 30 < 55 < 85 | | |
## | | IQR (CV) : 13 (0.2) | | |
## +-------------+---------------------------------+---------------------+----------+
## | DOCult1 | 1. No Growth | 2347 (78.0%) | 165 |
## | [character] | 2. Staphylococcus chromogene | 317 (10.5%) | (5.2%) |
## | | 3. Staphylococcus sp. | 82 ( 2.7%) | |
## | | 4. Bacillus sp. | 56 ( 1.9%) | |
## | | 5. Staphylococcus haemolytic | 34 ( 1.1%) | |
## | | 6. Corynebacterium sp. | 26 ( 0.9%) | |
## | | 7. Streptococcus uberis | 22 ( 0.7%) | |
## | | 8. Streptococcus sp. | 14 ( 0.5%) | |
## | | 9. Lactococcus garvieae | 13 ( 0.4%) | |
## | | 10. Staphylococcus simulans | 13 ( 0.4%) | |
## | | [ 22 others ] | 86 ( 2.9%) | |
## +-------------+---------------------------------+---------------------+----------+
## | DOCult2 | 1. Bacillus sp. | 8 (21.1%) | 3137 |
## | [character] | 2. Staphylococcus chromogene | 8 (21.1%) | (98.8%) |
## | | 3. Staphylococcus sp. | 8 (21.1%) | |
## | | 4. Streptococcus uberis | 4 (10.5%) | |
## | | 5. Staphylococcus haemolytic | 2 ( 5.3%) | |
## | | 6. Staphylococcus sciuri | 2 ( 5.3%) | |
## | | 7. Corynebacterium sp. | 1 ( 2.6%) | |
## | | 8. Micrococcus sp. | 1 ( 2.6%) | |
## | | 9. Staphylococcus xylosus/sa | 1 ( 2.6%) | |
## | | 10. Streptococcus dysgalactia | 1 ( 2.6%) | |
## | | [ 2 others ] | 2 ( 5.3%) | |
## +-------------+---------------------------------+---------------------+----------+
## | PCCult1 | 1. No Growth | 2449 (87.2%) | 368 |
## | [character] | 2. Staphylococcus chromogene | 100 ( 3.6%) | (11.59%) |
## | | 3. Staphylococcus sp. | 59 ( 2.1%) | |
## | | 4. Bacillus sp. | 56 ( 2.0%) | |
## | | 5. Staphylococcus sciuri | 52 ( 1.9%) | |
## | | 6. Corynebacterium sp. | 14 ( 0.5%) | |
## | | 7. Escherichia coli | 8 ( 0.3%) | |
## | | 8. Gram negative organism | 8 ( 0.3%) | |
## | | 9. Acinetobacter sp. | 6 ( 0.2%) | |
## | | 10. Gram positive coccus | 6 ( 0.2%) | |
## | | [ 19 others ] | 49 ( 1.8%) | |
## +-------------+---------------------------------+---------------------+----------+
## | PCCult2 | 1. Bacillus sp. | 5 (27.8%) | 3157 |
## | [character] | 2. Gram negative organism | 1 ( 5.6%) | (99.43%) |
## | | 3. Staphylococcus chromogene | 7 (38.9%) | |
## | | 4. Staphylococcus haemolytic | 2 (11.1%) | |
## | | 5. Staphylococcus sciuri | 1 ( 5.6%) | |
## | | 6. Staphylococcus sp. | 1 ( 5.6%) | |
## | | 7. Streptococcus uberis | 1 ( 5.6%) | |
## +-------------+---------------------------------+---------------------+----------+
## | PCSampDIM | min : 0 | 14 distinct values | 158 |
## | [difftime] | med : 5 | | (4.98%) |
## | | max : 13 | | |
## | | units : days | | |
## +-------------+---------------------------------+---------------------+----------+
## | IMIDO | Min : 0 | 0 : 2347 (78.0%) | 165 |
## | [numeric] | Mean : 0.2 | 1 : 663 (22.0%) | (5.2%) |
## | | Max : 1 | | |
## +-------------+---------------------------------+---------------------+----------+
## | IMIPC | Min : 0 | 0 : 2449 (87.2%) | 368 |
## | [numeric] | Mean : 0.1 | 1 : 358 (12.8%) | (11.59%) |
## | | Max : 1 | | |
## +-------------+---------------------------------+---------------------+----------+
## | Cure | Min : 0 | 0 : 40 ( 7.1%) | 2613 |
## | [numeric] | Mean : 0.9 | 1 : 522 (92.9%) | (82.3%) |
## | | Max : 1 | | |
## +-------------+---------------------------------+---------------------+----------+
## | NewIMI | Min : 0 | 0 : 2371 (89.0%) | 511 |
## | [numeric] | Mean : 0.1 | 1 : 293 (11.0%) | (16.09%) |
## | | Max : 1 | | |
## +-------------+---------------------------------+---------------------+----------+?summarytools::dfSummary
Compare treatment groups
table1::table1(~ factor(FARMID) + Age + Parity + factor(IMIDO) + SCCDO + MYDO + as.numeric(DIMDO) + CM1 + PeakSCC + as.numeric(DPlength) + as.numeric(PCSampDIM) | Tx, data=lockqtr)| Orbeseal (n=1580) |
Lockout (n=1595) |
Overall (n=3175) |
|
|---|---|---|---|
| factor(FARMID) | |||
| 1 | 343 (21.7%) | 352 (22.1%) | 695 (21.9%) |
| 2 | 144 (9.1%) | 154 (9.7%) | 298 (9.4%) |
| 3 | 560 (35.4%) | 565 (35.4%) | 1125 (35.4%) |
| 4 | 272 (17.2%) | 279 (17.5%) | 551 (17.4%) |
| 5 | 261 (16.5%) | 245 (15.4%) | 506 (15.9%) |
| Age | |||
| Mean (SD) | 46.7 (16.2) | 45.3 (14.6) | 46.0 (15.4) |
| Median [Min, Max] | 44.0 [18.0, 117] | 43.9 [17.0, 113] | 43.9 [17.0, 117] |
| Parity | |||
| 1 | 661 (41.8%) | 687 (43.1%) | 1348 (42.5%) |
| 2 | 452 (28.6%) | 475 (29.8%) | 927 (29.2%) |
| 3 | 288 (18.2%) | 296 (18.6%) | 584 (18.4%) |
| 4 | 179 (11.3%) | 137 (8.6%) | 316 (10.0%) |
| factor(IMIDO) | |||
| 0 | 1184 (74.9%) | 1163 (72.9%) | 2347 (73.9%) |
| 1 | 317 (20.1%) | 346 (21.7%) | 663 (20.9%) |
| Missing | 79 (5.0%) | 86 (5.4%) | 165 (5.2%) |
| SCCDO | |||
| Mean (SD) | 4.54 (1.21) | 4.57 (1.22) | 4.55 (1.21) |
| Median [Min, Max] | 4.60 [0.00, 8.92] | 4.53 [0.00, 8.85] | 4.55 [0.00, 8.92] |
| MYDO | |||
| Mean (SD) | 25.4 (8.82) | 25.4 (9.18) | 25.4 (9.00) |
| Median [Min, Max] | 26.3 [2.72, 48.5] | 25.4 [1.81, 49.0] | 25.9 [1.81, 49.0] |
| as.numeric(DIMDO) | |||
| Mean (SD) | 330 (63.2) | 330 (67.8) | 330 (65.5) |
| Median [Min, Max] | 308 [256, 817] | 307 [260, 869] | 307 [256, 869] |
| CM1 | |||
| 0 | 1170 (74.1%) | 1214 (76.1%) | 2384 (75.1%) |
| 1 | 410 (25.9%) | 381 (23.9%) | 791 (24.9%) |
| PeakSCC | |||
| Mean (SD) | 5.69 (1.16) | 5.80 (1.33) | 5.75 (1.25) |
| Median [Min, Max] | 5.55 [3.00, 9.21] | 5.58 [3.09, 9.21] | 5.56 [3.00, 9.21] |
| as.numeric(DPlength) | |||
| Mean (SD) | 54.9 (8.83) | 54.9 (8.64) | 54.9 (8.73) |
| Median [Min, Max] | 55.0 [30.0, 84.0] | 55.0 [30.0, 85.0] | 55.0 [30.0, 85.0] |
| as.numeric(PCSampDIM) | |||
| Mean (SD) | 5.17 (2.48) | 5.15 (2.39) | 5.16 (2.44) |
| Median [Min, Max] | 5.00 [0.00, 13.0] | 5.00 [0.00, 13.0] | 5.00 [0.00, 13.0] |
| Missing | 81 (5.1%) | 77 (4.8%) | 158 (5.0%) |
Compare herds
table1::table1(~ Age + Parity + SCCDO + MYDO + CM1 + PeakSCC + as.numeric(DPlength) + as.numeric(PCSampDIM) + factor(IMIDO) + factor(IMIPC) + factor(Cure) + factor(NewIMI) | factor(FARMID), data=lockqtr)| 1 (n=695) |
2 (n=298) |
3 (n=1125) |
4 (n=551) |
5 (n=506) |
Overall (n=3175) |
|
|---|---|---|---|---|---|---|
| Age | ||||||
| Mean (SD) | 43.2 (13.3) | 41.1 (9.93) | 46.9 (14.6) | 49.3 (17.6) | 47.2 (18.6) | 46.0 (15.4) |
| Median [Min, Max] | 42.3 [28.6, 90.4] | 37.6 [29.6, 65.2] | 44.9 [30.1, 103] | 46.2 [17.4, 113] | 44.5 [17.0, 117] | 43.9 [17.0, 117] |
| Parity | ||||||
| 1 | 314 (45.2%) | 157 (52.7%) | 443 (39.4%) | 226 (41.0%) | 208 (41.1%) | 1348 (42.5%) |
| 2 | 252 (36.3%) | 89 (29.9%) | 305 (27.1%) | 140 (25.4%) | 141 (27.9%) | 927 (29.2%) |
| 3 | 75 (10.8%) | 52 (17.4%) | 282 (25.1%) | 104 (18.9%) | 71 (14.0%) | 584 (18.4%) |
| 4 | 54 (7.8%) | 0 (0%) | 95 (8.4%) | 81 (14.7%) | 86 (17.0%) | 316 (10.0%) |
| SCCDO | ||||||
| Mean (SD) | 4.17 (1.32) | 4.45 (1.14) | 4.63 (1.02) | 4.55 (1.24) | 4.98 (1.32) | 4.55 (1.21) |
| Median [Min, Max] | 4.16 [0.00, 7.88] | 4.41 [2.64, 7.38] | 4.57 [2.56, 8.92] | 4.66 [0.00, 8.63] | 4.89 [0.00, 8.85] | 4.55 [0.00, 8.92] |
| MYDO | ||||||
| Mean (SD) | 15.7 (5.35) | 26.2 (4.85) | 30.4 (7.90) | 29.5 (7.50) | 23.0 (6.79) | 25.4 (9.00) |
| Median [Min, Max] | 15.9 [2.72, 30.8] | 26.8 [13.6, 36.3] | 31.8 [13.2, 48.5] | 29.9 [13.6, 49.0] | 23.6 [1.81, 47.2] | 25.9 [1.81, 49.0] |
| CM1 | ||||||
| 0 | 592 (85.2%) | 263 (88.3%) | 694 (61.7%) | 452 (82.0%) | 383 (75.7%) | 2384 (75.1%) |
| 1 | 103 (14.8%) | 35 (11.7%) | 431 (38.3%) | 99 (18.0%) | 123 (24.3%) | 791 (24.9%) |
| PeakSCC | ||||||
| Mean (SD) | 5.62 (1.16) | 5.17 (1.08) | 5.73 (1.33) | 5.88 (1.16) | 6.16 (1.20) | 5.75 (1.25) |
| Median [Min, Max] | 5.54 [3.47, 8.78] | 5.03 [3.18, 7.79] | 5.44 [3.00, 9.21] | 5.69 [3.40, 8.95] | 6.12 [3.09, 8.85] | 5.56 [3.00, 9.21] |
| as.numeric(DPlength) | ||||||
| Mean (SD) | 54.9 (9.57) | 55.2 (7.79) | 54.1 (9.93) | 57.8 (5.36) | 53.5 (7.38) | 54.9 (8.73) |
| Median [Min, Max] | 54.0 [30.0, 79.0] | 56.0 [36.0, 79.0] | 52.0 [30.0, 85.0] | 58.0 [35.0, 73.0] | 53.0 [30.0, 72.0] | 55.0 [30.0, 85.0] |
| as.numeric(PCSampDIM) | ||||||
| Mean (SD) | 3.66 (2.61) | 3.91 (2.36) | 5.77 (1.92) | 5.68 (2.44) | 5.89 (2.13) | 5.16 (2.44) |
| Median [Min, Max] | 3.00 [0.00, 12.0] | 4.00 [0.00, 9.00] | 6.00 [2.00, 9.00] | 5.00 [0.00, 13.0] | 6.00 [3.00, 12.0] | 5.00 [0.00, 13.0] |
| Missing | 50 (7.2%) | 31 (10.4%) | 38 (3.4%) | 27 (4.9%) | 12 (2.4%) | 158 (5.0%) |
| factor(IMIDO) | ||||||
| 0 | 419 (60.3%) | 235 (78.9%) | 1002 (89.1%) | 320 (58.1%) | 371 (73.3%) | 2347 (73.9%) |
| 1 | 184 (26.5%) | 53 (17.8%) | 112 (10.0%) | 198 (35.9%) | 116 (22.9%) | 663 (20.9%) |
| Missing | 92 (13.2%) | 10 (3.4%) | 11 (1.0%) | 33 (6.0%) | 19 (3.8%) | 165 (5.2%) |
| factor(IMIPC) | ||||||
| 0 | 530 (76.3%) | 203 (68.1%) | 1002 (89.1%) | 324 (58.8%) | 390 (77.1%) | 2449 (77.1%) |
| 1 | 55 (7.9%) | 29 (9.7%) | 40 (3.6%) | 157 (28.5%) | 77 (15.2%) | 358 (11.3%) |
| Missing | 110 (15.8%) | 66 (22.1%) | 83 (7.4%) | 70 (12.7%) | 39 (7.7%) | 368 (11.6%) |
| factor(Cure) | ||||||
| 0 | 2 (0.3%) | 3 (1.0%) | 3 (0.3%) | 25 (4.5%) | 7 (1.4%) | 40 (1.3%) |
| 1 | 146 (21.0%) | 35 (11.7%) | 99 (8.8%) | 143 (26.0%) | 99 (19.6%) | 522 (16.4%) |
| Missing | 547 (78.7%) | 260 (87.2%) | 1023 (90.9%) | 383 (69.5%) | 400 (79.1%) | 2613 (82.3%) |
| factor(NewIMI) | ||||||
| 0 | 466 (67.1%) | 198 (66.4%) | 995 (88.4%) | 331 (60.1%) | 381 (75.3%) | 2371 (74.7%) |
| 1 | 44 (6.3%) | 26 (8.7%) | 37 (3.3%) | 119 (21.6%) | 67 (13.2%) | 293 (9.2%) |
| Missing | 185 (26.6%) | 74 (24.8%) | 93 (8.3%) | 101 (18.3%) | 58 (11.5%) | 511 (16.1%) |
Outcome 1: Cure
library(gmodels)
CrossTable(lockqtr$Tx,lockqtr$Cure,prop.c=FALSE,prop.t=FALSE,prop.chisq = FALSE)##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## |-------------------------|
##
##
## Total Observations in Table: 562
##
##
## | lockqtr$Cure
## lockqtr$Tx | 0 | 1 | Row Total |
## -------------|-----------|-----------|-----------|
## Orbeseal | 22 | 240 | 262 |
## | 0.084 | 0.916 | 0.466 |
## -------------|-----------|-----------|-----------|
## Lockout | 18 | 282 | 300 |
## | 0.060 | 0.940 | 0.534 |
## -------------|-----------|-----------|-----------|
## Column Total | 40 | 522 | 562 |
## -------------|-----------|-----------|-----------|
##
##
Logistic regression model for dry period cure
Model building plan
Model type: Logistic regression with mixed effects (generalized linear mixed model with binomial family / logit link).
Step 1: Identify potential confouders using a directed acyclic graph (DAG)
Step 2: Identify correlated variables using pearson and kendalls correlation coefficients
Step 3: Create model with all potential confounders
Step 4: Investigate potential effect measure modification
Step 5: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if odds ratio for algorithm or culture changes by >10% after removing the covariate, the covariate is retained in the model)
Step 6: Report final model
Step 1: DAG
This is used to identify variables that could be confounders if they are not balanced between treatment groups.
library(DiagrammeR)
mermaid("graph LR
T(Treatment)-->U(Cure)
A(Age)-->T
P(Parity)-->T
M(Yield at dry-off)-->T
S(SCC during prev lactation)-->T
C(CM in prev lact)-->T
D(DIM at dry off) --> T
K(DIM at post calving sample) --> T
D-->M
D-->S
D-->U
K-->U
A-->U
P-->U
M-->U
S-->U
C-->U
C-->M
P-->C
P-->S
P-->M
A-->P
A-->C
A-->S
A-->M
M-->S
C-->S
style D fill:#FFFFFF, stroke-width:0px
style K fill:#FFFFFF, stroke-width:0px
style A fill:#FFFFFF, stroke-width:0px
style T fill:#FFFFFF, stroke-width:2px
style P fill:#FFFFFF, stroke-width:0px
style M fill:#FFFFFF, stroke-width:0px
style S fill:#FFFFFF, stroke-width:0px
style C fill:#FFFFFF, stroke-width:0px
style I fill:#FFFFFF, stroke-width:0px
style U fill:#FFFFFF, stroke-width:2px
")Parity [“Parity”] or Age [“Age”] <- likely to correlated
Yield at most recent test before dry off [“DOMY”]
Somatic cell count during previous lactation [“SCCDO” and “PeakSCC”]
Clinical mastitis in previous lactation [“CM1”]
Days in milk at dry-off [“DODIM”]
Days in milk at post-calving sample [“PCSampDIM”]
Step 2: Identify correlated covariates
Pearson correlation matrix among potential predictors
library(psych)
cor <- Desc1[, c(5,6,8,9,10,12,13)]
cor$Parity <- as.numeric(cor$Parity)
cor <- cor(cor, use = "complete.obs")
corPlot(cor,numbers=TRUE)
cor <- Desc1[, c(5,6,8,9,10,12,13)]
cor$Parity <- as.numeric(cor$Parity)
cor <- cor(cor, use = "complete.obs", method="kendal")
corPlot(cor,numbers=TRUE)
Age and Parity highly correlated as expected. Will only offer parity.
Steps 3 to 6 done in Stata. Log file pasted below.
. *Step 3: Create full model with all potential covariates
. meglm Cure i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(10) = 11.82
Log likelihood = -130.24057 Prob > chi2 = 0.2975
--------------------------------------------------------------
Cure | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .512229 .355489 -.1845167 1.208975
|
Parity |
2 | -.2742185 .4422871 -1.141085 .5926484
3 | .7200151 .628142 -.5111205 1.951151
4 | -.5752739 .5804639 -1.712962 .5624144
|
SCCDO | .117288 .1475205 -.1718469 .4064229
PeakSCC | -.287137 .1722732 -.6247862 .0505123
MYDO | -.0097148 .0285632 -.0656976 .046268
|
CM1 |
1 | .9204964 .4926131 -.0450075 1.886
DIMDO | -.0028965 .0027986 -.0083817 .0025887
PCSampDIM | .0369436 .0781341 -.1161965 .1900836
_cons | 4.726348 1.790483 1.217066 8.235631
-------------+------------------------------------------------
FARMID |
var(_cons)| .6741527 .606448 .1156225 3.930739
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 8.86e-34 1.11e-17 . .
--------------------------------------------------------------
LR test vs. logistic model: chibar2(01) = 9.93 Prob >= chibar2 = 0.0008
.
. *Step 4: Effect measure modification
. *Will test Tx:Farm, Tx:Parity, Tx:PrevCM
.
. *Step 4a: Tx:Farm
. meglm Cure i.Tx##i.FARMID i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(18) = 31.39
Log likelihood = -123.77899 Prob > chi2 = 0.0259
--------------------------------------------------------------
Cure | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .0366577 1.438829 -2.783395 2.856711
|
FARMID |
2 | -2.195981 1.515395 -5.166101 .7741389
3 | -1.503598 1.361501 -4.172092 1.164895
4 | -3.242125 1.176727 -5.548467 -.9357832
5 | -2.02928 1.185866 -4.353535 .2949742
|
Tx#FARMID |
1#2 | -.0872561 1.930424 -3.870818 3.696306
1#3 | .5758022 1.922322 -3.19188 4.343484
1#4 | .6237609 1.512506 -2.340695 3.588217
1#5 | .5327658 1.654455 -2.709906 3.775437
|
Parity |
2 | -.2087316 .4532388 -1.097063 .6796001
3 | .8060823 .6386669 -.4456818 2.057846
4 | -.5422512 .5993706 -1.716996 .6324935
|
SCCDO | .1534688 .1532957 -.1469852 .4539229
PeakSCC | -.2917319 .1775356 -.6396953 .0562315
MYDO | .0063618 .0294397 -.0513391 .0640626
|
CM1 |
1 | .9046163 .4963608 -.0682329 1.877465
DIMDO | -.0026624 .0030389 -.0086187 .0032938
PCSampDIM | .0551309 .0810745 -.1037722 .2140339
_cons | 5.897307 1.953007 2.069485 9.72513
-------------+------------------------------------------------
FARMID |
var(_cons)| 3.26e-35 2.69e-18 . .
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 9.88e-33 1.11e-16 . .
--------------------------------------------------------------
LR test vs. logistic model: chi2(0) = 0.00 Prob > chi2 = .
Note: LR test is conservative and provided only for reference.
. testparm Tx#FARMID
( 1) [Cure]2.Tx#2.FARMID = 0
( 2) [Cure]2.Tx#3.FARMID = 0
( 3) [Cure]2.Tx#4.FARMID = 0
( 4) [Cure]2.Tx#5.FARMID = 0
chi2( 4) = 0.40
Prob > chi2 = 0.9825
.
. *P > 0.05. Will not investigate further
.
. *Step 4b: Tx: Parity
. meglm Cure i.Tx##i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(13) = 15.83
Log likelihood = -128.2291 Prob > chi2 = 0.2586
--------------------------------------------------------------
Cure | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .121818 .5428949 -.9422365 1.185872
|
Parity |
2 | -.8349406 .5673 -1.946828 .276947
3 | .6940131 .8862026 -1.042912 2.430938
4 | -.4143782 .7796615 -1.942487 1.11373
|
Tx#Parity |
1#2 | 1.507879 .9083797 -.2725126 3.28827
1#3 | .0656075 1.179987 -2.247125 2.37834
1#4 | -.4157975 1.078838 -2.530281 1.698686
|
SCCDO | .1093517 .1476322 -.1800021 .3987055
PeakSCC | -.260975 .1736674 -.6013569 .0794069
MYDO | .0012534 .0301762 -.0578907 .0603976
|
CM1 |
1 | .9140898 .4953901 -.0568569 1.885037
DIMDO | -.0033123 .002864 -.0089256 .002301
PCSampDIM | .0497226 .0801312 -.1073316 .2067769
_cons | 4.605594 1.863781 .9526506 8.258538
-------------+------------------------------------------------
FARMID |
var(_cons)| .8009463 .7191471 .1378268 4.654502
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 9.66e-34 1.70e-17 . .
--------------------------------------------------------------
LR test vs. logistic model: chibar2(01) = 10.29 Prob >= chibar2 = 0.0007
. testparm Tx#Parity
( 1) [Cure]2.Tx#2.Parity = 0
( 2) [Cure]2.Tx#3.Parity = 0
( 3) [Cure]2.Tx#4.Parity = 0
chi2( 3) = 3.68
Prob > chi2 = 0.2979
. *P > 0.05. Will not investigate further
.
.
. *Step 4c: Tx:PrevCM
. meglm Cure i.Tx##i.CM1 i.Parity SCCDO PeakSCC MYDO DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(11) = 11.55
Log likelihood = -129.36034 Prob > chi2 = 0.3981
--------------------------------------------------------------
Cure | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .3018214 .3904861 -.4635173 1.06716
|
CM1 |
1 | .4580864 .5812234 -.6810906 1.597263
|
Tx#CM1 |
1#1 | 1.45075 1.200273 -.9017428 3.803243
|
Parity |
2 | -.2794865 .4427814 -1.147322 .588349
3 | .7441237 .6302965 -.4912348 1.979482
4 | -.6002023 .5812827 -1.739495 .5390908
|
SCCDO | .108524 .1496034 -.1846933 .4017413
PeakSCC | -.2789173 .170748 -.6135773 .0557427
MYDO | -.0099424 .0284513 -.0657058 .0458211
DIMDO | -.0030744 .0028495 -.0086594 .0025107
PCSampDIM | .0163779 .0802518 -.1409128 .1736686
_cons | 4.978886 1.819937 1.411875 8.545896
-------------+------------------------------------------------
FARMID |
var(_cons)| .6404598 .582882 .1076004 3.812149
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 7.73e-33 4.84e-17 . .
--------------------------------------------------------------
LR test vs. logistic model: chibar2(01) = 9.32 Prob >= chibar2 = 0.0011
. testparm Tx#CM1
( 1) [Cure]2.Tx#2.CM1 = 0
chi2( 1) = 1.46
Prob > chi2 = 0.2268
. *P > 0.05. Will not investigate further
.
.
. *Step 5: Removing unnecessary covariates using 10% rule. Will do so in this order:
.
. *DOMY DODIM PCSampDIM PrevCM DOSCC Parity
. *Step 5a: full model
. meglm Cure i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(10) = 11.82
Log likelihood = -130.24057 Prob > chi2 = 0.2975
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.669007 .5933137 .8315061 3.350048
|
Parity |
2 | .760166 .3362116 .3194721 1.808772
3 | 2.054464 1.290495 .5998231 7.03678
4 | .5625507 .3265404 .1803308 1.754904
|
SCCDO | 1.124443 .1658784 .8421081 1.501437
PeakSCC | .750409 .1292753 .5353759 1.05181
MYDO | .9903322 .028287 .936414 1.047355
|
CM1 |
1 | 2.510536 1.236723 .9559903 6.592947
DIMDO | .9971077 .0027905 .9916534 1.002592
PCSampDIM | 1.037634 .0810746 .8903003 1.209351
_cons | 112.8826 202.1144 3.377263 3773.019
-------------+------------------------------------------------
FARMID |
var(_cons)| .6741527 .606448 .1156225 3.930739
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 8.86e-34 1.11e-17 . .
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 9.93 Prob >= chibar2 = 0.0008
.
. *Step 5b: remove DOMY
. meglm Cure i.Tx i.Parity SCCDO PeakSCC i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(9) = 11.72
Log likelihood = -130.2983 Prob > chi2 = 0.2296
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.661797 .59031 .8283443 3.333843
|
Parity |
2 | .7946263 .3359804 .3469459 1.81997
3 | 2.146118 1.32451 .6402079 7.194258
4 | .5791328 .3325894 .1879069 1.784899
|
SCCDO | 1.130234 .1652456 .8486305 1.505283
PeakSCC | .7538218 .1294788 .5383487 1.055538
|
CM1 |
1 | 2.45861 1.199915 .9446354 6.399044
DIMDO | .9973368 .0027519 .9919578 1.002745
PCSampDIM | 1.036155 .0811755 .8886666 1.20812
_cons | 77.72179 111.1998 4.706443 1283.491
-------------+------------------------------------------------
FARMID |
var(_cons)| .7416456 .6210632 .1436778 3.828275
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 1.50e-33 2.35e-17 . .
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 16.10 Prob >= chibar2 = 0.0000
. *Changed by <10%. DOMY stays out
.
. *Step 5c: remove DODIM
. meglm Cure i.Tx i.Parity SCCDO PeakSCC i.CM1 PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 561
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.2 168
Cow | 367 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(8) = 10.91
Log likelihood = -130.7209 Prob > chi2 = 0.2070
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.699229 .6017471 .8488215 3.401633
|
Parity |
2 | .7412139 .3074409 .3287623 1.67111
3 | 2.141099 1.324396 .6369695 7.197057
4 | .574293 .3289759 .1868678 1.764951
|
SCCDO | 1.133209 .1635074 .8540687 1.503583
PeakSCC | .7436705 .1259901 .5335473 1.036545
|
CM1 |
1 | 2.498938 1.216688 .9623231 6.489185
PCSampDIM | 1.031659 .0804094 .885507 1.201934
_cons | 35.04308 40.46316 3.645409 336.8669
-------------+------------------------------------------------
FARMID |
var(_cons)| .7260559 .6081756 .1405941 3.749497
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 2.33e-29 2.33e-14 . .
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 15.89 Prob >= chibar2 = 0.0000
. *Changed by <10%. DODIM stays out
.
. *Step 5d: remove PCSampDIM
. meglm Cure i.Tx i.Parity SCCDO PeakSCC i.CM1 || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(7) = 10.82
Log likelihood = -130.82493 Prob > chi2 = 0.1469
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.665129 .5812004 .8401227 3.300299
|
Parity |
2 | .7382078 .3059527 .3276388 1.663267
3 | 2.129951 1.31803 .6333435 7.16308
4 | .5675259 .3249434 .1847654 1.743214
|
SCCDO | 1.124764 .1614888 .8488865 1.490299
PeakSCC | .7453258 .1265213 .5343824 1.039537
|
CM1 |
1 | 2.492523 1.210663 .9620446 6.457777
_cons | 42.28299 44.83497 5.29164 337.8634
-------------+------------------------------------------------
FARMID |
var(_cons)| .6982026 .5837121 .135631 3.594214
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| 5.01e-32 2.76e-16 . .
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 16.37 Prob >= chibar2 = 0.0000
. *Changed by <10%. PCSampDIM stays out
.
. *Step 5e: remove PrevCM
. meglm Cure i.Tx i.Parity SCCDO PeakSCC || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(6) = 7.50
Log likelihood = -132.85253 Prob > chi2 = 0.2769
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.604854 .5616123 .8082786 3.186473
|
Parity |
2 | .739246 .309952 .3250096 1.681442
3 | 2.384718 1.468877 .7130762 7.975137
4 | .6354926 .3706968 .202575 1.993587
|
SCCDO | 1.087728 .1578423 .8184663 1.445572
PeakSCC | .8043482 .1344563 .5796364 1.116176
_cons | 38.94173 42.98071 4.476395 338.7679
-------------+------------------------------------------------
FARMID |
var(_cons)| .7303932 .6097908 .1422019 3.751527
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .0687491 .7564114 2.96e-11 1.59e+08
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 17.09 Prob > chi2 = 0.0002
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. PrevCM stays out
.
. *Step 5f: remove DOSCC
. meglm Cure i.Tx i.Parity PeakSCC || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(5) = 7.12
Log likelihood = -133.01662 Prob > chi2 = 0.2118
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.594086 .5576207 .8030752 3.164223
|
Parity |
2 | .7536823 .3141544 .3329549 1.706048
3 | 2.473306 1.518896 .7422355 8.241646
4 | .681603 .3871933 .2238698 2.075236
|
PeakSCC | .8333465 .1308334 .6126169 1.133606
_cons | 46.2046 49.73164 5.604111 380.9461
-------------+------------------------------------------------
FARMID |
var(_cons)| .7314725 .6073575 .1436901 3.723653
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .0666384 .7613338 1.26e-11 3.54e+08
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 17.52 Prob > chi2 = 0.0002
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. DOSCC stays out
.
. *Step 5g: remove PeakSCC
. meglm Cure i.Tx i.Parity || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(4) = 5.86
Log likelihood = -133.67981 Prob > chi2 = 0.2100
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.531611 .5389857 .7684296 3.052761
|
Parity |
2 | .6875063 .2854363 .3047038 1.551227
3 | 2.057424 1.222176 .6422179 6.591207
4 | .5587272 .3077471 .1898269 1.64453
|
_cons | 17.28676 10.3898 5.322541 56.1446
-------------+------------------------------------------------
FARMID |
var(_cons)| .7240803 .6045697 .140954 3.719599
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .164989 .800493 .0000122 2224.9
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 17.19 Prob > chi2 = 0.0002
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. Stays out.
.
. *Step 5h: remove Parity
. meglm Cure i.Tx || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 1.54
Log likelihood = -135.8617 Prob > chi2 = 0.2150
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.586101 .590095 .7649776 3.288614
_cons | 18.88079 11.3833 5.791989 61.54783
-------------+------------------------------------------------
FARMID |
var(_cons)| .7069282 .6079811 .131013 3.814487
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6684589 .9850049 .0372212 12.00492
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 15.56 Prob > chi2 = 0.0004
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. Parity stays out
.
Final model: IMI Cure
.
. **************************
. *Step 6: Report final model
. meglm Cure i.Tx || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 1.54
Log likelihood = -135.8617 Prob > chi2 = 0.2150
--------------------------------------------------------------
Cure | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .4612787 .3720413 -.2679087 1.190466
_cons | 2.938145 .6029036 1.756476 4.119815
-------------+------------------------------------------------
FARMID |
var(_cons)| .7069282 .6079811 .131013 3.814487
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6684589 .9850049 .0372212 12.00492
--------------------------------------------------------------
LR test vs. logistic model: chi2(2) = 15.56 Prob > chi2 = 0.0004
Note: LR test is conservative and provided only for reference.
. meglm Cure i.Tx || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 562
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 38 112.4 168
Cow | 368 1 1.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 1.54
Log likelihood = -135.8617 Prob > chi2 = 0.2150
--------------------------------------------------------------
Cure | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.586101 .590095 .7649776 3.288614
_cons | 18.88079 11.3833 5.791989 61.54783
-------------+------------------------------------------------
FARMID |
var(_cons)| .7069282 .6079811 .131013 3.814487
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6684589 .9850049 .0372212 12.00492
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 15.56 Prob > chi2 = 0.0004
Note: LR test is conservative and provided only for reference.
.
. margins Tx
Adjusted predictions Number of obs = 562
Model VCE : OIM
Expression : Marginal predicted mean, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx |
0 | .9182151 .0326631 28.11 0.000 .8541967 .9822336
1 | .944484 .0241041 39.18 0.000 .8972408 .9917272
------------------------------------------------------------------------------
. margins, dydx(Tx)
Conditional marginal effects Number of obs = 562
Model VCE : OIM
Expression : Marginal predicted mean, predict()
dy/dx w.r.t. : 2.Tx
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx |
1 | .0262689 .0225771 1.16 0.245 -.0179815 .0705192
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
.
. *Report ICC
. meglm Cure || FARMID: || Cow:, family(binomial) link(logit) notable nolog nocnsreport nopvalues noheader
LR test vs. logistic model: chi2(2) = 15.21 Prob > chi2 = 0.0005
Note: LR test is conservative and provided only for reference.
. estat icc
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
FARMID | .1469917 .1063801 .031637 .4761412
Cow|FARMID | .3039145 .1912284 .069112 .7196969
------------------------------------------------------------------------------
Outcome 2: IMI at Calving
CrossTable(lockqtr$Tx,lockqtr$IMIPC,prop.c=FALSE,prop.t=FALSE,prop.chisq = FALSE)##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## |-------------------------|
##
##
## Total Observations in Table: 2807
##
##
## | lockqtr$IMIPC
## lockqtr$Tx | 0 | 1 | Row Total |
## -------------|-----------|-----------|-----------|
## Orbeseal | 1195 | 187 | 1382 |
## | 0.865 | 0.135 | 0.492 |
## -------------|-----------|-----------|-----------|
## Lockout | 1254 | 171 | 1425 |
## | 0.880 | 0.120 | 0.508 |
## -------------|-----------|-----------|-----------|
## Column Total | 2449 | 358 | 2807 |
## -------------|-----------|-----------|-----------|
##
##
Logistic regression model for IMI at calving
Model building plan
Model type: Logistic regression with mixed effects (generalized linear mixed model with binomial family / logit link).
Step 1: Identify potential confouders using a directed acyclic graph (DAG)
Step 2: Create model with all potential confounders
Step 3: Investigate potential effect measure modification
Step 4: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if odds ratio for algorithm or culture changes by >10% after removing the covariate, the covariate is retained in the model)
Step 5: Report final model
Step 1: DAG
This is used to identify variables that could be confounders if they are not balanced between treatment groups.
library(DiagrammeR)
mermaid("graph LR
T(Treatment)-->U(IMI at calving)
A(Age)-->T
P(Parity)-->T
M(Yield at dry-off)-->T
S(SCC during prev lactation)-->T
C(CM in prev lact)-->T
D(DIM at dry off) --> M
I(IMI at dry off) --> T
K(DIM at post calving sample) --> T
I-->U
P-->I
A-->I
C-->I
I-->S
I-->M
D-->S
D-->U
K-->U
A-->U
P-->U
M-->U
S-->U
C-->U
C-->M
P-->C
P-->S
P-->M
A-->P
A-->C
A-->S
A-->M
M-->S
C-->S
style D fill:#FFFFFF, stroke-width:0px
style K fill:#FFFFFF, stroke-width:0px
style A fill:#FFFFFF, stroke-width:0px
style T fill:#FFFFFF, stroke-width:2px
style P fill:#FFFFFF, stroke-width:0px
style M fill:#FFFFFF, stroke-width:0px
style S fill:#FFFFFF, stroke-width:0px
style C fill:#FFFFFF, stroke-width:0px
style I fill:#FFFFFF, stroke-width:0px
style U fill:#FFFFFF, stroke-width:2px
")According to this DAG, I may need to control for the following variables.
Parity [“Parity”] or Age [“Age”] <- will use Parity
Yield at most recent test before dry off [“MYDO”]
Somatic cell count during previous lactation [“SCCDO” and “PeakSCC”]
Clinical mastitis in previous lactation [“CM1”]
IMI at dry-off [“IMIDO”]
Days in milk at dry-off [“DODIM”]
Days in milk at post-calving sample [“PCSampDIM”]
Steps 2 to 5 done in Stata. Log file pasted below.
. *Step 2: Create full model with all potential confounders
. meglm IMIPC i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO IMIDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(11) = 19.16
Log likelihood = -883.49805 Prob > chi2 = 0.0583
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8526211 .1240094 .6411404 1.133859
|
Parity |
2 | 1.054916 .1905421 .7404084 1.503019
3 | .8605353 .1885691 .5600734 1.322186
4 | 1.297922 .3221896 .797904 2.111283
|
SCCDO | 1.105053 .0774154 .9632774 1.267695
PeakSCC | 1.092998 .0807955 .9455783 1.2634
MYDO | 1.019457 .0117154 .9967515 1.042679
|
CM1 |
1 | 1.330063 .2432873 .9293416 1.90357
DIMDO | 1.000524 .0013234 .9979334 1.003121
IMIDO | 1.071764 .1666775 .7901741 1.453702
PCSampDIM | 1.044958 .0331687 .9819294 1.112032
_cons | .0180352 .0152849 .0034255 .0949554
-------------+------------------------------------------------
FARMID |
var(_cons)| .7410145 .4875065 .2040935 2.690445
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5605919 .2191698 .2605313 1.20624
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 184.01 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Step 3: Explore effect measure modification
. *Will test Tx:Farm, Tx:Parity, Tx:IMIDO
.
. *Tx: Farm
. meglm IMIPC i.Tx##i.FARMID i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO IMIDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(19) = 159.56
Log likelihood = -871.81805 Prob > chi2 = 0.0000
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.096767 .3836544 .5525354 2.177052
|
FARMID |
2 | 2.002762 .8357318 .8839582 4.537607
3 | .2711118 .1080903 .1241025 .5922651
4 | 4.170508 1.477817 2.08241 8.352408
5 | 1.5492 .5378318 .7845089 3.059264
|
Tx#FARMID |
1#2 | .4811907 .2798198 .1539325 1.504194
1#3 | .8044829 .3950387 .307282 2.106185
1#4 | .7207913 .3122362 .3083767 1.684758
1#5 | .8559021 .3943238 .3469492 2.111457
|
Parity |
2 | 1.060631 .1913592 .7447158 1.510561
3 | .8494198 .1860658 .5529252 1.304904
4 | 1.287494 .3205117 .7903963 2.097226
|
SCCDO | 1.107777 .0779656 .9650383 1.271628
PeakSCC | 1.094783 .0808678 .947224 1.265329
MYDO | 1.020067 .0118425 .997118 1.043544
|
CM1 |
1 | 1.3615 .2483881 .9521974 1.946742
DIMDO | 1.000524 .0013237 .9979331 1.003122
IMIDO | 1.059593 .1645737 .7815065 1.436634
PCSampDIM | 1.047616 .0333123 .9843181 1.114984
_cons | .0137039 .0098903 .0033305 .0563859
-------------+------------------------------------------------
FARMID |
var(_cons)| 5.76e-34 6.42e-18 . .
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5335491 .2157549 .2415285 1.178638
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 9.15 Prob >= chibar2 = 0.0012
. testparm Tx#FARMID
( 1) [IMIPC]2.Tx#2.FARMID = 0
( 2) [IMIPC]2.Tx#3.FARMID = 0
( 3) [IMIPC]2.Tx#4.FARMID = 0
( 4) [IMIPC]2.Tx#5.FARMID = 0
chi2( 4) = 1.79
Prob > chi2 = 0.7742
.
. *P > 0.05. Will not investigate further.
.
. *Tx:Parity
. meglm IMIPC i.Tx##i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO IMIDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(14) = 23.95
Log likelihood = -881.15384 Prob > chi2 = 0.0465
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.224073 .2734098 .7901005 1.89641
|
Parity |
2 | 1.425634 .3538197 .8765034 2.318797
3 | 1.134152 .339253 .6310382 2.038388
4 | 1.846228 .5790093 .9984667 3.413791
|
Tx#Parity |
1#2 | .548477 .1923125 .2758681 1.090474
1#3 | .5797691 .2413201 .256422 1.310856
1#4 | .4556812 .2165122 .1795649 1.15638
|
SCCDO | 1.108314 .0773078 .9666947 1.270681
PeakSCC | 1.091295 .0802556 .9448073 1.260494
MYDO | 1.018514 .0116553 .9959247 1.041617
|
CM1 |
1 | 1.324941 .2402947 .9285822 1.890482
DIMDO | 1.00052 .0013194 .9979377 1.00311
IMIDO | 1.066585 .1653005 .7871824 1.445159
PCSampDIM | 1.047096 .0329797 .9844112 1.113772
_cons | .0152921 .0129669 .002902 .0805824
-------------+------------------------------------------------
FARMID |
var(_cons)| .7225974 .4754845 .19897 2.62425
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5107268 .2144791 .2242474 1.163187
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 178.74 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. testparm Tx#Parity
( 1) [IMIPC]2.Tx#2.Parity = 0
( 2) [IMIPC]2.Tx#3.Parity = 0
( 3) [IMIPC]2.Tx#4.Parity = 0
chi2( 3) = 4.71
Prob > chi2 = 0.1945
.
. *P > 0.05. Will not investigate further.
.
. *Tx:DOIMI
. meglm IMIPC i.Tx##i.IMIDO i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(12) = 19.63
Log likelihood = -883.25034 Prob > chi2 = 0.0745
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .9028598 .1504021 .6513639 1.25146
1.IMIDO | 1.191804 .2569769 .7810322 1.818616
|
Tx#IMIDO |
1#1 | .8082563 .2445578 .4466807 1.462517
|
Parity |
2 | 1.05328 .1903505 .7391175 1.500979
3 | .8584737 .1882909 .5585103 1.319541
4 | 1.296293 .322016 .7966249 2.10937
|
SCCDO | 1.104353 .0773994 .9626108 1.266966
PeakSCC | 1.094044 .0808679 .9464923 1.264599
MYDO | 1.019737 .0117355 .9969934 1.043
|
CM1 |
1 | 1.329352 .2433142 .9286302 1.902993
DIMDO | 1.000494 .001328 .9978949 1.003101
PCSampDIM | 1.044254 .0331819 .9812023 1.111357
_cons | .0176302 .0149819 .0033336 .0932388
-------------+------------------------------------------------
FARMID |
var(_cons)| .7439755 .4894462 .2049135 2.701137
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5625323 .2192438 .2620574 1.207532
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 184.43 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. testparm Tx#IMIDO
( 1) [IMIPC]2.Tx#1.IMIDO = 0
chi2( 1) = 0.49
Prob > chi2 = 0.4817
.
. *P > 0.05. Will not investigate further.
.
.
. *Step 4: Remove unnecessary covariates from the model using 10% rule
.
.
.
. *I will remove in this order: DODIM DOMY PCSampDIM Parity PrevCM DOSCC PeakSCC IMIDO
.
. *Step 4a: Full model
. meglm IMIPC i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO i.IMIDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(11) = 19.16
Log likelihood = -883.49805 Prob > chi2 = 0.0583
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8526211 .1240094 .6411404 1.133859
|
Parity |
2 | 1.054916 .1905421 .7404084 1.503019
3 | .8605353 .1885691 .5600734 1.322186
4 | 1.297922 .3221896 .797904 2.111283
|
SCCDO | 1.105053 .0774154 .9632774 1.267695
PeakSCC | 1.092998 .0807955 .9455783 1.2634
MYDO | 1.019457 .0117154 .9967515 1.042679
|
CM1 |
1 | 1.330063 .2432873 .9293416 1.90357
DIMDO | 1.000524 .0013234 .9979334 1.003121
1.IMIDO | 1.071764 .1666775 .7901741 1.453702
PCSampDIM | 1.044958 .0331687 .9819294 1.112032
_cons | .0180352 .0152849 .0034255 .0949554
-------------+------------------------------------------------
FARMID |
var(_cons)| .7410145 .4875065 .2040935 2.690445
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5605919 .2191698 .2605313 1.20624
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 184.01 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
.
. *Step 4b: remove DODIM
. meglm IMIPC i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 i.IMIDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(10) = 19.02
Log likelihood = -883.57533 Prob > chi2 = 0.0399
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8518846 .1239063 .6405807 1.13289
|
Parity |
2 | 1.059826 .1910461 .7443816 1.508946
3 | .8645008 .1892811 .5628545 1.327806
4 | 1.299683 .3225645 .7990611 2.113949
|
SCCDO | 1.104537 .0773133 .9629408 1.266955
PeakSCC | 1.093653 .0808304 .9461683 1.264127
MYDO | 1.018363 .0113743 .9963123 1.040902
|
CM1 |
1 | 1.332399 .2436823 .9310183 1.906824
1.IMIDO | 1.074175 .1669434 .7921098 1.456683
PCSampDIM | 1.045792 .0331286 .9828354 1.11278
_cons | .0218065 .0151888 .005568 .0854022
-------------+------------------------------------------------
FARMID |
var(_cons)| .7387983 .4860104 .2035037 2.682128
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5612556 .2190401 .2611945 1.206028
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 183.86 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. DODIM stays out
.
. *Step 4c: remove DOMY
. meglm IMIPC i.Tx i.Parity SCCDO PeakSCC i.CM1 DIMDO i.IMIDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(10) = 16.38
Log likelihood = -884.90464 Prob > chi2 = 0.0892
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8592784 .1254167 .6454997 1.143857
|
Parity |
2 | 1.014747 .1826062 .7131517 1.443888
3 | .8243104 .1806085 .5365256 1.266459
4 | 1.252307 .310417 .7704034 2.035651
|
SCCDO | 1.083721 .0746636 .946833 1.240399
PeakSCC | 1.081847 .0798498 .9361379 1.250236
|
CM1 |
1 | 1.348252 .2475241 .9408061 1.932156
DIMDO | .9999856 .0013109 .9974196 1.002558
1.IMIDO | 1.082805 .1685537 .798085 1.469101
PCSampDIM | 1.047183 .033323 .9838659 1.114574
_cons | .040304 .0281569 .0102492 .1584924
-------------+------------------------------------------------
FARMID |
var(_cons)| .7401815 .4864727 .2041265 2.683967
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5841656 .2218798 .2774787 1.229822
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 184.56 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. DOMY stays out
.
. *Step 4d: remove PCSampDIM
. meglm IMIPC i.Tx i.Parity SCCDO PeakSCC i.CM1 DIMDO i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(9) = 14.24
Log likelihood = -889.13484 Prob > chi2 = 0.1141
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .857747 .1250242 .6445982 1.141377
|
Parity |
2 | .9966681 .1779262 .702414 1.414191
3 | .8178438 .1791563 .5323616 1.256418
4 | 1.226873 .3036687 .7552926 1.992895
|
SCCDO | 1.072833 .0734531 .9381092 1.226905
PeakSCC | 1.091261 .0801763 .9449088 1.260282
|
CM1 |
1 | 1.35156 .2483127 .9428659 1.937406
DIMDO | 1.000041 .0013024 .9974911 1.002597
1.IMIDO | 1.069302 .1662611 .7884079 1.450274
_cons | .0502771 .0342101 .0132491 .1907896
-------------+------------------------------------------------
FARMID |
var(_cons)| .74412 .4886677 .2054254 2.695452
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5904299 .2217945 .2827583 1.232882
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 186.86 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. PCSampdim stays out
.
. *Step 4e: remove Parity
. meglm IMIPC i.Tx SCCDO PeakSCC i.CM1 i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(5) = 11.96
Log likelihood = -890.2503 Prob > chi2 = 0.0353
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8528697 .1241489 .641175 1.134459
SCCDO | 1.074486 .072636 .9411505 1.226712
PeakSCC | 1.088803 .0793807 .9438245 1.256051
|
CM1 |
1 | 1.360952 .2496945 .9498884 1.949904
1.IMIDO | 1.066383 .1657357 .7863586 1.446125
_cons | .0504162 .0280844 .0169203 .1502217
-------------+------------------------------------------------
FARMID |
var(_cons)| .7573574 .4970865 .2092283 2.741456
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6043032 .2235542 .2926603 1.247803
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 191.48 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. Parity stays out.
.
. *Step 4f: remove PrevCM
. meglm IMIPC i.Tx SCCDO PeakSCC i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(4) = 9.16
Log likelihood = -891.65389 Prob > chi2 = 0.0573
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .845582 .12293 .6359292 1.124353
SCCDO | 1.074486 .0724133 .941533 1.226214
PeakSCC | 1.127303 .0790526 .982539 1.293396
1.IMIDO | 1.07916 .1672113 .7965179 1.462096
_cons | .0444787 .0242799 .0152581 .1296594
-------------+------------------------------------------------
FARMID |
var(_cons)| .7126244 .4676333 .1969207 2.578874
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6042837 .2243598 .2918803 1.251056
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 190.35 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. PrevCM stays out
.
. *Step 4g: DOSCC
. meglm IMIPC i.Tx PeakSCC i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(3) = 8.02
Log likelihood = -892.22827 Prob > chi2 = 0.0455
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8439212 .1230008 .6342201 1.122959
PeakSCC | 1.168549 .0716712 1.036191 1.317813
1.IMIDO | 1.083526 .1681793 .7993191 1.468786
_cons | .0500799 .0267405 .0175857 .1426159
-------------+------------------------------------------------
FARMID |
var(_cons)| .7161972 .4700647 .1978609 2.59242
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6179893 .2251595 .3025885 1.262146
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 190.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. DOSCC stays out
.
. *Step 4h: PeakSCC
. meglm IMIPC i.Tx i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(2) = 1.64
Log likelihood = -895.45112 Prob > chi2 = 0.4413
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8591458 .1253886 .645413 1.143658
1.IMIDO | 1.129384 .1746726 .8340524 1.529291
_cons | .1196973 .0481548 .0544053 .2633462
-------------+------------------------------------------------
FARMID |
var(_cons)| .7257508 .4760928 .2006314 2.625282
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6387133 .2293791 .3159488 1.291205
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 193.16 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. Stays out.
. *Step 4i: IMIDO
. meglm IMIPC i.Tx || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,807
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 232 561.4 1,042
Cow | 776 1 3.6 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 1.49
Log likelihood = -953.29006 Prob > chi2 = 0.2223
--------------------------------------------------------------
IMIPC | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8373414 .1217953 .6296385 1.113561
_cons | .1220898 .0506964 .0541038 .2755062
-------------+------------------------------------------------
FARMID |
var(_cons)| .7872649 .5146736 .2185994 2.83526
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .7504504 .229786 .4117999 1.367596
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 234.69 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. IMIDO stays out
.
Final Model: IMI at calving
.
. *******************
. *Report final model
. meglm IMIPC i.Tx || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,807
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 232 561.4 1,042
Cow | 776 1 3.6 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 1.49
Log likelihood = -953.29006 Prob > chi2 = 0.2223
--------------------------------------------------------------
IMIPC | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | -.1775235 .1454547 -.4626095 .1075626
_cons | -2.102998 .4152387 -2.916851 -1.289145
-------------+------------------------------------------------
FARMID |
var(_cons)| .7872649 .5146736 .2185994 2.83526
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .7504504 .229786 .4117999 1.367596
--------------------------------------------------------------
LR test vs. logistic model: chi2(2) = 234.69 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. margins Tx
Adjusted predictions Number of obs = 2,807
Model VCE : OIM
Expression : Marginal predicted mean, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx |
0 | .1598742 .0478097 3.34 0.001 .066169 .2535794
1 | .1409829 .0439408 3.21 0.001 .0548605 .2271053
------------------------------------------------------------------------------
. margins, dydx(Tx)
Conditional marginal effects Number of obs = 2,807
Model VCE : OIM
Expression : Marginal predicted mean, predict()
dy/dx w.r.t. : 2.Tx
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx |
1 | -.0188913 .0159574 -1.18 0.236 -.0501673 .0123846
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
.
. *Report ICC
. meglm IMIPC || FARMID: || Cow:, family(binomial) link(logit) notable nolog nocnsreport nopvalues noheader
LR test vs. logistic model: chi2(2) = 234.68 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat icc
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
FARMID | .1627225 .0887857 .0513998 .4107503
Cow|FARMID | .3197727 .0816909 .1837868 .4953167
------------------------------------------------------------------------------
Outcome 3: New IMI
CrossTable(lockqtr$Tx,lockqtr$NewIMI,prop.c=FALSE,prop.t=FALSE,prop.chisq = FALSE)##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## |-------------------------|
##
##
## Total Observations in Table: 2664
##
##
## | lockqtr$NewIMI
## lockqtr$Tx | 0 | 1 | Row Total |
## -------------|-----------|-----------|-----------|
## Orbeseal | 1162 | 152 | 1314 |
## | 0.884 | 0.116 | 0.493 |
## -------------|-----------|-----------|-----------|
## Lockout | 1209 | 141 | 1350 |
## | 0.896 | 0.104 | 0.507 |
## -------------|-----------|-----------|-----------|
## Column Total | 2371 | 293 | 2664 |
## -------------|-----------|-----------|-----------|
##
##
Logistic regression model for new IMI
Model building plan
Model type: Logistic regression with mixed effects (generalized linear mixed model with binomial family / logit link).
Step 1: Identify potential confouders using a directed acyclic graph (DAG)
Step 2: Create model with all potential confounders
Step 3: Investigate potential effect measure modification
Step 4: Remove unneccesary covariates in backwards stepwise fashion using 10% rule (i.e. if odds ratio for algorithm or culture changes by >10% after removing the covariate, the covariate is retained in the model)
Step 5: Report final model
Step 1: DAG
This is used to identify variables that could be confounders if they are not balanced between treatment groups.
library(DiagrammeR)
mermaid("graph LR
T(Treatment)-->U(New IMI)
A(Age)-->T
P(Parity)-->T
M(Yield at dry-off)-->T
S(SCC during prev lactation)-->T
C(CM in prev lact)-->T
D(DIM at dry off) --> T
I(IMI at dry off) --> T
K(DIM at post calving sample) --> T
I-->U
P-->I
A-->I
C-->I
I-->S
I-->M
D-->S
D-->M
D-->U
K-->U
A-->U
P-->U
M-->U
S-->U
C-->U
C-->M
P-->C
P-->S
P-->M
A-->P
A-->C
A-->S
A-->M
M-->S
C-->S
style D fill:#FFFFFF, stroke-width:0px
style K fill:#FFFFFF, stroke-width:0px
style A fill:#FFFFFF, stroke-width:0px
style T fill:#FFFFFF, stroke-width:2px
style P fill:#FFFFFF, stroke-width:0px
style M fill:#FFFFFF, stroke-width:0px
style S fill:#FFFFFF, stroke-width:0px
style C fill:#FFFFFF, stroke-width:0px
style I fill:#FFFFFF, stroke-width:0px
style U fill:#FFFFFF, stroke-width:2px
")Parity [“Parity”] or Age [“Age”] <- will use Parity
Yield at most recent test before dry off [“MYDO”]
Somatic cell count during previous lactation [“SCCDO” and “PeakSCC”]
Clinical mastitis in previous lactation [“CM1”]
IMI at dry-off [“IMIDO”]
Days in milk at dry-off [“DODIM”]
Days in milk at post-calving sample [“PCSampDIM”]
Steps 2 to 5 done in Stata. Log file pasted below.
*Outcome 3: New IMI
. *Step 2: Full model with possible covariates
. meglm NewIMI i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(11) = 29.12
Log likelihood = -824.66806 Prob > chi2 = 0.0022
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8823876 .1330734 .6565824 1.18585
|
Parity |
2 | .9955547 .1871672 .6887106 1.439108
3 | .9461034 .2120247 .6097919 1.467897
4 | 1.221864 .3148114 .7374149 2.024574
|
SCCDO | 1.150886 .0856709 .9946482 1.331665
PeakSCC | 1.04425 .0811007 .8968025 1.215941
MYDO | 1.020653 .0121526 .9971105 1.044752
|
CM1 |
1 | 1.52801 .2880962 1.055936 2.211131
DIMDO | .9998069 .0014144 .9970386 1.002583
PCSampDIM | 1.052698 .0344933 .9872172 1.122521
1.IMIDO | .5517464 .098117 .3893771 .7818233
_cons | .0220487 .0194278 .0039207 .1239946
-------------+------------------------------------------------
FARMID |
var(_cons)| .7522128 .4965783 .2062597 2.743261
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5642543 .2322081 .2518715 1.264069
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 168.53 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Step 3: Check for effect measure modification
. *I will investigate: Tx:FARM Tx:Parity Tx:IMIDO
.
. *Tx:FARMD
. meglm NewIMI i.Tx##i.FARMID i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(19) = 142.67
Log likelihood = -812.81068 Prob > chi2 = 0.0000
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.151037 .4113481 .5713386 2.318914
|
FARMID |
2 | 1.713704 .7310513 .7427126 3.954131
3 | .2120549 .0876135 .0943544 .4765785
4 | 3.31937 1.210456 1.624249 6.783574
5 | 1.297225 .4648709 .6426585 2.618485
|
Tx#FARMID |
1#2 | .4163804 .2517536 .1273014 1.361907
1#3 | .7937819 .4004553 .2953101 2.133655
1#4 | .7121408 .3183826 .2964915 1.710486
1#5 | .8719572 .4127536 .3447995 2.205077
|
Parity |
2 | 1.001579 .1879038 .6934153 1.446695
3 | .9326265 .2087292 .6014536 1.44615
4 | 1.210038 .3124146 .7295094 2.007091
|
SCCDO | 1.156331 .0864341 .9987482 1.338777
PeakSCC | 1.045769 .0811464 .8982285 1.217544
MYDO | 1.02188 .0122967 .9980605 1.046267
|
CM1 |
1 | 1.571115 .2953242 1.086943 2.270959
DIMDO | .9998162 .0014146 .9970475 1.002593
PCSampDIM | 1.056168 .034659 .990376 1.126331
1.IMIDO | .5439701 .0965875 .3840922 .7703971
_cons | .0192131 .0144903 .0043816 .0842492
-------------+------------------------------------------------
FARMID |
var(_cons)| 3.77e-34 3.50e-18 . .
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5320089 .2282998 .2294271 1.233653
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chibar2(01) = 7.96 Prob >= chibar2 = 0.0024
. testparm Tx#FARMID
( 1) [NewIMI]2.Tx#2.FARMID = 0
( 2) [NewIMI]2.Tx#3.FARMID = 0
( 3) [NewIMI]2.Tx#4.FARMID = 0
( 4) [NewIMI]2.Tx#5.FARMID = 0
chi2( 4) = 2.38
Prob > chi2 = 0.6661
.
. *P > 0.05. Will not investigate further
.
. *Tx:Parity
. meglm NewIMI i.Tx##i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(14) = 33.97
Log likelihood = -822.32128 Prob > chi2 = 0.0021
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | 1.2467 .2895292 .7908279 1.965359
|
Parity |
2 | 1.242759 .3237966 .7457779 2.070926
3 | 1.306335 .3979602 .7190274 2.373359
4 | 1.812376 .5846508 .9630764 3.410638
|
Tx#Parity |
1#2 | .653044 .2384996 .3192077 1.336016
1#3 | .524748 .2237301 .227528 1.210227
1#4 | .3988503 .1995183 .1496271 1.063187
|
SCCDO | 1.151672 .0854406 .9958174 1.33192
PeakSCC | 1.04439 .080777 .8974859 1.21534
MYDO | 1.019804 .0120988 .9963645 1.043795
|
CM1 |
1 | 1.536405 .28746 1.064747 2.216995
DIMDO | .9997299 .0014125 .9969652 1.002502
PCSampDIM | 1.055431 .0343283 .9902481 1.124904
1.IMIDO | .5472463 .097121 .3864721 .7749033
_cons | .0191822 .0169158 .0034062 .1080264
-------------+------------------------------------------------
FARMID |
var(_cons)| .7383036 .4873611 .2024645 2.692285
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5128879 .2266224 .2157318 1.219356
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 164.82 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. testparm Tx#Parity
( 1) [NewIMI]2.Tx#2.Parity = 0
( 2) [NewIMI]2.Tx#3.Parity = 0
( 3) [NewIMI]2.Tx#4.Parity = 0
chi2( 3) = 4.68
Prob > chi2 = 0.1964
.
. *P<0.05. Will investigate further.
. margins Tx#Parity
Predictive margins Number of obs = 2,657
Model VCE : OIM
Expression : Marginal predicted mean, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx#Parity |
0#1 | .1287193 .042599 3.02 0.003 .0452267 .2122118
0#2 | .1507968 .0483652 3.12 0.002 .0560027 .2455909
0#3 | .156239 .0524243 2.98 0.003 .0534891 .2589888
0#4 | .195489 .0622394 3.14 0.002 .0735021 .317476
1#1 | .1511379 .046859 3.23 0.001 .0592961 .2429798
1#2 | .1298435 .0443053 2.93 0.003 .0430066 .2166804
1#3 | .1143677 .0429259 2.66 0.008 .0302344 .198501
1#4 | .1190691 .0495025 2.41 0.016 .0220459 .2160922
------------------------------------------------------------------------------
.
. *P > 0.05. Will not investigate further.
.
. *Tx:IMIDO
. meglm NewIMI i.Tx##i.IMIDO i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(12) = 29.12
Log likelihood = -824.61215 Prob > chi2 = 0.0038
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .9035005 .1504823 .6518636 1.252276
1.IMIDO | .5848235 .1448055 .359967 .9501384
|
Tx#IMIDO |
1#1 | .890981 .3075693 .4529301 1.752692
|
Parity |
2 | .9946082 .1870647 .6879535 1.437954
3 | .9446493 .2118569 .6086551 1.466121
4 | 1.220569 .3146216 .7364634 2.022895
|
SCCDO | 1.150454 .0856912 .9941864 1.331284
PeakSCC | 1.044736 .0811597 .8971835 1.216554
MYDO | 1.020794 .0121692 .9972192 1.044926
|
CM1 |
1 | 1.528364 .288288 1.056012 2.211999
DIMDO | .9997892 .0014174 .997015 1.002571
PCSampDIM | 1.052467 .0345073 .9869614 1.122321
_cons | .0218619 .0192902 .0038781 .1232417
-------------+------------------------------------------------
FARMID |
var(_cons)| .7535387 .4974648 .2066173 2.748176
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5658199 .232346 .2530138 1.265354
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 168.64 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. testparm Tx#IMIDO
( 1) [NewIMI]2.Tx#1.IMIDO = 0
chi2( 1) = 0.11
Prob > chi2 = 0.7381
. *P > 0.05. Will not investigate further.
.
. *Step 4: remove unnecessary covariates using 10% rule. I will remove in the following order: DODIM DOMY Parity DOSCC PCSampDIM PrevCM IMIDO
.
. *Step 4a: Full model
. meglm NewIMI i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 DIMDO PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(11) = 29.12
Log likelihood = -824.66806 Prob > chi2 = 0.0022
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8823876 .1330734 .6565824 1.18585
|
Parity |
2 | .9955547 .1871672 .6887106 1.439108
3 | .9461034 .2120247 .6097919 1.467897
4 | 1.221864 .3148114 .7374149 2.024574
|
SCCDO | 1.150886 .0856709 .9946482 1.331665
PeakSCC | 1.04425 .0811007 .8968025 1.215941
MYDO | 1.020653 .0121526 .9971105 1.044752
|
CM1 |
1 | 1.52801 .2880962 1.055936 2.211131
DIMDO | .9998069 .0014144 .9970386 1.002583
PCSampDIM | 1.052698 .0344933 .9872172 1.122521
1.IMIDO | .5517464 .098117 .3893771 .7818233
_cons | .0220487 .0194278 .0039207 .1239946
-------------+------------------------------------------------
FARMID |
var(_cons)| .7522128 .4965783 .2062597 2.743261
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5642543 .2322081 .2518715 1.264069
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 168.53 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
.
. *Step 4b: Removed DODIM
. meglm NewIMI i.Tx i.Parity SCCDO PeakSCC MYDO i.CM1 PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(10) = 29.10
Log likelihood = -824.67743 Prob > chi2 = 0.0012
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8825776 .1331118 .6567095 1.186131
|
Parity |
2 | .9940796 .1866003 .6880828 1.436156
3 | .9445171 .2113517 .6091708 1.46447
4 | 1.221263 .3147016 .7369991 2.023724
|
SCCDO | 1.150922 .0857067 .9946239 1.331782
PeakSCC | 1.044178 .0811042 .8967251 1.215877
MYDO | 1.021046 .0118133 .9981531 1.044464
|
CM1 |
1 | 1.526821 .2877842 1.055234 2.209162
PCSampDIM | 1.052377 .0344089 .9870519 1.122025
1.IMIDO | .5513717 .0980169 .389159 .7811994
_cons | .0205555 .0147361 .0050432 .0837816
-------------+------------------------------------------------
FARMID |
var(_cons)| .7533713 .4972699 .2066166 2.746963
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .5649549 .2322797 .252374 1.264687
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 169.06 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. *Changed by <10%. DODIM stays out
.
.
. *Step 4c: Removed DOMY
. meglm NewIMI i.Tx i.Parity SCCDO PeakSCC i.CM1 PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(9) = 25.97
Log likelihood = -826.30059 Prob > chi2 = 0.0021
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8901232 .1349192 .6613485 1.198036
|
Parity |
2 | .9506386 .1779071 .6587452 1.371871
3 | .8961212 .2005454 .5779284 1.389503
4 | 1.172613 .3022598 .7075283 1.943415
|
SCCDO | 1.124251 .0823199 .9739498 1.297747
PeakSCC | 1.031972 .080122 .8863006 1.201586
|
CM1 |
1 | 1.543373 .2926722 1.064281 2.238131
PCSampDIM | 1.053966 .0346075 .988273 1.124026
1.IMIDO | .557347 .0992448 .3931472 .7901255
_cons | .041337 .0245808 .0128877 .1325871
-------------+------------------------------------------------
FARMID |
var(_cons)| .7346272 .4844321 .2017264 2.675292
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .598346 .2360968 .2761107 1.296646
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 167.12 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. DOMY stays out
.
.
. *Step 4d: Removed Parity
. meglm NewIMI i.Tx SCCDO PeakSCC i.CM1 PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(6) = 24.98
Log likelihood = -826.7996 Prob > chi2 = 0.0003
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8856087 .1338138 .6586079 1.190849
SCCDO | 1.125731 .0813045 .9771422 1.296916
PeakSCC | 1.032318 .079505 .8876819 1.200521
|
CM1 |
1 | 1.552579 .293357 1.072064 2.248468
PCSampDIM | 1.05374 .0344471 .988342 1.123465
1.IMIDO | .5561222 .0989328 .3924132 .7881283
_cons | .0403506 .0239251 .0126225 .1289895
-------------+------------------------------------------------
FARMID |
var(_cons)| .7442489 .4904555 .2045416 2.708039
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6020971 .2374896 .2779207 1.304404
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 170.88 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. Parity stays out
.
. *Step 4e: Removed DOSCC
. meglm NewIMI i.Tx PeakSCC i.CM1 PCSampDIM i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,657
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 222 531.4 1,032
Cow | 766 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(5) = 22.24
Log likelihood = -828.17187 Prob > chi2 = 0.0005
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8818227 .1339351 .6547825 1.187587
PeakSCC | 1.096166 .0738278 .9606098 1.250851
|
CM1 |
1 | 1.559795 .2970607 1.073885 2.265571
PCSampDIM | 1.049809 .0344033 .9844992 1.119451
1.IMIDO | .5581793 .0996566 .3933701 .7920382
_cons | .0497063 .02878 .0159795 .1546175
-------------+------------------------------------------------
FARMID |
var(_cons)| .749555 .4941241 .2059072 2.728572
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6319215 .2397648 .3003991 1.329314
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 170.97 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
.
. *Changed by <10%. DOSCC stays out
.
. *Step 4f: Removed PCSampDIM
. meglm NewIMI i.Tx PeakSCC i.CM1 i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(4) = 20.34
Log likelihood = -832.29595 Prob > chi2 = 0.0004
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8835279 .1339003 .6564764 1.189108
PeakSCC | 1.099794 .0738815 .9641166 1.254564
|
CM1 |
1 | 1.56217 .2973392 1.075754 2.268526
1.IMIDO | .5523014 .0984613 .3894292 .7832921
_cons | .0623561 .0345454 .0210529 .1846913
-------------+------------------------------------------------
FARMID |
var(_cons)| .7519559 .4953053 .2067831 2.734448
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6340916 .2391797 .3027459 1.328084
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 172.25 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. PCSampDIM stays out
.
. *Step 4g: Removed PeakSCC
. meglm NewIMI i.Tx i.CM1 i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(3) = 18.35
Log likelihood = -833.29586 Prob > chi2 = 0.0004
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8945491 .135549 .6646967 1.203885
|
CM1 |
1 | 1.707501 .3080109 1.19899 2.431681
1.IMIDO | .5614905 .1000692 .3959503 .7962402
_cons | .1040656 .0434544 .0459064 .2359071
-------------+------------------------------------------------
FARMID |
var(_cons)| .7683075 .5055526 .2115619 2.790182
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .644518 .2410856 .3096266 1.341627
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 178.20 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Step 4g: Removed PrevCM
. meglm NewIMI i.Tx i.IMIDO || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(2) = 9.84
Log likelihood = -837.64384 Prob > chi2 = 0.0073
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8876924 .1348038 .6591742 1.195432
1.IMIDO | .5873966 .1039058 .4152988 .8308109
_cons | .116967 .0463651 .0537838 .2543753
-------------+------------------------------------------------
FARMID |
var(_cons)| .6955475 .4582592 .1912121 2.530103
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6673437 .2457953 .3242171 1.373609
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 169.76 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
.
. *Changed by <10%. PrevCM stays out
.
.
. *Step 4h: Removed IMIDO
. meglm NewIMI i.Tx || FARMID: || Cow:, family(binomial) link(logit) or nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 0.82
Log likelihood = -842.42692 Prob > chi2 = 0.3652
--------------------------------------------------------------
NewIMI | Odds Ratio Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | .8713214 .1325574 .6466687 1.174018
_cons | .1048718 .0398007 .049844 .2206504
-------------+------------------------------------------------
FARMID |
var(_cons)| .6326601 .4180353 .1732735 2.309983
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6926578 .2469965 .3443394 1.393319
--------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test vs. logistic model: chi2(2) = 160.35 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
Final model: New IMI
. *Step 5: Report final model
. meglm NewIMI i.Tx || FARMID: || Cow:, family(binomial) link(logit) nolog nocnsreport nopvalues
Mixed-effects GLM Number of obs = 2,664
Family: binomial
Link: logit
-------------------------------------------------------------
| No. of Observations per Group
Group Variable | Groups Minimum Average Maximum
----------------+--------------------------------------------
FARMID | 5 224 532.8 1,032
Cow | 769 1 3.5 4
-------------------------------------------------------------
Integration method: mvaghermite Integration pts. = 7
Wald chi2(1) = 0.82
Log likelihood = -842.42692 Prob > chi2 = 0.3652
--------------------------------------------------------------
NewIMI | Coef. Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
Tx |
1 | -.1377444 .1521338 -.4359212 .1604324
_cons | -2.255017 .3795177 -2.998858 -1.511176
-------------+------------------------------------------------
FARMID |
var(_cons)| .6326601 .4180353 .1732735 2.309983
-------------+------------------------------------------------
FARMID>Cow |
var(_cons)| .6926578 .2469965 .3443394 1.393319
--------------------------------------------------------------
LR test vs. logistic model: chi2(2) = 160.35 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. margins Tx
Adjusted predictions Number of obs = 2,664
Model VCE : OIM
Expression : Marginal predicted mean, predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx |
0 | .1376321 .0396795 3.47 0.001 .0598617 .2154025
1 | .1241345 .0368807 3.37 0.001 .0518496 .1964194
------------------------------------------------------------------------------
. margins, dydx(Tx)
Conditional marginal effects Number of obs = 2,664
Model VCE : OIM
Expression : Marginal predicted mean, predict()
dy/dx w.r.t. : 2.Tx
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tx |
1 | -.0134976 .0151591 -0.89 0.373 -.043209 .0162137
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
.
. *Report ICC
. meglm NewIMI || FARMID: || Cow:, family(binomial) link(logit) notable nolog nocnsreport nopvalues noheader
LR test vs. logistic model: chi2(2) = 160.39 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. estat icc
Intraclass correlation
------------------------------------------------------------------------------
Level | ICC Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
FARMID | .137017 .0778794 .0418387 .3660068
Cow|FARMID | .2876195 .0775701 .1612458 .4588534
------------------------------------------------------------------------------