Yt. Grohn et al., MODELING THE EFFECT OF A DISEASE ON CULLING - AN ILLUSTRATION OF THE USE OF TIME-DEPENDENT COVARIATES FOR SURVIVAL ANALYSIS, Journal of dairy science, 80(8), 1997, pp. 1755-1766
This study demonstrated five different approaches, with and without ti
me-dependent covariates, to determine the effect of disease on culling
. It was also of interest to determine whether the time of the disease
had an effect on subsequent culling (i.e., whether disease should be
treated as a time-dependent covariate). To this purpose, five separate
models were studied: Models 1 through 4 were Cox proportional hazards
models, and Model 5 was a Weibull model. Model 1 treated disease as a
binary, time-independent covariate. Model 2 treated disease as a time
-dependent covariate, and one change of status was assumed to occur at
the time of disease. Model 3 also assumed that one change in status o
ccurred at the time of disease, but the effect of that change was assu
med to be different depending on when the disease occurred. Models 4 (
Cox) and 5 (Weibull) assumed an interaction between the occurrence of
disease (time of disease) and the occurrence of culling (time of culli
ng). As an illustration, the effect of mastitis on culling was studied
for 2998 Holstein dairy cows in 10 herds. Parity and previous 305-d m
ilk yield were also included as covariates; the data were stratified b
y herd. For all models, mastitis was a significant factor for culling.
The significance tests for the estimates from Models 4 and 5 demonstr
ated that the hazard of culling differed for different stages of lacta
tion, depending on when mastitis had occurred and when its effect on c
ulling occurred; that is, time dependence exists between time of masti
tis and time of culling.