Censoring in survival analysis: a simulation study of the effect of milk yield on conception

Survival-analysis methods often are used to analyze data from dairy herds where the outcome of interest is the interval from calving to conception. The purpose of this study was to determine whether an association between milk yield and culling biases the estimation of the effect of milk yield on conception. This was done by simulating four different scenarios modeling dairy-cattle milk yield and reproductive performance with known relationships among study factors. Cox's proportional-hazards model was used to analyze the effect of milk yield on days open under the following four scenarios: (1) no association between milk yield and culling or between milk yield and conception; (2) association between milk yield and culling only; (3) association between milk yield and conception only; (4) associations between milk yield and both culling and conception. The analyses also were repeated for data sets with an association between milk yield and culling, but with probabilities of culling ranging from 0.01 to 0.4. An effect of milk production on culling appeared to cause a small increase in the parameter estimates for the association of milk yield and days open - particularly when the probability of culling was high. The effect of high milk production on median days open (as estimated by survival functions) changed by 2 to 4 days when an association between milk yield and culling was programmed in the simulated data sets.