Extensions of the Proportional Hazards Model
Up to this point, we have made several simplifying assumptions in developing and interpreting proportional hazards models. We have used a model with a common unspecified baseline hazard function where all the study covariates had values that remained fixed over the follow-up period. Additionally, we have assumed that the observations of the time variable were continuous and subject only to right censoring. In some settings, one or more of these assumptions may not be appropriate.
We may have data from a study in which subjects were randomized within study sites. If we account for site by including it as a covariate, the model forces the baseline hazards to be proportional across study sites. This may not be justified and, if it is not, a careful analysis of the proportional hazards assumption (as discussed in Chapter 6) for site may reveal the problem. One possible solution is to use site as a stratification variable, whereby each site would have a separate baseline hazard function. This same line of thought might apply to cohort year in the Worcester Heart Attack Study. Also, stratification can sometimes be employed with fixed covariates that, on testing, show evidence of non-proportional hazards.
When study subjects are observed on a regular basis during the follow-up period, the course of some covariates over time may be more predictive of survival experience than were the original baseline values. For ...