TABLE OF CONTENTS We have already seen how non-proportionality may be addressed by generalising the model by the addition of a function of the suspect predictor variable as a time dependent covariate. However, this approach requires that the functional form describing the pattern of time variation be specified (e.g., a linear trend). Where the variable for which the proportionality assumption is in question is a categorical variable, then a more general approach is possible using stratification. Dividing the subjects into strata g, we specify a hazard of the form:
in which the effects for the covariate vector x (now shortened by the omission of the stratum identifying variable g) remain assumed to be proportional, but the baseline hazard is now quite separately estimated for each stratum. The contribution to the partial likelihood from each failure event is modified such that the risk set over which the denominator is calculated, is no longer all those at risk at that time, but only the subset of those who belong to the same stratum as the failing individual.
In practice, stratification is used to achieve a variety of goals:
It can be applied to groups who either a priori may have quite different survival patterns] e.g., for example men and women, or post-hoc to groups defined by a variable that has failed a test of proportionality.
It can be applied so as to obtain distinct estimates of survivor, hazard or integrated hazard functions for...
