Refinements of the Semiparametric Proportional Hazards Model

Abstract

In Chapter 8, we modeled the hazard function for an individual as a function of fixed-time covariates. These are explanatory variables recorded at the start of the study whose values are fixed throughout the course of the study. For instance, in Example 8.4, where acute leukemia patients were given a bone marrow transplant, we considered the three risk groups, donor age, recipient age, and several other variables, as fixed-time covariates. The basic interest there was to evaluate the relationship of the risk groups to the hazard of relapse or death, controlling for possible confounding variables which might be related to relapse or death. As is typical in many survival studies, individuals are monitored during the study, and other explanatory variables are recorded whose values may change during the course of the study. Some of these variables may be instrumental in predicting survival and need to be taken into consideration in evaluating the survival distribution. Such variables which change over time are called time-dependent variables. A covariate that takes on the value 0 until some intermediate event occurs when it becomes 1 is an example of a discrete-time covariate. It is also possible to include time-dependent covariates that are essentially continuous where the value of the covariate is a series of measurements of some explanatory characteristic.