ABSTRACT
A time-dependent explanatory variable is one whose value for any given individual may change over time. This chapter considers the inclusion of such variables in the log linear proportional hazards model. It discusses the partial likelihood estimation of the coefficients of time-dependent explanatory variables and explains the asymptotic efficiency of this method with that of fully parametric analysis of the same model. The chapter shows how a number of two-sample tests can be derived within the context of the log linear hazards model by the introduction of stochastic covariates. It provides a technique for reducing the computational burden for fitting the log linear proportional hazards model, which also has wider applicability in industrial life-testing situations, where the values of relevant covariates may be determined only through destructive testing. The partial likelihood involves the value of every explanatory variable evaluated at each failure time for each subject surviving to that time.
