Categorical Auxiliary Data in the Discrete Time Proportional Hazards Model

Abstract

This chapter focuses on the joint discrete-time proportional hazards model and investigates the extent of efficiency gains for various scenarios of censoring, failure-time and auxiliary data Y . The discrete-time model is a natural choice when survival data are grouped. This occurs, for example, when survival status is noted at a sequence of scheduled follow-up visits. When survival time is grouped, but not coarsely grouped, the discrete-time models may be reasonable approximations to continuous-time models. The numbers of parameters in the joint model are large but do not depend on sample size, so that the asymptotic relative efficiency (ARE) is a valid means of comparing the joint and standard models. The chapter outlines the standard and joint models. The ARE, which is computed as the amount of censoring and probability law for ( Y | T, Z ), is varied. In investigation of ARE presented in the chapter, survival parameters and the shape for censoring are fixed. The chapter presents efficiency gains for repeated categorical measurements. This includes the case of baseline binary and polychotomous measurement and the case of two binary measurements. Recurrence time as auxiliary data is investigated and the alternative specifications for the censoring shape and survival distribution are discussed.