ABSTRACT
Our main emphasis in this chapter is on semiparametric methods which arise in the analysis of the proportional hazards or relative risk model proposed by Cox (1972). The extensive literature on fully parametric models receives little of our attention here, due to space limitations. We consider primarily applications in which the purpose of experimentation is to compare two or more treatments, or to evaluate the effect of covariates
on the risk of an event occurring over time. For these applications, the methodology based on the proportional hazards model has high efficiency compared with its parametric competitors and provides a great deal of flexibility in modeling. We present some of the theoretical underpinnings of the methodology, and discuss and illustrate simple methods of data summary and presentation that are closely allied with the formal analyses and that help communicate the principal results to nonstatisticians.
