ABSTRACT
This chapter considers the simple form of the proportional hazards model. In the presence of censoring, a similar argument applies if it can be assumed that censorings can only occur immediately after failures. Calculation of fully unconditional expectations would require a fuller specification of the censoring mechanism. The chapter reviews the three main methods for statistical analysis based on log likelihoods, namely the likelihood ratio test, the score test and the direct use of the maximum likelihood estimates. It shows that, for uncensored data, the log rank test reduces to a test based on exponential order statistics. In any case, work on asymptotic theory points to the use of observed information matrices and to tests and confidence interval procedures that use the likelihood as directly as possible. Censoring mechanisms that do depend on the same parameters as the failure mechanism.
