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Abstract
The proportional hazards (PH) model (Cox, 1972) is a regression model widely used in the analysis of failure time data. The estimator for the regression coefficients in the PH model most commonly used is the maximum partial likelihood estimator (MPLE). However, its consistency and asymptotic normality have been demonstrated only heuristically (Cox, 1975). Recently, Liu and Crowley (1978) and Tsiatis (1981) rigorously established the strong consistency and asymptotic normality of the MPLE for the special case of time-independent, almost-surely bounded covariates. Using the theory of weak convergence, we extend the approach of Tsiatis (1981) to rigorously demonstrate the strong consistency and asymptotic normality of the MPLE in the general case of time-dependent covariates. Approaches for outlier detection, residual plots and robust testing/estimation procedures for the PH model are also discussed.
