For the proportional hazards model of survival analysis, an appropriate large-sample theory is developed for cases of staggered entry and sequential analysis. The principal techniques involve an approximation of the score process by a suitable martingale and a random rescaling of time based on the observed Fisher information. As a result we show that the score process of the partial likelihood and the maximum partial likelihood estimator behave asymptotically like Brownian motion.
Sellke et al. (1983) studied this question.