Sequential Analysis of the Proportional Hazards Model
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 maximum partial likelihood estimator behaves asymptotically like Brownian motion..-~~A ccession ?or j NTIS GRA&I W DTIC TAB Unannounced 01
... Unannounced 01 Justifieatio ,. Distribution/ Availability Codes it 7i~Avil and/o -Dit Special scale behaves like a Brownian otion process. Previous work on this problem seems to be limited'to a Monte Carlo study by Gail, DeMets, and Slud (1981) , the paper of Tsiatis (1981b), and a recent manuscript of Slud (1982). Although Slud is concerned with the special case of testing a simple nul1 hypothesis, there is some overlap with our work, which we discuss later. The results of this paper are not unexpected. However, it is quite surprising to find their complete justification to be so difficult, particularly in comparison to proofs of the superficially similar results of the authors cited above. In this regard it is interesting to note that Jortes and Whitehead (1979) are willing to accept a cursory justification for related results, which they regard as almost obvious and propose to use as a basis for certain sequential tests. For the somewhat related Gehan test they offer a similar informal argument, but according to Slud and Wei (1982), their conclusion is incorrect in this case. Our methods do not provide satisfactory results concerning the joint 4(istribution of the Gehan statistic, which seems to involve a substantially more difficult problem. The multivariate case is also more difficult -even in its formulation -and our results here are not yet complete.