Sequential Analysis of the Cox Model under Response Dependent Allocation

Abstract

Sellke and Siegmund (1983) developed the Brownian approximation to the Cox partial likelihood score as a process of calendar time, laying the foundation for group sequential analysis of survival studies. We extend their results to cover situations in which treatment allocations may depend on observed outcomes. The new development makes use of the entry time and calendar time along with the corresponding σ-filtrations to handle the natural information accumulation. Large sample properties are established under suitable regularity conditions.

Keywords: Brownian approximation; Survival analysis; clinical trials; group sequential methods; outcome dependent allocation; proportional hazards regression; staggered entry; weak convergence.

Figure 1

${\mathcal{F}}_{n,t}\left(s\right)$: σ-filtrations defined along calendar time and survival time.

Figure 2

${\mathcal{F}}_{n,t,u}$: σ-filtrations defined along calendar time and entry time.