Sequential Analysis of Cox Model under Response Dependent Allocation

TL;DR

This paper extends the Brownian approximation for Cox model score processes to scenarios where treatment allocation depends on observed outcomes, enabling more flexible sequential analysis in survival studies.

Contribution

It introduces a novel framework incorporating response-dependent treatment allocation into the Cox model's sequential analysis using entry and calendar times.

Findings

Established large sample properties under new framework

Extended Brownian approximation to response-dependent settings

Facilitated more adaptive survival analysis methods

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 $\sigma$-filtrations to handle the natural information accumulation. Large sample properties are established under suitable regularity conditions.