  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.
