Abstract: A general Cox-type partial likelihood score process for staggered entry data with covariate adjustment is shown to be asymptotically equivalent to a Gaussian process with independent increments, regardless of whether or not the covariates being adjusted for are independent of the covariates of primary interest. The approximation yields new and simple group sequential tests as well as repeated confidence intervals that effectively incorporate information from ancillary concomitant variables. A recursive formula is derived for computing discrete boundary values when the parameter of interest is multidimensional. A prostatic cancer data set is implemented to illustrate usefulness of the new approach. Results of simulation studies with moderate sample sizes are reported, showing that the group sequential tests with covariate adjustment perform markedly well in terms of efficiency improvement and bias reduction.
Key words and phrases: Censoring, covariate adjustment, Gaussian process, group sequential test, independent increments, martingale, proportional hazards regression, repeated confidence intervals, survival data.