EXACT PERMUTATIONAL TESTS FOR GROUP SEQUENTIAL CLINICAL-TRIALS

An efficient numerical algorithm is developed for computing stopping b oundaries for group sequential clinical trials. Patients arrive in seq uence, and are randomized to one of two treatments. The data are monit ored at interim time points, with a fresh block of patients entering t he study from one monitoring point to the next. The stopping boundarie s are derived from the exact joint permutational distribution of the l inear rank statistics observed across all the monitoring times. Specif ically, the algorithm yields the exact boundary generating function, P r(W-1 < b(1), W-2 < b(2), ..., W-i-1 < b(i-1), W-i = w(i)), where W-j is the linear rank statistic at the jth interim time point. The distri bution theory is based on assigning ranks after pooling all the patien ts who have entered the study, and then permuting the patients to the two treatments independently within each block of newly arrived patien ts. The methods are applicable for an arbitrary number of monitoring t imes, which need not be specified at the start of the study. The data may be continuous or categorical, and censored or uncensored. The rand omization rule for treatment allocation can be adaptive. The algorithm is especially useful during the early stages of a clinical trial, whe n very little data have been gathered, and stopping boundaries are bas ed on the extreme tails of the relevant boundary generating function. In that case the corresponding large-sample theory is not very reliabl e. To illustrate the techniques we present a group sequential analysis of a recently completed study by the Eastern Cooperative Oncology Gro up.