Confidence intervals for secondary parameters following a sequential test

In sequential studies, formal interim analyses are usually restricted to a consideration of a single null hypothesis concerning a single parameter of interest. Valid frequentist methods of hypothesis testing and of point and interval estimation for the primary parameter have already been devised for use at the end of such a study. However, the completed data set may warran t a more detailed analysis, involving the estimation of parameters correspo nding to effects that were not used to determine when to stop, and yet corr elated with those that were. This paper describes methods for setting confi dence intervals for secondary parameters in a way which provides the correc t coverage probability in repeated frequentist realizations of the sequenti al design used. The method assumes that information accumulates on the prim ary and secondary parameters at proportional rates. This requirement will b e valid in many potential applications, but only in limited situations in s urvival analysis.