A class of sequential conditional probability ratio tests

A new class of sequential testing procedures, sequential conditional probability ratio tests (SCPRT's), is proposed. These procedures have the property of having a maximum sample size no larger than a fixed-sample test with an almost identical power function. The efficiency of the SCPRT, in terms of expected sample size, is close to that of Wald's SPRT. Group sequential testing procedures derived from the SCPRT are not restricted to the choices of group sizes and number of groups. At the same time, the SCPRT, the group-SCPRT, and the reference fixed sample size test (RFSST) are agreeable in the sense of having very small probability of leading to different rejection/acceptance results. For the SCPRT or the group-SCPRT, stopping boundaries are decided by appropriate deflection factors determined by controlling absorption probabilities of a random bridge on the SCPRT boundaries. In this article the basic idea for the SCPRT is introduced in a general setup. But examples and technical discussions are restricted mainly to dichotomous distributions, in which the power functions and expected sample sizes for the sequential procedures can be easily computed by a method developed by Xiong.