A CLASS OF SEQUENTIAL CONDITIONAL-PROBABILITY RATIO TESTS

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