A Test for Treatment Effects Based on the Exact Distribution of an Ordinary Least-Square Estimator in Sequential Parallel Comparison Design

Abstract

Sequential parallel comparison design (SPCD) is used to deal with high placebo response when evaluating treatment effects in clinical trials. Several analysis methods assuming a continuous variable have been proposed within the SPCD framework. In particular, statistical tests using an ordinal least-square (OLS) estimator of an overall treatment effect have been discussed. These tests are usually adequate because the test statistic is asymptotically distributed as a normal distribution from the central limit theorem. However, the exact distribution of the OLS estimator has not been derived and the comprehensive performance of the test statistics is unknown. In this work, we derived the exact distribution of the OLS estimator and constructed a test based on the derived distribution within the SPCD framework. The performances (Type I error rate and power) of the test were compared with those of tests based on an asymptotic distribution (asymptotic tests). The Type I error rate of the exact test was well controlled, whereas that of the asymptotic method tended to deviate from the significance level. The results show that the power of the exact test is almost equivalent to that of the asymptotic tests.