Tests of non‐null hypothesis on proportions for stratified data

It is more reasonable to interpret the efficacy of therapies under non-null hypothesis, hence tests of non-null hypothesis have been carried out. Most clinical trials adopt multi-center campaign and yield stratified data. However, the existing non-null hypothesis tests are not suitable for stratified data. This paper proposes the tests of non-null hypothesis on proportions for stratified data. Averaging the treatment-control difference in each stratum yields the mean treatment-control difference. Comparing its expectation with the minimal detectable difference leads to set up a non-null hypothesis. Its variance is used to construct the equation of the basic relationship for stratified designs under the non-null hypothesis. Then follow the derivations for the one- and two-sample tests. Their performance is demonstrated by the Monte Carlo method. As far as the two-sample tests are concerned, they reduce to the Cochran test and the Mantel-Haenszel test, on setting the minimal detectable difference equal to zero, and to the Dunnett-Gent test when there is only one stratum. As for the one-sample test, it also reduces to its classical counterparts in these situations. The observed power coincides with the prescribed power and the relevant operating characteristic curves. The tests can be applied to the active control clinical trials with multi-center or stratified designs for establishing the clinical superiority or non-inferiority of a tested drug versus control. Worked examples illustrate the methodology.