Journal of Biometrics & Biostatistics

Exact Tests for the Weak Causal Null Hypothesis on a Binary Out come in Randomized Trials

Abstract

Yasutaka Chiba

There are two principal exact tests for evaluation of data in two-by-two contingency tables: the tests of Fisher and Barnard. The latter cannot be a hypothesis test for the causal null hypothesis unless exchangeability can be assumed. Fisher’s exact test is a hypothesis test for the sharp causal null hypothesis (i.e., that there is no effect for all individuals), but not for the weak causal null hypothesis (i.e., that the true risk difference is zero). Rejection of the sharp causal null hypothesis does not mean that the weak causal null hypothesis is rejected (i.e., that the true risk difference is not zero). In this article, we provide exact tests for the weak causal null hypothesis, in the absence of any assumption, in the context of randomized trials. Using the concept of principal stratification, which considers four types of subjects to define four principal strata, we derive an unconditional exact test, for which neither marginal total is fixed, and a conditional exact test, for which one marginal total is fixed. In addition, we show that Fisher’s exact test can be a hypothesis test for the weak causal null hypothesis when monotonicity can be assumed. The derived exact tests are extended to hypothesis testing for non-inferiority trials and to construct confidence intervals linking to the exact tests. The derived exact tests and confidence intervals are illustrated using data from two clinical trials.