Complementary hypotheses in safety surveillance

Abstract Postmarketing safety surveillance studies address two actionable questions: (1) Is the test product riskier than a standard? (2) Is the risk associated with the test product within some tolerable margin by comparison to the standard? Established techniques, not commonly applied to the setting of such complementary one-sided hypotheses, lead to useful conclusions in practice. For two-group studies, a search over possible one-sided binomial test results yields sample sizes that guarantee that the confidence bounds exclude one or the other of the hypotheses. With continuous monitoring, simple curtailment reduces the sample size. Point and interval estimates follow from the binomial distribution of events at the end of the study or from component negative binomials for crossing a bound of simple curtailment with continuous monitoring and earlier stopping. An asymptotic derivation corresponds to the problem of constructing a confidence interval that is smaller than the distance between the parameter values for tolerable excess and the absence of excess risk. Studies with guaranteed rejection of one of the pair of complementary hypotheses are somewhat larger than corresponding studies of a single hypothesis under usual power requirements, but the increase may be tolerable in return for certainty that there will be an actionable conclusion.