Detecting dose-response using contrasts: asymptotic power and sample size determination for binomial data

Recently, Stewart and Ruberg proposed the use of contrast tests for detecting dose-response relationships. They considered in particular bivariate contrasts for healing rates and gave several possibilities of defining adequate sets of coefficients. This paper extends their work in several directions. First, asymptotic power expressions for both single and multiple contrast tests are derived. Secondly, well known trend tests are rewritten as multiple contrast tests, thus alleviating the inherent problem of choosing adequate contrast coefficients. Thirdly, recent results on the efficient calculation of multivariate normal probabilities overcome the traditional simulation-based methods for the numerical computations. Modifications of the power formulae allow the calculation of sample sizes for given type I and II errors, the spontaneous rate, and the dose-response shape. Some numerical results of a power study for small to moderate sample sizes show that the nominal power is a reasonably good approximation to the actual power. An example from a clinical trial illustrates the practical use of the results.