Multiple testing with close to equally correlated structure

Abstract

In clinical trials with multiple primary endpoints or with multiple observations on the same sampling unit, the maximum of all observations is a convenient statistic that controls the familywise error rate. The quantile of this statistic depends on the correlation among multiple observations. To simplify modeling, the compound symmetry (CS) covariance structure is frequently used. The assumption of exact compound symmetry cannot usually be justified, and further sensitivity studies under more varied correlations are recommended. The need for multiple simulations may impose an increased demand on computer and time resources. To evaluate the sensitivity of simulation results restricted to CS structure, we calculated the linear part of the Taylor expansion of the cumulative distribution function (CDF) for the maximum statistic. Furthermore, we derived the Taylor expansion for quantiles of the maximum statistic. Our simulation studies on the linear approximation of quantiles confirmed good performance of the linearization formula.