Maximally selected χ2 statistics for kx2 tables

It is common in epidemiologic analyses to summarize continuous outcomes as falling above or below a threshold. With such a dichotomized outcome, the usual chi(2) statistics for association or trend can be used to test for equality of proportions across strata of the study population. However, if the threshold is chosen to maximize the test statistic, the nominal chi(2) reference distributions are incorrect. In this paper, the asymptotic distributions of maximally selected chi(2) statistics for association and for trend for the k x 2 table are derived. The methodology is illustrated with data from an AIDS clinical trial. The results of simulation experiments that assess the accuracy of the asymptotic distributions in moderate sample sizes are also reported.