Maximally selected chi(2) 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 u sual chi(2) statistics for association or trend can be used to test for equ ality of proportions across strata of the study population. However, if the threshold is chosen to maximize the test statistic, the nominal chi(2) ref erence distributions are incorrect. In this paper, the asymptotic distribut ions 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 f rom an AIDS clinical trial. The results of simulation experiments that asse ss the accuracy of the asymptotic distributions in moderate sample sizes ar e also reported.