Power Estimation for Multiple Co-Primary Endpoints: a comparision among conservative solutions

The problem of estimating the power of the multivariate Intersection Union test (IUT) is studied. Four classical parametric solutions and a bootstrap nonparametricone, providing statistical lower bounds (i.e. one directional confidence intervals) for the power, are considered. The performances of these techniques in several bivariate IUT settings are compared through a simulation study. All solutions are biased, since their actual coverage probabilities are higher than the nominalone. The bootstrap solution shows the smallest bias, and the variability of its estimates is the lowest. Moreover, the bias of the bootstrap solution reduces faster than those of the other techniques when the pilot sample size, or the correlation, or the rate between the two noncentrality parameters increases. Also, the nonparametric bootstrap solution can be improved by calibration, with a considerable bias reduction.