A flexible test for early-stage studies with multiple endpoints

This paper builds on the recently proposed prediction test for muliple endpoints. The prediction test combines information across multiple endpoints while accounting for the correlation between them. The test performs well with small samples relative to the number of endpoints of interest and is flexible in the hypotheses across the individual endpoints that can be combined. The prediction test addresses a global hypothesis that is of particular interest in early-stage studies and can be used as justification for continuing on to a larger trial. However, the prediction test has several limitations which we seek to address. First, the prediction test is overly conservative when both the effect sizes across all endpoints and the number of endpoints are small. By using a parametric bootstrap to estimate the null distribution, we show that the test achieves the nominal error rate in this situation and increases the power of the test. Second, we provide a framework to allow for predictions of a difference on one or more endpoints. Finally, we extend the test with a composite null hypothesis that allows for different null hypothesized predictive abilities across the endpoints which can be especially useful if the study contains both familiar and novel endpoints. We use an example from a physical activity trial to illustrate these extensions.