A prediction-based test for multiple endpoints

Abstract

This article introduces a global hypothesis test intended for studies with multiple endpoints. Our test makes use of a priori predictions about the direction of the result of each endpoint and we weight these predictions using the sample correlation matrix. The global alternative hypothesis concerns a parameter, $\varphi$ , defined as the researcher's ability to correctly predict the direction of each measure, essentially a binomial parameter. This allows for the test to include expected effects that are all positive, all negative or both while still using the cumulative information across those endpoints. A rejection of the null hypothesis ( $H_0:\varphi \le {\varphi }_0$ ) provides evidence that the researcher's underlying theory about the natural process provides a better prediction of the observed results relative to the null hypothesized predictive ability, thus indicating the theory is worthy of further study. We compare our test to O'Brien's ordinary least squares (OLS) test and show that for small samples and situations where the effect is not in the same direction across all endpoints our approach has better power, while if the effect is equidirectional across all endpoints the OLS test can have greater power.

Keywords: O'Brien's OLS; correlated endpoints; multiplicity.