Properties of composite time to first event versus joint marginal analyses of multiple outcomes

The Imperative to Enhance Cost-Effectiveness for Cardiovascular Therapeutic Development

Cardiovascular disease (CVD) is the leading cause of mortality worldwide. Therapeutic agents, such as those that lower low-density lipoprotein cholesterol, have been a critical factor in mitigating CVD event risk and demonstrate the important role that drug discovery plays in reducing morbidity and mortality. However, rapidly rising development costs, diminishing returns, and an increasingly challenging regulatory environment have all contributed to a declining number of cardiovascular (CV) therapeutic agents entering the health care marketplace. For pharmaceutical companies, a traditional cardiovascular outcomes trial (CVOT) can be a major financial burden and impediment to CV agent development. They can take as long as a decade to conduct, delaying potential investment return while carrying risk of failure. For patients, lengthy CVOTs delay drug accessibility. Without cost-effective CVOTs, drug innovation may be compromised, with CV patients bearing the consequences. This paper reviews potential approaches for making CV drug development more cost-effective.

Closed testing using surrogate hypotheses with restricted alternatives

Introduction

The closed testing principle provides strong control of the type I error probabilities of tests of a set of hypotheses that are closed under intersection such that a given hypothesis H can only be tested and rejected at level α if all intersection hypotheses containing that hypothesis are also tested and rejected at level α. For the higher order hypotheses, multivariate tests (> 1df) are generally employed. However, such tests are directed to an omnibus alternative hypothesis of a difference in any direction for any component that may be less meaningful than a test directed against a restricted alternative hypothesis of interest.

Methods

Herein we describe applications of this principle using an α-level test of a surrogate hypothesis H˜ such that the type I error probability is preserved if H⇒H˜ such that rejection of H˜ implies rejection of H. Applications include the analysis of multiple event times in a Wei-Lachin test against a one-directional alternative, a test of the treatment group difference in the means of K repeated measures using a 1 df test of the difference in the longitudinal LSMEANS, and analyses within subgroups when a test of treatment by subgroup interaction is significant. In such cases the successive higher order surrogate tests can be aimed at detecting parameter values that fall within a more desirable restricted subspace of the global alternative hypothesis parameter space.

Conclusion

Closed testing using α-level tests of surrogate hypotheses will protect the type I error probability and detect specific alternatives of interest, as opposed to the global alternative hypothesis of any difference in any direction.