Testing for efficacy in multiple endpoints has emerged as an important statistical problem. The Food and Drug Administration (FDA) will issue a guidance on Multiple
Endpoints in the near future.
When there are primary and secondary endpoints, efficacy in the secondary endpoint
is only relevant if efficacy in the primary endpoint has been shown. There are
thus defined paths to decision-making.
The current approach to this problem is based on closed testing, that is, testing
all possible intersection hypotheses, and collating the results. For decision-making to
follow pre-defined paths, strategic choices of test statistics and critical values must be
made. As the number of doses and endpoints increases, such strategic choices become
increasingly difficult.
Partition testing is an alternative to closed testing. It gives insights on confidence
sets for step-wise tests, and can be more powerful than closed testing. It can also
simplify problem formulation when decision-making follows specific paths. We show,
for the primary-secondary endpoints problem, that partition testing has advantages.
Using it to implement what we call the Decision Path Principle, we find that partition
testing not only drastically reduces the number of hypotheses to be tested, but
also guides decision-making along pre-defined paths. With our way of setting critical
values, we achieve higher probabilities of correctly inferring efficacious primary endpoints
as efficacious compared to gatekeeping methods, while maintaining the same
level of strong FWER control. These advantages are illustrated with a real data
example, and by simulation.