Trial design to minimize expected p-value of Kaplan–Meier estimator of mortality for fixed N?

by OrangeSherbet   Last Updated June 30, 2020 02:19 AM - source

In randomized controlled trials, mortality is often compared between treatment and placebo using the Kaplan-Meier estimator (for instance, the remdesivir trial ACTT-1). The trial design could have a 1:1 ratio of treatment vs placebo, or some other ratio.

This question assumes the number of trial participants, $N$, is fixed.

The question is what ratio of placebo:treatment, if any, minimizes the expected p-value under the assumption the treatment has a mortality effect? Since p-values, especially p-value thresholds for statistical significance, play a traditional role in rejecting the null hypothesis (for instance no mortality benefit until p<0.05), is it possible to design a trial for fixed $N$ explicitly to minimize expected p-value with some ratio of placebo:treatment? Do some ratios of placebo:treatment, such as 2:1, 1:1, or 1:2, have different expected p-values under the assumption of an effect?

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Updated June 02, 2019 15:19 PM