Starting Small: Prioritizing Safety over Efficacy in Randomized Experiments Using the Exact Finite Sample Likelihood

TL;DR

This paper introduces finite sample likelihood-based decision rules that prioritize safety over efficacy in randomized experiments, demonstrating improved performance in small samples and providing insights into clinical trial outcomes.

Contribution

It develops finite sample Bayesian and maximum likelihood decision rules that explicitly prioritize safety, offering a new approach for analyzing small-sample randomized experiments.

Findings

Finite sample rules outperform bounds-based rules in small samples.

Application to clinical trial data highlights safety considerations in efficacy estimates.

Proposes a finite sample maximum likelihood criterion for decision-making.

Abstract

We use the exact finite sample likelihood and statistical decision theory to answer questions of ``why?'' and ``what should you have done?'' using data from randomized experiments and a utility function that prioritizes safety over efficacy. We propose a finite sample Bayesian decision rule and a finite sample maximum likelihood decision rule. We show that in finite samples from 2 to 50, it is possible for these rules to achieve better performance according to established maximin and maximum regret criteria than a rule based on the Boole-Frechet-Hoeffding bounds. We also propose a finite sample maximum likelihood criterion. We apply our rules and criterion to an actual clinical trial that yielded a promising estimate of efficacy, and our results point to safety as a reason for why results were mixed in subsequent trials.