Strategic Hypothesis Testing
Yatong Chen, Safwan Hossain, Yiling Chen
We study hypothesis testing in a principal-agent setting where the agent with a private belief about a product's effectiveness interacts with a principal who evaluates approval based on clinical trial outcomes. The principal's goal is to set a p-value to control for both false positives (Type I errors) and false negatives (Type II errors) while accounting for the agent's decision.Building upon earlier works, we develop a game-theoretic model that characterizes the agent's participation in the trial and the request sample size as a response to the regulator's p-value threshold with minimum assumptions. Despite intricate dynamics, we show that the principal's errors exhibit clear monotonic behavior when segmented by an efficiently computable critical p-value threshold. We use this to characterize the principal's optimal p-value. We also empirically validate our model and insights using publicly available data on drug approvals. Overall, our work offers a comprehensive perspective on strategic interactions within hypothesis testing, providing technical and regulatory insights.