HEAM seminar: A discussion on minimax-regret optimal statistical treatment rules and their applications in health

A common approach used to make/recommend a decision (assign a treatment) based on available experimental data (e.g., clinical trial data) has been hypothesis testing. However, from a decision-making perspective, this practice lacks a clear formal justification (optimality with respect to some criterion). Existing literature offers several ways to formalize the decision-making problem in the presence of uncertainty and ambiguity that include maximin- and minimax-regret criteria, and Bayesian criteria. Focusing on minimax-regret that minimizes the maximum sub-optimality gap, we are going to discuss the rationale for using these approaches as well as some of the resulting optimal statistical treatment rules in static (dataset is given and fixed) and dynamic (data arrive sequentially) settings. Finally, recent contributions on exact minimax-regret optimal rules in finite samples are going to be reviewed including the presenter’s contribution on exact minimax optimal rules for bounded outcomes.