Balanced and Robust Randomized Treatment Assignments: The Finite Selection Model for the Health Insurance Experiment and Beyond

Abstract The Finite Selection Model (FSM) was developed by Carl Morris in the 1970s for the design of the RAND Health Insurance Experiment (HIE) (Morris 1979, Newhouse et al. 1993), one of the largest and most comprehensive social science experiments conducted in the U.S. The idea behind the FSM is that each treatment group takes turns selecting units in a fair and random order to optimize a common assignment criterion. At each of its turns, a treatment group selects the available unit that maximally improves the combined quality of its resulting group of units in terms of the criterion. In the HIE and beyond, we revisit, formalize, and extend the FSM as a general tool for experimental design. Leveraging the idea of D-optimality, we propose and analyze a new selection criterion in the FSM. The FSM using the D-optimal selection function has no tuning parameters for covariate balance, is affine invariant, and when appropriate, retrieves several classical designs such as randomized block and matched-pair designs. For multi-arm experiments, we propose algorithms to generate a fair and random selection order of treatments. We demonstrate FSM’s performance in a case study based on the HIE and in ten randomized studies from the health and social sciences. On average, the FSM achieves 68% better covariate balance than complete randomization and 56% better covariate balance than rerandomization in a typical study. We recommend the FSM be considered in experimental design for its conceptual simplicity, efficiency, and robustness.