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

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. In the FSM, a treatment group at each of its turns selects the available unit that maximally improves the combined quality of its resulting group of units according to a common optimality 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, 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, a simulation study, and in ten randomized studies from the health and social sciences. We recommend the FSM be considered in experimental design for its conceptual simplicity, efficiency, and robustness.