Balanced and robust randomized treatment assignments: the Finite Selection Model

The Finite Selection Model (FSM) was proposed and developed by Carl Morris in the 1970s for the experimental design of RAND's 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 treatment groups take turns selecting units in a fair and random order to optimize a common 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. Herein, we revisit, formalize, and extend the FSM as a general tool for experimental design. Leveraging the idea of D-optimality, we propose and evaluate a new selection criterion in the FSM. The FSM using the D-optimal selection function has no tuning parameters, is affine invariant, and achieves near-exact mean-balance on a class of covariate transformations. In addition, the FSM using the D-optimal selection function is shown to retrieve several classical designs such as randomized block and matched-pair designs. For a range of cases with multiple treatment groups, we propose algorithms to generate a fair and random selection order of treatments. We demonstrate FSM's performance in terms of balance and efficiency in a simulation study and a case study based on the HIE data. We recommend the FSM be considered in experimental design for its conceptual simplicity, practicality, and robustness.