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BMC Med Res Methodol. 2019 Dec 16;19(1):239. doi: 10.1186/s12874-019-0883-9.

Simulation and minimization: technical advances for factorial experiments designed to optimize clinical interventions.

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Boston Medical Center, 72 E. Concord St, Boston, MA, USA.
Boston University School of Public Health, 801 Massachusetts Ave, Boston, MA, USA.
Boston Medical Center, 72 E. Concord St, Boston, MA, USA.
Boston University School of Medicine, 72 E. Concord St, Boston, MA, USA.
DotHouse Health Center, 1353 Dorchester Ave, Dorchester, MA, USA.



The Multiphase Optimization Strategy (MOST) is designed to maximize the impact of clinical healthcare interventions, which are typically multicomponent and increasingly complex. MOST often relies on factorial experiments to identify which components of an intervention are most effective, efficient, and scalable. When assigning participants to conditions in factorial experiments, researchers must be careful to select the assignment procedure that will result in balanced sample sizes and equivalence of covariates across conditions while maintaining unpredictability.


In the context of a MOST optimization trial with a 2x2x2x2 factorial design, we used computer simulation to empirically test five subject allocation procedures: simple randomization, stratified randomization with permuted blocks, maximum tolerated imbalance (MTI), minimal sufficient balance (MSB), and minimization. We compared these methods across the 16 study cells with respect to sample size balance, equivalence on key covariates, and unpredictability. Leveraging an existing dataset to compare these procedures, we conducted 250 computerized simulations using bootstrap samples of 304 participants.


Simple randomization, the most unpredictable procedure, generated poor sample balance and equivalence of covariates across the 16 study cells. Stratified randomization with permuted blocks performed well on stratified variables but resulted in poor equivalence on other covariates and poor balance. MTI, MSB, and minimization had higher complexity and cost. MTI resulted in balance close to pre-specified thresholds and a higher degree of unpredictability, but poor equivalence of covariates. MSB had 19.7% deterministic allocations, poor sample balance and improved equivalence on only a few covariates. Minimization was most successful in achieving balanced sample sizes and equivalence across a large number of covariates, but resulted in 34% deterministic allocations. Small differences in proportion of correct guesses were found across the procedures.


Based on the computer simulation results and priorities within the study context, minimization with a random element was selected for the planned research study. Minimization with a random element, as well as computer simulation to make an informed randomization procedure choice, are utilized infrequently in randomized experiments but represent important technical advances that researchers implementing multi-arm and factorial studies should consider.


Clinical intervention studies; Clinical trials; Factorial design; Minimization; Multi-phase optimization strategy; Randomization; Subject allocation

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