Distributive randomization: a pragmatic fractional factorial design to screen or evaluate multiple simultaneous...

In some medical indications, numerous interventions have a weak presumption of efficacy, but a good track record or presumption of safety. This makes it feasible to evaluate them simultaneously. This study evaluates a pragmatic fractional factorial trial design that randomly allocates a pre-specified number of interventions to each participant, and statistically tests main intervention effects. We compare it to factorial trials, parallel-arm trials and multiple head-to-head trials, and derive some good practices for its design and analysis.

We simulated various scenarios involving 4 to 20 candidate interventions among which 2 to 8 could be simultaneously allocated. A binary outcome was assumed. One or two interventions were assumed effective, with various interactions (positive, negative, none). Efficient combinatorics algorithms were created. Sample sizes and power were obtained by simulations in which the statistical test was either difference of proportions or multivariate logistic regression Wald test with or without interaction terms for adjustment, with Bonferroni multiplicity-adjusted alpha risk for both. Native R code is provided without need for compiling or packages.

Distributive trials reduce sample sizes 2- to sevenfold compared to parallel arm trials, and increase them 1- to twofold compared to factorial trials, mostly when fewer allocations than for the factorial design are possible. An unexpectedly effective intervention causes small decreases in power (< 10%) if its effect is additive, but large decreases (possibly down to 0) if not, as for factorial designs. These large decreases are prevented by using interaction terms to adjust the analysis, but these additional estimands have a sample size cost and are better pre-specified. The issue can also be managed by adding a true control arm without any intervention.

Distributive randomization is a viable design for mass parallel evaluation of interventions in constrained trial populations. It should be introduced first in clinical settings where many undercharacterized interventions are potentially available, such as disease prevention strategies, digital behavioral interventions, dietary supplements for chronic conditions, or emerging diseases. Pre-trial simulations are recommended, for which tools are provided.