Background: Because of the difficulty in obtaining reliable parameter estimates in small cohorts, stratification by balancing scores such as propensity may fail to achieve covariate balance.
Objectives: To demonstrate a nonparametric technique for cohort stratification that achieves excellent balance, and to compare it to stratification by propensity score (PS).
Methods: We created a loss function based on the within-strata and overall Euclidean distances (ED) between treated and untreated. Stratum assignments for individual records that minimized the loss function were identified using a standard package implementing a nonparametric evolutionary algorithm. Covariate balance in the resulting stratified data was investigated through simulation with comparison to propensity-decile stratification and in a real-world cohort.
Results: In 100 trials using simulated data of 300 records with a binary treatment and four dissimilar covariate predictors, minimizing the loss function led to stratum assignments that reduced covariate imbalance by a median of over 99%. In the same simulations, PS stratification produced median reductions from 72% to 81%. ED minimization applied to a cohort of 361 children undergoing immunotherapy for psoriasis reduced covariate imbalance by over 99% for four strongly predictive clinical and temporal covariates. Reductions in imbalance through PS decile stratification for the same predictors ranged from 85% to 91%. For eight additional variables that were less predictive of treatment, imbalance reduction ranged from 75% to 100% with ED-based optimization and from -64% (imbalance increased) to 99% with stratification by PS deciles.
Conclusions: Balancing of covariates through nonparametric stratification is well adapted to the analysis of small cohorts.