Randomized controlled trials (RCTs) often include subgroup analyses to assess whether treatment effects vary across prespecified patient populations. However, these analyses frequently suffer from small sample sizes, which limit the power to detect heterogeneous effects. Power can be improved by leveraging predictors of the outcome-that is, through covariate adjustment-as well as by borrowing external data from similar RCTs or observational studies. The benefits of covariate adjustment may be limited when the trial sample is small. Borrowing external data can increase the effective sample size and improve power, but it introduces two key challenges: (i) integrating data across sources can lead to model misspecification, and (ii) practical violations of the positivity assumption-where the probability of receiving the target treatment is near zero for some covariate profiles in the external data-can lead to extreme inverse-probability weights and unstable inferences, ultimately negating potential power gains. To account for these shortcomings, we present an approach to improving power in preplanned subgroup analyses of small RCTs that leverages both baseline predictors and external data. We propose de-biased estimators that accommodate parametric, machine learning (ML), and nonparametric Bayesian methods. To address practical positivity violations (PPVs), we introduce three estimators: A covariate-balancing approach, an automated de-biased machine learning (DML) estimator, and a calibrated-DML estimator. We show improved power in various simulations and offer practical recommendations for the application of the proposed methods. Finally, we apply them to evaluate the effectiveness of citalopram for negative symptoms in first-episode schizophrenia (FES) patients across subgroups defined by duration of untreated psychosis (DUP), using data from two small RCTs.
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