Psych-ECA: A Reproducible Semi-Synthetic Benchmark for Synthetic Control Arms in Longitudinal Psychiatry

Abstract

External and synthetic control arms (ECAs) are entering psychiatric drug development, but the field lacks a benchmark that evaluates the properties regulators care about: not only how accurately a method reconstructs untreated trajectories, but whether its uncertainty is calibrated, whether it is robust to the informative observation times common in mental-health records (sicker patients are seen more often), and what false-positive rate it induces in go/no-go trial decisions. Real psychiatric trial data (e.g. STAR-D and registry cohorts) require credentialed access and lack ground-truth counterfactuals, so, following established semi-synthetic benchmarks in causal inference (IHDP, ACIC, and the PK-PD tumor-growth simulator), we release Psych-ECA, a fully reproducible generator of longitudinal symptom trajectories for depression (PHQ-9), anxiety (HAM-A), and psychosis (PANSS) with known counterfactual control arms, informative visits, and validated-scale measurement noise. We benchmark eight estimators spanning carry-forward, pooled real-world-data averages, nearest-neighbour matching, linear mixed models, gradient boosting, and the Scribe trajectory-bridge method. Three findings emerge. First, trajectory and flexible machine learning methods achieve the best counterfactual accuracy (about 2.3 PHQ-9 RMSE), outperforming cross-sectional baselines. Second, only Scribe is both accurate and calibrated, achieving 93-96% empirical coverage of nominal 90% prediction intervals, compared with 87-88% for gradient boosting and 62-75% for uncalibrated SDE models. Third, inverse-intensity correction reduces bias under informative sampling, while Scribe's calibrated intervals are the only trajectory method that maintains nominal false-positive rates as informativeness increases. We release all code, data-generation scripts, and random seeds to enable fully reproducible evaluation.