Estimating the average treatment effect in cluster-randomized trials with misclassified outcomes and non-random validation subsets

Randomized trials are viewed as the benchmark for assessing causal effects of treatments on outcomes of interest. Nonetheless, challenges such as measurement error can undermine the standard causal assumptions for randomized trials. In ASPIRE, a cluster-randomized trial, pediatric primary care clinics were assigned to one of two treatments aimed at promoting clinician delivery of a secure firearm program to parents during well-child visits. A key outcome of interest is thus parent receipt of the program at each visit. Clinicians documented program delivery in patients' electronic health records for all visits, but their reporting is a proxy measure for the parent receipt outcome. Parents were also surveyed to report directly on program receipt after their child's visit; however, only a small subset of them completed the survey. Here, we develop a causal inference framework for a binary outcome that is subject to misclassification through silver-standard measures (clinician reports), but gold-standard measures (parent reports) are only available for a non-random internal validation subset. We propose a method for identifying the average treatment effect (ATE) that addresses the risk of bias due to misclassification and non-random validation selection, even when the outcome (parent receipt) may directly impact selection propensity (survey responsiveness). We show that ATE estimation relies on specifying the relationship between the gold- and silver-standard outcome measures in the validation subset, which may depend on treatment and covariates. Additionally, the clustered design is reflected in our causal assumptions and in our cluster-robust approach to estimation of the ATE. Simulation studies demonstrate acceptable finite-sample operating characteristics of our ATE estimator, supporting its application to ASPIRE.