“Causal Inference with Intermediate Outcomes: methods for Principal Stratum Identification and Estimation of Principal Causal Effects” Department of Biostatistics and Health Data Science, School of Public Health.
Gong Tang, advisor and committee chair
Abstract:
In recent years, controlled neoadjuvant cancer clinical trials have become a promising approach for the early evaluation of treatment efficacy where systemic treatments are given before surgery. Tumors removed at surgery are evaluated for pathological complete response (pCR). The intermediate outcome, pCR, is highly predictive of survival outcomes. However, directly comparing survival outcomes across treatment arms by pCR status does not have causal interpretations. Principal stratification provides a useful framework for estimating causal treatment effects on survival, conditional on potential intermediate outcomes like pCR. Standard approaches often rely on counterfactual modeling and sensitivity analyses to address the causal estimands of
interest, given the inherent identifiability challenges. This dissertation focuses on developing statistical methods to address these challenges.
Within the principal stratification framework, patients are categorized into latent subgroups, or principal strata, based on their potential intermediate outcomes under both control and treatment. Since principal stratum membership is never observed, Tan et al. (2022) proposed a novel method to identify principal causal effects (PCEs) via a probabilistic equation under a monotonicity assumption on the intermediate outcome. Parameters of the counterfactual model are estimated by minimizing the Euclidean distance between empirical and model- based estimates of certain probabilities. To provide a more natural measure of discrepancy between those estimates, here we propose to use the Kullback-Leibler divergence instead. This method yields similar and
sometimes more efficient and stable estimation of PCEs in simulation studies.
Given that the estimation of the principal strata distribution given continuous auxiliary variables under the monotonicity assumption is never established, the second project focuses on developing nonparametric methods to address this need. Assuming monotonicity, we introduce a suite of flexible estimators, including logistic regression with B-splines, M-splines, a modified k*-nearest neighbor approach, and a novel weighted least squares (WLS) kernel estimator. Notably, the WLS kernel estimator is highly adaptable, accommodating
continuous outcomes, multiple covariates, and multi-arm trials, making it well-suited to contemporary clinical settings. We assess the performance of these methods through simulation studies and apply them to the NSABP B-40 and B-41 trial to predict pCR with gene expression data by treatment arms under the monotonicity assumption.
The third project builds on this foundation to estimate PCEs by leveraging a continuous auxiliary variable and the estimated stratum distribution. Unlike existing methods that rely on sensitivity analyses or assume ordinal trends in counterfactual models, our proposed approach is more flexible. This method is applied to the NSABP B-40 and B-41 trial using gene signature data to estimate the survival benefit among patients who would achieve pCR under the new treatment regimen. Collectively, these three projects establish a comprehensive framework for causal inference in the presence of intermediate outcomes, with direct relevance to neoadjuvant cancer clinical trials and other similar settings.
Public health significance: This dissertation lays a rigorous statistical foundation for evaluating treatment efficacy in settings involving intermediate outcomes. The proposed methods enhance the interpretability of neoadjuvant trial results and support more informed clinical decisions based on benefit of the new treatment across principal strata. Together, these contributions facilitate causal interpretation in clinical trials, promote evidence-based oncology, and ultimately advance precision medicine to benefit patients and public health.