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Primary Submission Category: Bayesian Causal Inference

Bayesian Nonparametric Estimation of Principal Causal Effects in Presence of Partial Compliance from Patients

Authors: Biraj Guha, Ashkan Ertefaie, Michael Kosorok,

Presenting Author: Benjamin Baer*

In causal inference, the average causal treatment effect is typically studied conditional on given baseline covariates of patients and is termed Conditional Average Treatment Effect (CATE). In the presence of post-treatment variables like potential compliance values of patients, Principal Stratification (PS) groups them to allow for causal interpretation of the Principal Causal Effect (PCE) estimates. This estimation procedure requires the learning of the latent, partially observed stratum for each patient. The outcome model learns the relation between the outcomes and the potential compliance variables, while the strata model encodes the missing information due to the potential compliance framework. Current literature lacks the use of flexible nonparametric Bayesian regression models for the outcomes, while the strata models in several works do not enjoy a rich, yet identifiable model. Our contribution includes a modeling novelty on both these fronts. For the outcomes, we propose a random covariate Gaussian Process regression model, where the two potential outcomes are separately modeled, then connected. We discuss how to solve ensuing identifiability issues. For the strata model, we use a novel Dirichlet Process mixture of Beta distribution based Generalized Linear Models (GLM), ensuring high flexibility in learning the latent strata values. The unobserved potential compliances are discriminatively modeled in contrast to generative joint modeling in previous works.