Targeted Smooth Bayesian Causal Forests: An analysis of heterogeneous treatment effects for simultaneous vs. interval medical abortion regimens over gestation

Abstract

We introduce Targeted Smooth Bayesian Causal Forests (tsBCF), a nonparametric Bayesian approach for estimating heterogeneous treatment effects which vary smoothly over a single covariate in the observational data setting. The tsBCF method induces smoothness by parameterizing terminal tree nodes with smooth functions and allows for separate regularization of treatment effects vs. prognostic effect of control covariates. Smoothing parameters for prognostic and treatment effects can be chosen to reflect prior knowledge or tuned in a data-dependent way.

We use tsBCF to analyze a new clinical protocol for early medical abortion. Our aim is to assess the relative effectiveness of simultaneous vs. interval administration of mifepristone and misoprostol over the first nine weeks of gestation. Our analysis yields important clinical insights into how to best counsel patients seeking early medical abortion, where understanding even small differences in relative effectiveness can yield dramatic returns to public health. The model reflects our expectation that the treatment effect varies smoothly over gestation but not necessarily over other covariates. We demonstrate the performance of the tsBCF method on benchmarking experiments. Software for tsBCF is available at https://github.com/jestarling/tsbcf/ and in the Supplementary Material (Starling (2020)).