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

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 versus 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 relative effectiveness of simultaneous versus interval administration of mifepristone and misoprostol over the first nine weeks of gestation. The model reflects our expectation that the relative effectiveness 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/.