Combining BART and Principal Stratification to estimate the effect of intermediate on primary outcomes with application to estimating the effect of family planning on employment in sub-Saharan Africa

There is interest in learning about the causal effect of family planning (FP) on empowerment related outcomes. Experimental data related to this question are available from trials in which FP programs increase access to FP. While program assignment is unconfounded, FP uptake and subsequent empowerment may share common causes. We use principal stratification to estimate the causal effect of an intermediate FP outcome on a primary outcome of interest, among women affected by a FP program. Within strata defined by the potential reaction to the program, FP uptake is unconfounded. To minimize the need for parametric assumptions, we propose to use Bayesian Additive Regression Trees (BART) for modeling stratum membership and outcomes of interest. We refer to the combined approach as Prince BART. We evaluate Prince BART through a simulation study and use it to assess the causal effect of modern contraceptive use on employment in six cities in Nigeria, based on quasi-experimental data from a FP program trial during the first half of the 2010s. We show that findings differ between Prince BART and alternative modeling approaches based on parametric assumptions.