Contrast-specific propensity scores for causal inference with multiple interventions.

Existing methods that use propensity scores for heterogeneous treatment effect estimation on non-experimental data do not readily extend to the case of more than two treatment options. In this work, we develop a new propensity score-based method for heterogeneous treatment effect estimation when there are three or more treatment options, and prove that it generates unbiased estimates. We demonstrate our method on a real patient registry of patients in Singapore with diabetic dyslipidemia. On this dataset, our method generates heterogeneous treatment recommendations for patients among three options: Statins, fibrates, and non-pharmacological treatment to control patients' lipid ratios (total cholesterol divided by high-density lipoprotein level). In our numerical study, our proposed method generated more stable estimates compared to a benchmark method based on a multi-dimensional propensity score.