Primary Submission Category: Multiple treatments/positivity violations
Vector Incremental Treatment Effects for Causal Inference with Multiple Binary Treatments
Authors: Denis Agniel, Max Rubinstein, Sharon-Lise Normand, Marcela Horvitz-Lennon,
Presenting Author: Denis Agniel*
Estimating causal effects with m > 1 binary treatments faces challenges: positivity violations when combinations are rare, exponential growth in potential outcomes (2^m), and difficulty choosing meaningful treatment contrasts. We extend incremental propensity score interventions to vector treatments, defining causal effects through intervention distributions scaling odds of each treatment. These effects capture the joint effect of the many treatments. The method selects an intervention treatment distribution Q_δ minimizing a user-specified divergence (e.g., KL, Hellinger, f-divergence) from the original propensity score distribution P_0 subject to marginal odds constraints: Q_δ(A_k = 1|X) / {1 – Q_δ(A_k = 1|X)} = δ_k × P_0(A_k = 1|X) / {1 – P_0(A_k = 1|X)}. This preserves the joint treatment distribution in the intervention distribution and allows the intervention to affect treatments differently. We derive the efficient influence function, which is not a straightforward extension of the univariate incremental propensity score one, and derive doubly robust estimators from it. The efficient influence function accounts for uncertainty in nuisance estimation as well as Q_δ computation. We establish asymptotic normality and provide inference. We apply these methods to study the effect of quality of care (captured by many binary indicators of quality) on clinical outcomes (treatment discontinuation, mortality) for New York Medicaid patients diagnosed with schizophrenia.