# Causal inference for additive multiple treatments

I encountered a causal inference problem in practice and want to find if there is a previously established statistical toolset that can be applied to my problem.

My problem is characterized as follows:

• My goal is to characterize the causal effects of each $$T$$ treatment $$X_1, \cdots X_T$$ on outcome $$Y$$ where the values of treatments and outcomes are binary (0 or 1).
• Unlike a typical multiple treatment setting, multiple treatments can be active simultaneously. For example, it is possible for a sample to have $$X_1 =1$$ and $$X_2 =1$$.
• If necessary, the additivity assumption can be introduced. For example, the causal effect of having $$(X_1, X_2)=(1, 1)$$ is the sum of the causal effects of the two cases: $$(X_1, X_2)=(1,0)$$ and $$(X_1, X_2)=(0, 1)$$.
• As in typical causal inference settings such as that of propensity score matching, there can be multiple common cause variables.

Q1. Is there a specific term describing the problem setting described above? If there is such a term, could you cite a few pedagogical materials?

Q2. If the problem is not studied before, how can it be tackled using existing causal inference methods?