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?