Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions
This work addresses causal inference challenges in observational studies with binary outcomes and treatments, offering methods applicable to domains like education and healthcare, though it is incremental in extending existing frameworks.
The paper tackles causal inference under outcome-based sampling, showing that strong ignorability is less effective than under random sampling, and that monotonicity assumptions yield comparable sharp identified intervals, with the odds ratio serving as a sharp upper bound on causal relative risk.
We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the potential outcome framework. It is shown that strong ignorability is not always as powerful as it is under random sampling and that certain monotonicity assumptions yield comparable results in terms of sharp identified intervals. Specifically, the usual odds ratio is shown to be a sharp identified upper bound on causal relative risk under the monotone treatment response and monotone treatment selection assumptions. We offer algorithms for inference on the causal parameters that are aggregated over the true population distribution of the covariates. We show the usefulness of our approach by studying three empirical examples: the benefit of attending private school for entering a prestigious university in Pakistan; the relationship between staying in school and getting involved with drug-trafficking gangs in Brazil; and the link between physicians' hours and size of the group practice in the United States.