General sample size analysis for probabilities of causation: a delta method approach
This work addresses a gap in sample size analysis for causal inference, providing a practical tool for researchers and practitioners in fields like epidemiology and social sciences, though it is incremental as it builds on existing bound estimation methods.
The paper tackles the problem of determining required sample sizes for estimating bounds on probabilities of causation, which are crucial for decision-making but often not directly measurable, by proposing a general framework based on the delta method. The result shows that this approach leads to stable estimation of these bounds, as demonstrated through simulation studies.
Probabilities of causation (PoCs), such as the probability of necessity and sufficiency (PNS), are important tools for decision making but are generally not point identifiable. Existing work has derived bounds for these quantities using combinations of experimental and observational data. However, there is very limited research on sample size analysis, namely, how many experimental and observational samples are required to achieve a desired margin of error. In this paper, we propose a general sample size framework based on the delta method. Our approach applies to settings in which the target bounds of PoCs can be expressed as finite minima or maxima of linear combinations of experimental and observational probabilities. Through simulation studies, we demonstrate that the proposed sample size calculations lead to stable estimation of these bounds.