Probabilities of Causation: Adequate Size of Experimental and Observational Samples
This work addresses a practical issue for researchers and practitioners in causal inference who need to design studies with sufficient statistical power, though it is incremental as it builds on existing bounds without introducing new causal paradigms.
The authors tackled the problem of determining adequate sample sizes for accurately estimating bounds on probabilities of causation, such as the probability of necessity and sufficiency, using experimental and observational data. They proposed a method to calculate required sample sizes for given confidence intervals and demonstrated through simulation that this approach yields stable estimations of the bounds.
The probabilities of causation are commonly used to solve decision-making problems. Tian and Pearl derived sharp bounds for the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of necessity (PN) using experimental and observational data. The assumption is that one is in possession of a large enough sample to permit an accurate estimation of the experimental and observational distributions. In this study, we present a method for determining the sample size needed for such estimation, when a given confidence interval (CI) is specified. We further show by simulation that the proposed sample size delivered stable estimations of the bounds of PNS.