Probabilities of Causation: Adequate Size of Experimental and Observational Samples

TL;DR

This paper addresses how large experimental and observational samples need to be to accurately estimate probabilities of causation, providing a method to determine sample size for specified confidence intervals and validating it through simulations.

Contribution

It introduces a method for calculating the necessary sample size to estimate bounds of probabilities of causation with desired confidence levels.

Findings

Sample size method yields stable bounds estimations

Simulation confirms effectiveness of the proposed sample size calculation

Provides practical guidance for experimental design in causation studies

Abstract

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.