General sample size analysis for probabilities of causation: a delta method approach

TL;DR

This paper introduces a delta method-based framework for determining the sample sizes needed to accurately estimate bounds on probabilities of causation, addressing a key gap in causal inference research.

Contribution

It provides a novel, general approach for sample size calculation for PoC bounds expressed as linear combinations, enhancing causal decision-making.

Findings

Sample size calculations improve estimation stability.

Simulation studies validate the proposed method.

Framework applicable to various causal inference settings.

Abstract

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.