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

2026-02-18

AI Summary

This study addresses a critical gap in causal inference: the absence of sample size analysis methods for estimating bounds on causal probabilities—such as probabilities of necessity and sufficiency—hindering principled design of experimental and observational studies to meet desired precision. We propose the first general framework for sample size calculation applicable to finite extremal settings where causal probability bounds can be expressed as linear combinations of experimental and observational probabilities. Our approach integrates the Delta method, extreme value theory, and confounding data fusion techniques from causal inference to derive theoretical sample size requirements. Simulation studies demonstrate that the proposed method effectively controls estimation error and reliably achieves target precision, thereby filling a key void in statistical power analysis and sample design for causal probability bound estimation.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• probabilities of causation
• sample size analysis
• margin of error
• causal inference
• observational data

Innovation

• probabilities of causation
• sample size analysis
• delta method
• bounds estimation
• causal inference