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

arXiv: https://arxiv.org/abs/2602.17070 · HTML: https://mlsanity.com/paper/2602.17070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Causes of Effects: Learning individual responses from population data](https://mlsanity.com/paper/2104.13730/) (2021)
- [Personalized Decision Making -- A Conceptual Introduction](https://mlsanity.com/paper/2208.09558/) (2022)
- [Probabilities of Causation with Nonbinary Treatment and Effect](https://mlsanity.com/paper/2208.09568/) (2022)
- [Unit Selection with Causal Diagram](https://mlsanity.com/paper/2109.07556/) (2021)
- [Probabilities of Causation: Adequate Size of Experimental and Observational Samples](https://mlsanity.com/paper/2210.05027/) (2022)

## Abstract (arXiv)

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.