zbMATH — the first resource for mathematics

Bounding the probability of causation in mediation analysis. (English) Zbl 1357.62036
Di Battista, Tonio (ed.) et al., Topics on methodological and applied statistical inference. Selected papers based on the presentations at the 47th scientific meeting of the Italian Statistical Society, SIS, Cagliari, Italy, June 2014. Cham: Springer (ISBN 978-3-319-44092-7/hbk; 978-3-319-44093-4/ebook). Studies in Theoretical and Applied Statistics. Selected Papers of the Statistical Societies, 75-84 (2016).
Summary: Given empirical evidence for the dependence of an outcome variable on an exposure variable, we can typically only provide bounds for the “probability of causation” in the case of an individual who has developed the outcome after being exposed. We show how these bounds can be adapted or improved if further information becomes available. In addition to reviewing existing work on this topic, we provide a new analysis for the case where a mediating variable can be observed. In particular, we show how the probability of causation can be bounded when there is no direct effect and no confounding.
For the entire collection see [Zbl 1357.62012].

62C12 Empirical decision procedures; empirical Bayes procedures
62D05 Sampling theory, sample surveys
62F03 Parametric hypothesis testing
Full Text: DOI
[1] Dawid, A.P.: The role of scientific and statistical evidence in assessing causality. In: Goldberg, R. (ed.) Perspectives on Causation, pp. 133–147. Hart Publishing, Oxford (2011)
[2] Dawid, A.P.: Statistical causality from a decision-theoretic perspective. Ann. Rev. Stat. Appl. 2, 273–303 (2015) · doi:10.1146/annurev-statistics-010814-020105
[3] Dawid, A.P., Fienberg, S., Faigman, D.: Fitting science into legal contexts: assessing effects of causes or causes of effects? Sociol. Methods Res. 43, 359–390 (2014) · doi:10.1177/0049124113515188
[4] Dawid, A.P., Musio, M., Fienberg, S.E.: From statistical evidence to evidence of causality. Bayesian Analysis. Advance Publication, 26 August 2015. http://projecteuclid.org/euclid.ba/1440594950 (2014) · Zbl 1357.62020
[5] Pearl, J.: Probabilities of causation: three counterfactual interpretations and identification. Synthese 121, 93–149 (1999) · Zbl 0951.03023 · doi:10.1023/A:1005233831499
[6] Silber, J.H., Rosenbaum, P.R., Polsky, D., Ross, R.N., Even-Shoshan, O., Schwartz, J.S., Armstrong, K.A., Randall, T.C.: Does ovarian cancer treatment and survival differ by the specialty providing chemotherapy? J. Clin. Oncol. 10, 1169–1175 (2007) · doi:10.1200/JCO.2006.08.2933
[7] Tian, J., Pearl, J.: Probabilities of causation: bounds and identification. Ann. Math. Artif. Intell. 28, 287–313 (2000) · Zbl 1048.03502 · doi:10.1023/A:1018912507879
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.