A Nonparametric Projection-Based Estimator for the Probability of Causation, with Application to Water Sanitation in Kenya

24 Pages Posted: 23 Oct 2018

See all articles by Maria Cuellar

Maria Cuellar

University of Pennsylvania

Edward Kennedy

Carnegie Mellon University - Department of Statistics

Date Written: September 30, 2018

Abstract

Current estimation methods for the probability of causation (PC) make strong parametric assumptions or are inefficient. We derive a nonparametric influence-function-based estimator for a projection of PC, which allows for simple interpretation and valid inference by making weak structural assumptions. We apply our estimator to real data from an experiment in Kenya, which found, by estimating the average treatment effect, that protecting water springs reduces childhood disease. However, before scaling up this intervention, it is important to determine whether it was the exposure, and not something else, that caused the outcome. Indeed, we find that some children, who were exposed to a high concentration of bacteria in drinking water and had a diarrheal disease, would likely have contracted the disease absent the exposure since the estimated PC for an average child in this study is 0.12 with a 95% confidence interval of (0.11, 0.13). Our nonparametric method offers researchers a way to estimate PC, which is essential if one wishes to determine not only the average treatment effect, but also whether an exposure likely caused the observed outcome.

Keywords: causal inference, probability of causation, projection, influence functions, nonparametric, public health

Suggested Citation

Cuellar, Maria and Kennedy, Edward, A Nonparametric Projection-Based Estimator for the Probability of Causation, with Application to Water Sanitation in Kenya (September 30, 2018). Available at SSRN: https://ssrn.com/abstract=3257980 or http://dx.doi.org/10.2139/ssrn.3257980

Maria Cuellar (Contact Author)

University of Pennsylvania ( email )

483 McNeil Building
Philadelphia, PA 19104
United States

HOME PAGE: http://web.sas.upenn.edu/mcuellar/

Edward Kennedy

Carnegie Mellon University - Department of Statistics ( email )

Baker Hall
Pittsburgh, PA 15213
United States

HOME PAGE: http://https://www.ehkennedy.com/

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