A non-parametric projection-based estimator for the probability of causation, with application to water sanitation in Kenya

Current estimation methods for the probability of causation 'PC' make strong parametric assumptions or are inefficient. We derive a non-parametric 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. This experiment 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 diarrhoeal disease, would probably 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 non-parametric method offers researchers a way to estimate PC, which is essential if we wish to determine not only the average treatment effect, but also whether an exposure probably caused the observed outcome.