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.

中文翻译：

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基于因果关系的非参数估算方法，适用于肯尼亚的水卫生

对于因果关系“ PC”的可能性的当前估计方法做出了强有力的参数假设或效率低下。我们为PC的投影推导了一个基于非参数影响函数的估计量，该估计量可以通过进行弱结构假设来进行简单的解释和有效的推断。我们将估算器应用于肯尼亚实验的真实数据。该实验通过估计平均治疗效果，发现保护水泉可以减少儿童疾病。但是，在扩大此干预措施之前，重要的是确定是否是暴露因素而不是其他因素导致了结果。确实，我们发现一些儿童在饮用水中暴露于高浓度细菌并有腹泻病，由于该研究中普通儿童的PC估计值为0.12，而95％的置信区间为（0.11，0.13），因此可能没有暴露就患有该疾病。我们的非参数方法为研究人员提供了一种估算PC的方法，这对于我们不仅要确定平均治疗效果，而且还要确定暴露是否可能导致观察到的结果至关重要。