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TECHNICAL REPORT #23 Uncertainties in Probability of Causation Estimates. by Duncan Thomas Abstract Estimates of the probability that a case of a disease was caused by a particular exposure (known as the probability of causation, PC) are usually derived from the attributable risk. In compensation cases and litigations, these probabilities are used to decide whether a causal relationship has been established in the clamant's case. However, PC estimates are inherently uncertain and there is no clearly accepted basis for allowing for this uncertainty in reaching such judgements. Two components of uncertainty are considered: sampling variation in the epidemiologic risk estimates from which the PC is computed; and between-individual variation in unmeasured factors, including baseline risks, sensitivity to the exposure, and exposure measurement errors. It is suggested that the appropriate parameter that should be measured is the posterior expectation of the PC, averaging over all possible values of the unknown parameters that are consistent with the data. The influence of sampling variation is explored quantitatively for a variety of assumptions about the distribution of true relative risks. For individual variation, it is shown that although cases will generally not be representative of the population at risk in terms of unmeasured factors, the posterior expectation of the PC is generally identical to the usual estimator. Although individuals will indeed vary in their true PCs, lacking any data on the unmeasured factors, the average estimate is the most appropriate. Keywords: probability of causation; attributable risk; compensation; sampling variation; heterogenity; measurement error; biostatistics.
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