Probabilities of causation and post-infection outcomes

Probabilities of causation provide explanatory information on the observed occurrence (causal necessity) and non-occurrence (causal sufficiency) of events. Here, we adapt these probabilities (probability of necessity, probability of sufficiency, and probability of necessity and sufficiency) to an important class of epidemiologic outcomes, post-infection outcomes. A defining feature of studies on these outcomes is that they account for the post-treatment variable, infection acquisition, which means that, for individuals who remain uninfected, the outcome is not defined. Following previous work by Hudgens and Halloran, we describe analyses of post-infection outcomes using the principal stratification framework, and then derive expressions for the probabilities of causation in terms of principal strata-related parameters. Finally, we show that these expressions provide insights into the contributions of different processes (absence or occurrence of infection, and disease severity), implicitly encoded in the definition of the outcome, to causation.