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In failure-time settings, a competing risk event is any event that makes itimpossible for the event of interest to occur. For example, cardiovasculardisease death is a competing event for prostate cancer death because anindividual cannot die of prostate cancer once he has died of cardiovasculardisease. Various statistical estimands have been defined as possible targets ofinference in the classical competing risks literature. Many reviews havedescribed these statistical estimands and their estimating procedures withrecommendations about their use. However, this previous work has not used aformal framework for characterizing causal effects and their identifyingconditions, which makes it difficult to interpret effect estimates and assessrecommendations regarding analytic choices. Here we use a counterfactualframework to explicitly define each of these classical estimands. We clarifythat, depending on whether competing events are defined as censoring events,contrasts of risks can define a total effect of the treatment on the event ofinterest, or a direct effect of the treatment on the event of interest notmediated through the competing event. In contrast, regardless of whethercompeting events are defined as censoring events, counterfactual hazardcontrasts cannot generally be interpreted as causal effects. We illustrate howidentifying assumptions for all of these counterfactual estimands can berepresented in causal diagrams in which competing events are depicted astime-varying covariates. We present an application of these ideas to data froma randomized trial designed to estimate the effect of estrogen therapy onprostate cancer mortality.

A causal framework for classical statistical estimands in failure time settings with competing events