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

Abstract

In failure‐time settings, a competing event is any event that makes it impossible for the event of interest to occur. For example, cardiovascular disease death is a competing event for prostate cancer death because an individual cannot die of prostate cancer once he has died of cardiovascular disease. Various statistical estimands have been defined as possible targets of inference in the classical competing risks literature. Many reviews have described these statistical estimands and their estimating procedures with recommendations about their use. However, this previous work has not used a formal framework for characterizing causal effects and their identifying conditions, which makes it difficult to interpret effect estimates and assess recommendations regarding analytic choices. Here we use a counterfactual framework to explicitly define each of these classical estimands. We clarify that, depending on whether competing events are defined as censoring events, contrasts of risks can define a total effect of the treatment on the event of interest or a direct effect of the treatment on the event of interest not mediated by the competing event. In contrast, regardless of whether competing events are defined as censoring events, counterfactual hazard contrasts cannot generally be interpreted as causal effects. We illustrate how identifying assumptions for all of these counterfactual estimands can be represented in causal diagrams, in which competing events are depicted as time‐varying covariates. We present an application of these ideas to data from a randomized trial designed to estimate the effect of estrogen therapy on prostate cancer mortality.

Mortality prediction models, causal effects, and end-of-life decision making in the intensive care unit

“…Because the quality of life at 6 months is not defined among individuals who die before the end of 6 months of follow-up, defining a meaningful causal effect of interest requires careful handling of competing events. 10 …”

On Null Hypotheses in Survival Analysis

“…Analogous to the log‐rank test, the Gray test has low power if the subdistribution hazard curves are crossing (Latouche and Porcher, ). However, we are often interested in evaluating the cumulative incidence at a time , without making assumptions about the subdistribution hazards, which are even harder to interpret causally than standard hazard functions (Young et al ., ). By expressing the cumulative incidence on the form (see Supporting Information 1.3 for details), we use our transformation procedure to obtain a test statistic for the cumulative incidence at .…”

“…In more advanced settings, for example, scenarios with competing risks, hypotheses like are less transparent, leading to issues with interpretation. For example, in competing risk settings where competing events are treated as censoring events, the null hypothesis in is based on cause‐specific hazards, which are often not the target of inference (Young et al ., ).…”

Effects of intergenerational exposure interventions on adolescent outcomes: An application of inverse probability weighting to longitudinal pre‐birth cohort data

“…We considered other approaches to handling pregnancy loss as sensitivity analysis (Supplemental Materials 2). 42 We also censored participants in interval k if the questionnaire for that interval was returned after the corresponding age (eg if the 3-year-old questionnaire was returned after the child turned 4). We rely on an assumed temporal order (C k , L k , A k ) in each k.…”