Interval Estimation of the Absolute Risk of an Event with Competing Risks Using Proportional Regression of Cause-Specific Hazards

Abstract

It is often important to account for the effects of a competing risk when estimating the risk of a particular event of interest by estimating its absolute risk. Available methodology for interval estimation of the absolute risk using the proportional regression of cause-specific hazards (CSH) has been limited to situations with time-invariant covariates and a single random censoring mechanism, without accommodation of cohort sampling study designs. Here we derive asymptotic pointwise confidence intervals in closed form for the absolute risk of an event at a specified time (the value of the cumulative incidence function) in the presence of competing risks using proportional CSH regression, accommodating external time-dependent covariates, cohort sampling study designs and multiple censoring mechanisms. Different covariates may be used for the event of interest and the various competing risks. Consistent with the definition of absolute risk, the CSH method produces absolute risk estimates that are less than or approximately equal to corresponding “conditional” risk estimates that do not account for competing risks. An example shows that this property is not necessarily shared by methods based on subdistribution hazard regression. Simulation studies indicate that the CSH method confidence intervals computed on the log cumulative hazard or the risk scale have coverage probabilities that approximate the nominal level for small and moderate samples, provided that the number of events per covariate is at least 10 and, when using cohort sampling, the ratio of patients without events to patients with events is at least 2:1.