A Multiple Imputation Approach for the Cumulative Incidence, with Implications for Variance Estimation

We present an alternative approach to estimating the cumulative incidence function that uses non-parametric multiple imputation to reduce the problem to that of estimating a binomial proportion. In the standard competing risks setting, we show mathematically and empirically that our imputation-based estimator is equivalent to the Aalen-Johansen estimator of the cumulative incidence given a sufficient number of imputations. However, our approach allows for the use of a wider variety of methods for the analysis of binary outcomes, including preferred options for uncertainty estimation. While we focus on the cumulative incidence function, the multiple imputation approach likely extends to more complex problems in competing risks.