Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative incidence. Covariates affect cause-specific hazards in our model, and we assume that separate proportional hazards models hold for each cause-specific hazard. Simulation studies show that procedures based on asymptotic theory have near nominal operating characteristics in cohorts of 200 and 400 subjects, both for cumulative incidence and for prediction error. The methods are illustrated with data on survival after breast cancer, obtained from the National Surgical Adjuvant Breast and Bowel Project (NSABP).