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Robust prediction of the cumulative incidence function under non‐proportional subdistribution hazards

Prediction of a cause‐specific cumulative incidence function (CIF) for data containing competing risks is of primary interest to clinicians when making treatment decisions for patients given their prognostic characteristics. The Fine–Gray regression model is widely used to incorporate multiple prognostic factors, yet it is not applicable when the assumption of proportional subdistribution hazards (PSH) does not hold. In this study we investigate the properties of the partial‐likelihood estimator from the Fine–Gray model under non‐proportionality and propose a robust risk prediction procedure that is not sensitive to the assumption and is more favourable in practice because it bypasses the complicated modelling of time‐varying covariate effects. We evaluate the prediction performance of our procedure in simulations and demonstrate an application in predicting the absolute risk of locoregional recurrence for breast cancer patients, given a set of prognostic factors in which not all of them satisfy the PSH assumption. The Canadian Journal of Statistics 44: 127–141; 2016 © 2016 Statistical Society of Canada