Estimating effects on cumulative incidence probabilities by direct polytomous regression and polytomous log-odds product.

In competing-risks analysis, modeling each cause separately may yield specification of cumulative incidence functions that are not jointly coherent, because the resulting cause-specific probabilities need not satisfy the natural sum-to-one constraint. We address this problem by introducing a direct polytomous regression approach that models all causes jointly and enforces coherence through a reparameterization based on polytomous log-odds products. Our approach is applicable to semiparametric models with common multiplicative effects over time as well as models focused on a specific time point. For estimation under right-censoring, we develop stratified inverse probability of censoring weighted (IPCW) estimators for the effect parameters. Within a specified class of augmented IPCW estimators, the proposed estimators attain the minimum asymptotic variance under the stated regularity conditions, without the computational burden of deriving augmentation terms for each cause. The utility of our coherent modeling is demonstrated through simulation studies and its applications to a cohort study of type 2 diabetes and a randomized trial of prostate cancer.