Efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks
The cumulative incidence is the probability of failure from the cause of interest over a certain time period in the presence of other risks. A semiparametric regression model proposed by Fine and Gray has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modelling of the censoring distribution and is not statistically efficient. We present a broad class of semiparametric transformation models which extends the Fine and Gray model, and we allow for unknown causes of failure. We derive the non‐parametric maximum likelihood estimators and develop simple and fast numerical algorithms using the profile likelihood. We establish the consistency, asymptotic normality and semiparametric efficiency of the non‐parametric maximum likelihood estimators. In addition, we construct graphical and numerical procedures to evaluate and select models. Finally, we demonstrate the advantages of the proposed methods over the existing methods through extensive simulation studies and an application to a major study on bone marrow transplantation.
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