Efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 79; no. 2; pp. 573 - 587
• Main Authors: Mao, Lu, Lin, D.Y.
• Format: Journal Article
• Language: English
• Published: England John Wiley & Sons Ltd 01.03.2017; Oxford University Press
• Subjects: Algorithms; Bone marrow; bone marrow transplant; Censoring; Consistency; equations; Estimating techniques; Failure; Incidence; Mathematical models; Maximum likelihood estimators; Maximum likelihood method; Non‐parametric maximum likelihood estimation; Probability; Profile likelihood; Proportional hazards; Regression; regression analysis; Risk; Semiparametric efficiency; Statistical methods; Statistics; Studies; Survival analysis; Transformations; Transplants & implants; Semiparametric efficiency; Profile likelihood; Survival analysis; Proportional hazards; Censoring; Nonparametric maximum likelihood estimation
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/rssb.12177

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.