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Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks.

Abstract

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 (1999) has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modeling of the censoring distribution and is not statistically efficient. In this paper, 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 nonparametric maximum likelihood estimators (NPMLEs) and develop simple and fast numerical algorithms using the profile likelihood. We establish the consistency, asymptotic normality, and semiparametric efficiency of the NPMLEs. 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 ones through extensive simulation studies and an application to a major study on bone marrow transplantation.

Authors+Show Affiliations

Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7420, USA.Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599-7420, USA.

Pub Type(s)

Journal Article

Language

eng

PubMed ID

28239261

Citation

Mao, Lu, and D Y. Lin. "Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks." Journal of the Royal Statistical Society. Series B, Statistical Methodology, vol. 79, no. 2, 2017, pp. 573-587.
Mao L, Lin DY. Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks. J R Stat Soc Series B Stat Methodol. 2017;79(2):573-587.
Mao, L., & Lin, D. Y. (2017). Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 79(2), pp. 573-587. doi:10.1111/rssb.12177.
Mao L, Lin DY. Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks. J R Stat Soc Series B Stat Methodol. 2017;79(2):573-587. PubMed PMID: 28239261.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Efficient Estimation of Semiparametric Transformation Models for the Cumulative Incidence of Competing Risks. AU - Mao,Lu, AU - Lin,D Y, Y1 - 2016/04/14/ PY - 2017/2/28/entrez PY - 2017/2/28/pubmed PY - 2017/2/28/medline KW - Censoring KW - Nonparametric maximum likelihood estimation KW - Profile likelihood KW - Proportional hazards KW - Semiparametric efficiency KW - Survival analysis SP - 573 EP - 587 JF - Journal of the Royal Statistical Society. Series B, Statistical methodology JO - J R Stat Soc Series B Stat Methodol VL - 79 IS - 2 N2 - 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 (1999) has become the method of choice for formulating the effects of covariates on the cumulative incidence. Its estimation, however, requires modeling of the censoring distribution and is not statistically efficient. In this paper, 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 nonparametric maximum likelihood estimators (NPMLEs) and develop simple and fast numerical algorithms using the profile likelihood. We establish the consistency, asymptotic normality, and semiparametric efficiency of the NPMLEs. 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 ones through extensive simulation studies and an application to a major study on bone marrow transplantation. SN - 1369-7412 UR - https://www.unboundmedicine.com/medline/citation/28239261/Efficient_Estimation_of_Semiparametric_Transformation_Models_for_the_Cumulative_Incidence_of_Competing_Risks_ L2 - https://www.ncbi.nlm.nih.gov/pmc/articles/pmid/28239261/ DB - PRIME DP - Unbound Medicine ER -