TY - JOUR
T1 - Partially linear hazard regression for multivariate survival data
AU - Cai, Jianwen
AU - Fan, Jianqing
AU - Jiang, Jiancheng
AU - Zhou, Haibo
N1 - Funding Information:
Jianwen Cai is Professor, Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (E-mail: [email protected]). Jianqing Fan is Frederick L. Moore Professor of Finance, Department of Operation Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: [email protected]). Jiancheng Jiang is Assistant Professor, Department of Mathematics and Statistics, University of North Carolina at Charlotte, NC 28223 (E-mail: [email protected]) and Associate Research Scholar, Department of Operation Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: [email protected]). Haibo Zhou is Associate Professor, Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599 (E-mail: [email protected]). This research was supported in part by National Institutes of Health (NIH) grant R01 HL69720. Additional support was also provided by National Science Foundation grant DMS-03-54223 and NIH grant R01 GM072611 for Fan, National Science Foundation of China grant 10471006 for Jiang, and NIH grant R01 CA 79949 for Zhou. The authors gratefully acknowledge the constructive suggestions and comments from the associate editor and two anonymous referees that greatly improved this article.
PY - 2007/6
Y1 - 2007/6
N2 - This article studies estimation of partially linear hazard regression models for multivariate survival data. A profile pseudo-partial likelihood estimation method is proposed under the marginal hazard model framework. The estimation on the parameters for the linear part is accomplished by maximization of a pseudo-partial likelihood profiled over the nonparametric part. This enables us to obtain √o-consistent estimators of the parametric component. Asymptotic normality is obtained for the estimates of both the linear and nonlinear parts. The new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit. An algorithm of fast implementation of our proposed method is presented. Consistent standard error estimates using sandwich-type ideas are also developed, which facilitates inferences for the model. It is shown that the nonparametric component can be estimated as well as if the parametric components were known and the failure times within each subject were independent. Simulations are conducted to demonstrate the performance of the proposed method. A real dataset is analyzed to illustrate the proposed methodology.
AB - This article studies estimation of partially linear hazard regression models for multivariate survival data. A profile pseudo-partial likelihood estimation method is proposed under the marginal hazard model framework. The estimation on the parameters for the linear part is accomplished by maximization of a pseudo-partial likelihood profiled over the nonparametric part. This enables us to obtain √o-consistent estimators of the parametric component. Asymptotic normality is obtained for the estimates of both the linear and nonlinear parts. The new technical challenge is that the nonparametric component is indirectly estimated through its integrated derivative function from a local polynomial fit. An algorithm of fast implementation of our proposed method is presented. Consistent standard error estimates using sandwich-type ideas are also developed, which facilitates inferences for the model. It is shown that the nonparametric component can be estimated as well as if the parametric components were known and the failure times within each subject were independent. Simulations are conducted to demonstrate the performance of the proposed method. A real dataset is analyzed to illustrate the proposed methodology.
KW - Local pseudo-partial likelihood
KW - Marginal hazard model
KW - Multivariate failure time
KW - Partially linear
KW - Profile pseudo-partial likelihood
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U2 - 10.1198/016214506000001374
DO - 10.1198/016214506000001374
M3 - Article
AN - SCOPUS:34250698351
SN - 0162-1459
VL - 102
SP - 538
EP - 551
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 478
ER -