Nonparametric maximum likelihood analysis of clustered current status data with the gamma-frailty Cox model

The Cox model with frailties has been popular for regression analysis of clustered event time data under right censoring. However, due to the lack of reliable computation algorithms, the frailty Cox model has been rarely applied to clustered current status data, where the clustered event times are subject to a special type of interval censoring such that we only observe for each event time whether it exceeds an examination (censoring) time or not. Motivated by the cataract dataset from a cross-sectional study, where bivariate current status data were observed for the occurrence of cataracts in the right and left eyes of each study subject, we develop a very efficient and stable computation algorithm for nonparametric maximum likelihood estimation of gamma-frailty Cox models with clustered current status data. The algorithm proposed is based on a set of self-consistency equations and the contraction principle. A convenient profile-likelihood approach is proposed for variance estimation. Simulation and real data analysis exhibit the nice performance of our proposal.

[1]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[2]  Jian Huang,et al.  Efficient Estimation for the Cox Model with Interval Censoring Efficient Estimation for the Cox Model with Interval Censoring , 1994 .

[3]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[4]  Chi-Chung Wen,et al.  A PROFILE LIKELIHOOD THEORY FOR THE CORRELATED GAMMA-FRAILTY MODEL WITH CURRENT STATUS FAMILY DATA , 2007 .

[5]  L T Chylack,et al.  The Lens Opacities Case-Control Study. Risk factors for cataract. , 1991, Archives of ophthalmology.

[6]  Jianguo Sun,et al.  The Statistical Analysis of Interval-censored Failure Time Data , 2006 .

[7]  H. D. Brunk,et al.  AN EMPIRICAL DISTRIBUTION FUNCTION FOR SAMPLING WITH INCOMPLETE INFORMATION , 1955 .

[8]  Zhiliang Ying,et al.  Semiparametric analysis of the additive risk model , 1994 .

[9]  J P Klein,et al.  Semiparametric estimation of random effects using the Cox model based on the EM algorithm. , 1992, Biometrics.

[10]  G Molenberghs,et al.  The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data , 2009, Statistics in medicine.

[11]  S. Bennett,et al.  Analysis of survival data by the proportional odds model. , 1983, Statistics in medicine.

[12]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[13]  Jian Huang,et al.  Efficient estimation for the proportional hazards model with interval censoring , 1996 .

[14]  Jon A. Wellner,et al.  A Hybrid Algorithm for Computation of the Nonparametric Maximum Likelihood Estimator from Censored Data , 1997 .

[15]  C. P. Farrington,et al.  Estimation of the basic reproduction number for infectious diseases from age‐stratified serological survey data , 2001 .

[16]  J. Wellner,et al.  Information Bounds and Nonparametric Maximum Likelihood Estimation , 1992 .

[17]  Erik T. Parner,et al.  Asymptotic theory for the correlated gamma-frailty model , 1998 .

[18]  Philip Hougaard,et al.  Analysis of Multivariate Survival Data , 2001 .

[19]  D. Cox.  Regression Models and Life-Tables , 1972 .

[20]  Donglin Zeng,et al.  Maximum likelihood estimation in semiparametric regression models with censored data , 2007, Statistica Sinica.

[21]  Jong-Sung Kim,et al.  New statistical software for the proportional hazards model with current status data , 2008, Comput. Stat. Data Anal..

[22]  Jianguo Sun,et al.  A Multiple Imputation Approach to the Analysis of Current Status Data with the Additive Hazards Model , 2009 .