Estimation in the Cox proportional hazards model with doubly censored and truncated data

In longitudinal studies, the proportional hazard model is often used to analyse covariate effects on the duration time, defined as the elapsed time between the first and second event. In this article, we consider the situation when the first event suffers partly interval-censoring and the second event suffers left-truncation and right-censoring. We proposed a two-step estimation procedure for estimating the regression coefficients of the proportional model. A simulation study is conducted to investigate the performance of the proposed estimator.

[1]  A Alioum,et al.  A proportional hazards model for arbitrarily censored and truncated data. , 1996, Biometrics.

[2]  Xingqiu Zhao,et al.  Estimating equation approach for regression analysis of failure time data in the presence of interval-censoring , 2005 .

[3]  C. Geyer,et al.  Maximum likelihood for interval censored data: Consistency and computation , 1994 .

[4]  M. L. Calle,et al.  Non-parametric estimation with doubly censored data , 1999 .

[5]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[6]  Anton Schick,et al.  Asymptotic properties of the GMLE with case 2 interval-censored data , 1998 .

[7]  Anton Schick,et al.  Consistency of the GMLE with Mixed Case Interval‐Censored Data , 2000 .

[8]  H. Frydman.  A note on nonparametric estimation of the distribution function from interval-censored and truncated observations , 1994 .

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

[10]  M. Hudgens.  On nonparametric maximum likelihood estimation with interval censoring and left truncation , 2005 .

[11]  I. Langner.  Survival Analysis: Techniques for Censored and Truncated Data , 2006 .

[12]  Jianguo Sun.  Self-Consistency Estimation of Distributions Based on Truncated and Doubly Censored Survival Data with Applications to AIDS Cohort Studies , 1997, Lifetime data analysis.

[13]  S W Lagakos,et al.  Analysis of doubly-censored survival data, with application to AIDS. , 1989, Biometrics.

[14]  S. Lagakos,et al.  Estimation of the infection time and latency distribution of AIDS with doubly censored data. , 1994, Biometrics.

[15]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[16]  S. Lagakos,et al.  Analysis of doubly-censored survival data , 1989 .

[17]  Laurence L. George,et al.  The Statistical Analysis of Failure Time Data , 2003, Technometrics.

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

[19]  G. Y. Wong,et al.  ASYMPTOTIC VARIANCE OF THE GMLE OF A SURVIVAL FUNCTION WITH INTERVAL-CENSORED DATA , 1998 .

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

[21]  Hudgens,et al.  Hudgens , MG NPMLE with interval censoring and truncation On Nonparametric Maximum Likelihood Estimation with Interval Censoring and Truncation , 2004 .