Analysis of left-truncated right-censored or doubly censored data with linear transformation models

We analyze left-truncated right-censored (LTRC) data or doubly censored data using semiparametric transformation models. It is demonstrated that the extended estimating equations of both Cheng et al. (Biometrika 82:835–845, 1995) and Chen et al. (Biometrika 89:659–668, 2002) can be used to analyze LTRC data or doubly censored data when left-censored variables are always observed. The asymptotic properties of the proposed estimators are derived. A simulation study is conducted to investigate the performance of the proposed estimators.

[1]  Melinda Wang Product limit estimates: a generalized maximum likelihood study , 1987 .

[2]  Zhiliang Ying,et al.  Estimating a distribution function with truncated and censored data , 1991 .

[3]  B. Turnbull Nonparametric Estimation of a Survivorship Function with Doubly Censored Data , 1974 .

[4]  W. Pan,et al.  Estimation in the Cox Proportional Hazards Model with Left‐Truncated and Interval‐Censored Data , 2002, Biometrics.

[5]  Nicholas P. Jewell,et al.  A note on the product-limit estimator under right censoring and left truncation , 1987 .

[6]  P. Leiderman,et al.  African Infant Precocity and Some Social Influences during the First Year , 1973, Nature.

[7]  Pao-Sheng Shen,et al.  The Product-Limit Estimate as an Inverse-Probability-Weighted Average , 2003 .

[8]  Susan A. Murphy,et al.  Maximum Likelihood Estimation in the Proportional Odds Model , 1997 .

[9]  Myron N. Chang Weak Convergence of a Self-Consistent Estimator of the Survival Function with Doubly Censored Data , 1990 .

[10]  On self-consistent estimators and kernel density estimators with doubly censored data , 1997 .

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

[12]  Grace L. Yang,et al.  Strong Consistency of a Nonparametric Estimator of the Survival Function with Doubly Censored Data , 1987 .

[13]  Zhiliang Ying,et al.  Semiparametric analysis of transformation models with censored data , 2002 .

[14]  P. Shen Semiparametric analysis of transformation models with doubly censored data , 2011 .

[15]  P. Mykland,et al.  Algorithms for computing self-consistent and maximum likelihood estimators with doubly censored data , 1996 .

[16]  Z. Ying,et al.  Analysis of transformation models with censored data , 1995 .

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

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

[19]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .

[20]  T. Cai,et al.  Semiparametric regression analysis for doubly censored data , 2004 .

[21]  Song Yang,et al.  Semiparametric Inference in the Proportional Odds Regression Model , 1999 .

[22]  Lin Li,et al.  Asymptotic Properties of Self-Consistent Estimators with Doubly-Censored Data , 2001 .

[23]  M. Mandel Censoring and Truncation—Highlighting the Differences , 2007 .

[24]  D. Pollard Empirical Processes: Theory and Applications , 1990 .

[25]  P. Shen An inverse-probability-weighted approach to the estimation of distribution function with doubly censored data , 2009 .

[26]  J. Crowley,et al.  Correction: A Large Sample Study of Generalized Maximum Likelihood Estimators from Incomplete Data via Self-Consistency , 1985 .

[27]  Mei-Cheng Wang,et al.  Nonparametric Estimation from Cross-Sectional Survival Data , 1991 .

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

[29]  A Generalized Time-Dependent Conditional Linear Model with Left-Truncated and Right-Censored Data , 2012 .

[30]  W. Manteiga,et al.  Strong representation of a generalized product-limit estimator for truncated and censored data with some applications , 1999 .