Survival Curve Estimation with Dependent Left Truncated Data Using Cox's Model

Abstract The Kaplan-Meier and closely related Lynden-Bell estimators are used to provide nonparametric estimation of the distribution of a left-truncated random variable. These estimators assume that the left-truncation variable is independent of the time-to-event. This paper proposes a semiparametric method for estimating the marginal distribution of the time-to-event that does not require independence. It models the conditional distribution of the time-to-event given the truncation variable using Cox's model for left truncated data, and uses inverse probability weighting. We report the results of simulations and illustrate the method using a survival study.

[1]  Wei-Yann Tsai,et al.  Testing the assumption of independence of truncation time and failure time , 1990 .

[2]  Niels Keiding,et al.  Random truncation models and Markov processes , 1990 .

[3]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[4]  M. Gail,et al.  Comments on ‘Choice of time scale and its effect on significance of predictors in longitudinal studies’ by Michael J. Pencina, Martin G. Larson and Ralph B. D'Agostino, Statistics in Medicine 2007; 26:1343–1359 , 2009, Statistics in medicine.

[5]  Jia-gang Wang,et al.  A Note on the Uniform Consistency of the Kaplan-Meier Estimator , 1987 .

[6]  Mei-Cheng Wang,et al.  Hazards regression analysis for length-biased data , 1996 .

[7]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[8]  D. Lynden-Bell,et al.  A Method of Allowing for Known Observational Selection in Small Samples Applied to 3CR Quasars , 1971 .

[9]  David B Wolfson,et al.  Length-Biased Sampling With Right Censoring , 2002 .

[10]  Bradley Efron,et al.  Survival analysis of the gamma-ray burst data , 1994 .

[11]  J. Crowley,et al.  Nonparametric tests of the Markov model for survival data , 1992 .

[12]  Niels Keiding,et al.  Independent Delayed Entry , 1992 .

[13]  Somnath Datta,et al.  The Kaplan–Meier Estimator as an Inverse-Probability-of-Censoring Weighted Average , 2001, The American statistician.

[14]  V. Vieland,et al.  NONPARAMETRIC ESTIMATION OF MARGINAL DISTRIBUTIONS UNDER BIVARIATE TRUNCATION WITH APPLICATION TO TESTING FOR AGE-OF-ONSET ANTICIPATION , 2001 .

[15]  J. Robins,et al.  Recovery of Information and Adjustment for Dependent Censoring Using Surrogate Markers , 1992 .

[16]  W. Pan,et al.  A Note on Inconsistency of NPMLE of the Distribution Function from Left Truncated and Case I Interval Censored Data , 1999, Lifetime data analysis.

[17]  W. Weeks,et al.  Impact of rural residence on survival of male veterans affairs patients after age 65. , 2010, The Journal of rural health : official journal of the American Rural Health Association and the National Rural Health Care Association.

[18]  何书元 ESTIMATING A DISTRIBUTION FUNCTION WITH TRUNCATED DATA , 1994 .

[19]  Wei-Yann Tsai,et al.  The Product-Moment Correlation Coefficient and Linear Regression for Truncated Data , 1996 .

[20]  L. Lakhal-Chaieb,et al.  Archimedean copula model selection under dependent truncation , 2008, Statistics in medicine.

[21]  Mei-Cheng Wang,et al.  A Semiparametric Model for Randomly Truncated Data , 1989 .

[22]  Belkacem Abdous,et al.  Estimating survival under a dependent truncation , 2006 .

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

[24]  Bradley Efron,et al.  A simple test of independence for truncated data with applications to redshift surveys , 1992 .

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

[26]  M. Woodroofe Estimating a Distribution Function with Truncated Data , 1985 .

[27]  D. Horvitz,et al.  A Generalization of Sampling Without Replacement from a Finite Universe , 1952 .

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

[29]  Rebecca A. Betensky,et al.  Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau , 2005 .

[30]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .