Statistical Methods for Analyzing Right‐Censored Length‐Biased Data under Cox Model
- 1 June 2010
- journal article
- Published by Oxford University Press (OUP) in Biometrics
- Vol. 66 (2), 382-392
- https://doi.org/10.1111/j.1541-0420.2009.01287.x
Abstract
Summary Length‐biased time‐to‐event data are commonly encountered in applications ranging from epidemiological cohort studies or cancer prevention trials to studies of labor economy. A longstanding statistical problem is how to assess the association of risk factors with survival in the target population given the observed length‐biased data. In this article, we demonstrate how to estimate these effects under the semiparametric Cox proportional hazards model. The structure of the Cox model is changed under length‐biased sampling in general. Although the existing partial likelihood approach for left‐truncated data can be used to estimate covariate effects, it may not be efficient for analyzing length‐biased data. We propose two estimating equation approaches for estimating the covariate coefficients under the Cox model. We use the modern stochastic process and martingale theory to develop the asymptotic properties of the estimators. We evaluate the empirical performance and efficiency of the two methods through extensive simulation studies. We use data from a dementia study to illustrate the proposed methodology, and demonstrate the computational algorithms for point estimates, which can be directly linked to the existing functions in S‐PLUS or R.Keywords
This publication has 24 references indexed in Scilit:
- Analyzing Length-Biased Data With Semiparametric Transformation and Accelerated Failure Time ModelsJournal of the American Statistical Association, 2009
- Covariate Bias Induced by Length-Biased Sampling of Failure TimesJournal of the American Statistical Association, 2008
- Checking stationarity of the incidence rate using prevalent cohort survival dataStatistics in Medicine, 2005
- A Reevaluation of the Duration of Survival after the Onset of DementiaNew England Journal of Medicine, 2001
- Hazards regression analysis for length-biased dataBiometrika, 1996
- A Semiparametric Model for Randomly Truncated DataJournal of the American Statistical Association, 1989
- Large Sample Theory of Empirical Distributions in Biased Sampling ModelsThe Annals of Statistics, 1988
- Empirical Distributions in Selection Bias ModelsThe Annals of Statistics, 1985
- Nonparametric Estimation in the Presence of Length BiasThe Annals of Statistics, 1982