A Class of Functional Methods for Error-Contaminated Survival Data Under Additive Hazards Models with Replicate Measurements

ABSTRACT Covariate measurement error has attracted extensive interest in survival analysis. Since Prentice, a large number of inference methods have been developed to handle error-prone data that are modulated with proportional hazards models. In contrast to proportional hazards models, additive hazards models offer a flexible tool to delineate survival processes. However, there is little research on measurement error effects under additive hazards models. In this article, we systematically investigate this important problem. New insights into measurement error effects are revealed, as opposed to well-documented results for proportional hazards models. In particular, we explore asymptotic bias of ignoring measurement error in the analysis. To correct for the induced bias, we develop a class of functional correction methods for measurement error effects. The validity of the proposed methods is carefully examined, and we investigate issues of model checking and model misspecification. Theoretical results are established, and are complemented with numerical assessments. Supplementary materials for this article are available online.

[1]  D. Spiegelman,et al.  Corrected score estimation in the proportional hazards model with misclassified discrete covariates , 2008, Statistics in medicine.

[2]  Xiao Song,et al.  On Corrected Score Approach for Proportional Hazards Model with Covariate Measurement Error , 2004, Biometrics.

[3]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[4]  J. Buzas.  Unbiased scores in proportional hazards regression with covariate measurement error , 1998 .

[5]  Yijian Huang,et al.  Cox Regression with Accurate Covariates Unascertainable: A Nonparametric-Correction Approach , 2000 .

[6]  D. Lin,et al.  Semiparametric Failure Time Regression With Replicates of Mismeasured Covariates , 2004 .

[7]  Zhiliang Ying,et al.  Semiparametric Analysis of General Additive-Multiplicative Hazard Models for Counting Processes , 1995 .

[8]  Zhiliang Ying,et al.  Additive Hazards Regression Models for Survival Data , 1997 .

[9]  Some properties of misspecified additive hazards models , 2006 .

[10]  Jon A. Wellner,et al.  Confidence bands for a survival curve from censored data , 1980 .

[11]  J. Lawless,et al.  A corrected likelihood method for the proportional hazards model with covariates subject to measurement error , 2007 .

[12]  Grace Y. Yi,et al.  A NOTE ON MIS-SPECIFIED ESTIMATING FUNCTIONS , 2010 .

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

[14]  Jianguo Sun,et al.  Additive hazards regression of failure time data with covariate measurement errors , 2006 .

[15]  Goodness-of-Fit Tests for the Additive Risk Model with (p > 2)-Dimensional Time-Invariant Covariates , 1998, Lifetime data analysis.

[16]  R. Kay.  The Analysis of Survival Data , 2012 .

[17]  G. Larry Bretthorst,et al.  Estimating the Parameters , 1988 .

[18]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[19]  N. Breslow,et al.  Statistical methods in cancer research: volume 1- The analysis of case-control studies , 1980 .

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

[21]  R. Prentice.  Covariate measurement errors and parameter estimation in a failure time regression model , 1982 .

[22]  O. Aalen,et al.  Survival and Event History Analysis: A Process Point of View , 2008 .

[23]  Lin,et al.  Functional Inference in Frailty Measurement Error Models for Clustered Survival Data Using the SIMEX Approach , 2006 .

[24]  Michal Kulich,et al.  Additive Hazards Regression with Covariate Measurement Error , 2000 .

[25]  D.,et al.  Regression Models and Life-Tables , 2022 .

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

[27]  Z. Ying,et al.  Checking the Cox model with cumulative sums of martingale-based residuals , 1993 .

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

[29]  T. Nakamura,et al.  Proportional hazards model with covariates subject to measurement error. , 1992, Biometrics.

[30]  S. Hammer,et al.  A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter. AIDS Clinical Trials Group Study 175 Study Team. , 1996, The New England journal of medicine.

[31]  M. Davidian,et al.  Estimating the parameters in the Cox model when covariate variables are measured with error. , 1998, Biometrics.