Methods for Bivariate Survival Data with Mismeasured Covariates Under an Accelerated Failure Time Model

Accelerated failure time models are useful in survival data analysis, but such models have received little attention in the context of measurement error. In this paper we discuss an accelerated failure time model for bivariate survival data with covariates subject to measurement error. In particular, methods based on the marginal and joint models are considered. Consistency and efficiency of the resultant estimators are investigated. Simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring the measurement error of covariates. As an illustration we apply the proposed methods to analyze a data set arising from the Busselton Health Study (Knuiman et al., 1994).

[1]  Kathleen G. Purdy,et al.  Likelihood analysis for errors-in-variables regression with replicate measurements , 1996 .

[2]  Charles J. Kowalski,et al.  Non-Normal Bivariate Distributions with Normal Marginals , 1973 .

[3]  J. R. Cook,et al.  Simulation-Extrapolation Estimation in Parametric Measurement Error Models , 1994 .

[4]  Anastasios A. Tsiatis,et al.  A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error , 2001 .

[5]  Jerald F. Lawless,et al.  Bivariate location–scale models for regression analysis, with applications to lifetime data , 2005 .

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

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

[8]  R. Prentice,et al.  Regression calibration in failure time regression. , 1997, Biometrics.

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

[10]  N. L. Johnson,et al.  Multivariate Analysis , 1958, Nature.

[11]  Haoxuan Zhou,et al.  Failure time regression with continuous covariates measured with error , 2000 .

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

[13]  Charles J. Kowalski,et al.  The Performance of Some Rough Tests for Bivariate Normality Before and After Coordinate Transformations to Normality , 1970 .

[14]  R. Prentice,et al.  A risk set calibration method for failure time regression by using a covariate reliability sample , 2001 .

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

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

[17]  R J Carroll,et al.  Transformations to additivity in measurement error models. , 1997, Biometrics.

[18]  Yi Li,et al.  Covariate measurement errors in frailty models for clustered survival data , 2000 .

[19]  J. Klein,et al.  Modeling Random Effects for Censored Data by a Multivariate Normal Regression Model , 1999, Biometrics.

[20]  D. Oakes,et al.  Regression in a bivariate copula model , 2000 .

[21]  David Ruppert,et al.  Transformations to symmetry and homoscedasticity , 1989 .

[22]  James R. Kenyon,et al.  Analysis of Multivariate Survival Data , 2002, Technometrics.

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

[24]  Daniel O. Stram,et al.  The Errors-in-Variables Problem: Considerations Provided by Radiation Dose-Response Analyses of the A-Bomb Survivor Data , 1992 .

[25]  D. Ruppert,et al.  Measurement Error in Nonlinear Models , 1995 .

[26]  M W Knuiman,et al.  Mortality trends, 1965 to 1989, in Busselton, the site of repeated health surveys and interventions. , 2010, Australian journal of public health.

[27]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[28]  J Cai.  Hypothesis Testing of Hazard Ratio Parameters in Marginal Models for Multivariate Failure Time Data , 1999, Lifetime data analysis.

[29]  S B Hulley,et al.  Overall and coronary heart disease mortality rates in relation to major risk factors in 325,348 men screened for the MRFIT. Multiple Risk Factor Intervention Trial. , 1986, American heart journal.