Likelihood‐based and marginal inference methods for recurrent event data with covariate measurement error

Recurrent event data arise commonly in medical and public health studies. The analysis of such data has received extensive research attention and various methods have been developed in the literature. Depending on the focus of scientific interest, the methods may be broadly classified as intensity-based counting process methods, mean function-based estimating equation methods, and the analysis of times to events or times between events. These methods and models cover a wide variety of practical applications. However, there is a critical assumption underlying those methods–variables need to be correctly measured. Unfortunately, this assumption is frequently violated in practice. It is quite common that some covariates are subject to measurement error. It is well known that covariate measurement error can substantially distort inference results if it is not properly taken into account. In the literature, there has been extensive research concerning measurement error problems in various settings. However, with recurrent events, there is little discussion on this topic. It is the objective of this paper to address this important issue. In this paper, we develop inferential methods which account for measurement error in covariates for models with multiplicative intensity functions or rate functions. Both likelihood-based inference and robust inference based on estimating equations are discussed. The Canadian Journal of Statistics 40: 530–549; 2012 © 2012 Statistical Society of Canada Les donnees d'evenements recurrents se retrouvent frequemment dans les etudes en medecine et en sante publique. L'analyse de telles donnees a ete l'objet de recherches exhaustives et plusieurs methodes ont ete proposees dans la litterature. Selon leur interet scientifique, elles peuvent etre grossierement classees comme etant des methodes basees sur l'intensite des processus de comptage, des methodes basees sur les equations d'estimation de la moyenne et les analyses des durees de vie ou le temps d'attente entre deux evenements. Ces methodes et modeles couvrent une grande variete d'applications. Cependant, un presuppose critique sous-jacent a ces methodes est que les variables doivent etre mesurees exactement. Malheureusement, en pratique, ce presuppose est souvent viole. Il arrive assez souvent que quelques covariables soient mesurees avec erreur. Il est bien connu que les erreurs de mesure sur les covariables peuvent grandement modifier les resultats de l'inference s'ils ne sont pas bien pris en charge. Il existe une litterature exhaustive sur le probleme des erreurs de mesure dans differents contextes. Cependant, il y a peu de recherche faite dans le contexte des evenements recurrents. Ainsi, l'objectif de cet article est de developper des methodes d'inference prenant en compte les erreurs de mesure des covariables dans les modeles avec des fonctions d'intensite ou de taux multiplicatives. Nous considerons l'inference basee sur la fonction de vraisemblance et celle robuste basee sur les equations d'estimation. La revue canadienne de statistique 40: 530–549; 2012 © 2012 Societe statistique du Canada

[1]  Viswanath Devanarayan,et al.  Empirical simulation extrapolation for measurement error models with replicate measurements , 2002 .

[2]  Yijian Huang,et al.  Consistent Functional Methods for Logistic Regression With Errors in Covariates , 2001 .

[3]  Shu-Hui Chang,et al.  Nonparametric Estimation of a Recurrent Survival Function. , 1999, Journal of the American Statistical Association.

[4]  L. Stefanski.  Unbiased estimation of a nonlinear function a normal mean with application to measurement err oorf models , 1989 .

[5]  Raymond J. Carroll,et al.  Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models , 1998 .

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

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

[8]  Wenqing He,et al.  Flexible Maximum Likelihood Methods for Bivariate Proportional Hazards Models , 2003, Biometrics.

[9]  D. Lin,et al.  Cox Regression with Covariate Measurement Error , 2002 .

[10]  Yanyuan Ma,et al.  Cure Rate Model With Mismeasured Covariates Under Transformation , 2008 .

[11]  B. Turnbull,et al.  Regression models for recurrent event data: parametric random effects models with measurement error. , 1997, Statistics in medicine.

[12]  Wenqing He,et al.  Accelerated failure time models with covariates subject to measurement error , 2007 .

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

[14]  Richard J. Cook,et al.  Marginal Methods for Incomplete Longitudinal Data Arising in Clusters , 2002 .

[15]  J. F. Lawless,et al.  Analysis of interval‐grouped recurrent‐event data using piecewise constant rate functions , 1998 .

[16]  H. Fuchs,et al.  Effect of aerosolized recombinant human DNase on exacerbations of respiratory symptoms and on pulmonary function in patients with cystic fibrosis. The Pulmozyme Study Group. , 1994, The New England journal of medicine.

[17]  Tsuyoshi Nakamura.  Corrected score function for errors-in-variables models : Methodology and application to generalized linear models , 1990 .

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

[19]  Bruce W. Turnbull,et al.  Semiparametric Regression Models for Repeated Events with Random Effects and Measurement Error , 1999 .

[20]  Jerald F. Lawless,et al.  Some Simple Robust Methods for the Analysis of Recurrent Events , 1995 .

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

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

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

[24]  Raymond J. Carroll,et al.  Asymptotics for the SIMEX Estimator in Nonlinear Measurement Error Models , 1996 .

[25]  Grace Y. Yi,et al.  A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error , 2012, Biometrika.

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