A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error

Abstract Covariate measurement error and missing responses are typical features in longitudinal data analysis. There has been extensive research on either covariate measurement error or missing responses, but relatively little work has been done to address both simultaneously. In this paper, we propose a simple method for the marginal analysis of longitudinal data with time-varying covariates, some of which are measured with error, while the response is subject to missingness. Our method has a number of appealing properties: assumptions on the model are minimal, with none needed about the distribution of the mismeasured covariate; implementation is straightforward and its applicability is broad. We provide both theoretical justification and numerical results.

[1]  M. Pepe,et al.  A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data , 1994 .

[2]  Anastasios A. Tsiatis,et al.  Locally efficient semiparametric estimators for functional measurement error models , 2004 .

[3]  Hua Liang,et al.  Generalized partially linear mixed-effects models incorporating mismeasured covariates , 2009, Annals of the Institute of Statistical Mathematics.

[4]  Raymond J. Carroll,et al.  Conditional scores and optimal scores for generalized linear measurement-error models , 1987 .

[5]  Xihong Lin,et al.  Estimation in Semiparametric Transition Measurement Error Models for Longitudinal Data , 2009, Biometrics.

[6]  Dylan S. Small,et al.  Marginal regression analysis of longitudinal data with time‐dependent covariates: a generalized method‐of‐moments approach , 2007 .

[7]  Andrew W. Roddam,et al.  Measurement Error in Nonlinear Models: a Modern Perspective , 2008 .

[8]  Raymond J. Carroll,et al.  Generalized Linear Mixed Measurement Error Models , 1997 .

[9]  Marie Davidian,et al.  Conditional Estimation for Generalized Linear Models When Covariates Are Subject‐Specific Parameters in a Mixed Model for Longitudinal Measurements , 2004, Biometrics.

[10]  Nedjeljko Frančula.  The National Academies Press , 2013 .

[11]  W. Riley,et al.  Evaluation of a PDA-based Dietary Assessment and Intervention Program: A Randomized Controlled Trial , 2006, Journal of the American College of Nutrition.

[12]  Raymond J. Carroll,et al.  Measurement error in nonlinear models: a modern perspective , 2006 .

[13]  Wei Liu,et al.  Simultaneous Inference for Semiparametric Nonlinear Mixed‐Effects Models with Covariate Measurement Errors and Missing Responses , 2007, Biometrics.

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

[15]  Naisyin Wang,et al.  Joint Models for a Primary Endpoint and Multiple Longitudinal Covariate Processes , 2007, Biometrics.

[16]  M Palta,et al.  Latent variables, measurement error and methods for analysing longitudinal binary and ordinal data. , 1999, Statistics in medicine.

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

[18]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

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

[20]  Lang Wu,et al.  Simultaneous inference and bias analysis for longitudinal data with covariate measurement error and missing responses. , 2011, Biometrics.

[21]  Runze Li,et al.  Variable Selection in Measurement Error Models. , 2010, Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability.

[22]  Michael Woodroofe,et al.  Estimation in Large Samples , 1988 .

[23]  P. Hall,et al.  Semiparametric estimators of functional measurement error models with unknown error , 2007 .

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

[25]  Expected Estimating Equations for Missing Data, Measurement Error, and Misclassification, with Application to Longitudinal Nonignorable Missing Data , 2008, Biometrics.

[26]  R. Carroll,et al.  Semiparametric estimation in general repeated measures problems , 2006 .

[27]  Grace Y Yi,et al.  A simulation-based marginal method for longitudinal data with dropout and mismeasured covariates. , 2008, Biostatistics.

[28]  David Couper,et al.  Modeling Partly Conditional Means with Longitudinal Data , 1997 .

[29]  C. Davis,et al.  High levels of low energy reporting on 24-hour recalls and three questionnaires in an elderly low-socioeconomic status population. , 2007, The Journal of nutrition.

[30]  J. Shao,et al.  GMM in linear regression for longitudinal data with multiple covariates measured with error , 2010 .

[31]  Hua Liang,et al.  Statistical inference for semiparametric varying-coefficient partially linear models with error-prone linear covariates , 2009, 0903.0499.

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