Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable

SUMMARY We propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable. We develop a Monte Carlo EM algorithm for estimating the parameters in the model via the Gibbs sampler. For the normal random effects model, we derive a novel analytical form for the E- and M-steps, which is facilitated by integrating out the random effects. This form leads to a computationally feasible and extremely efficient Monte Carlo EM algorithm for computing maximum likelihood estimates and standard errors. In addition, we propose a very general joint multinomial model for the missing data indicators, which can be specified via a sequence of one-dimensional conditional distributions. This multinomial model allows for an arbitrary correlation structure between the missing data indicators, and has the potential of reducing the number of nuisance parameters. Real datasets from the International Breast Cancer Study Group and an environmental study involving dyspnoea in cotton workers are presented to illustrate the proposed methods.

[1]  Ying Nian Wu,et al.  Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t Distribution , 2001 .

[2]  J. Robins,et al.  Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models , 1999 .

[3]  J. Booth,et al.  Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm , 1999 .

[4]  Xiao-Li Meng,et al.  Fast EM‐type implementations for mixed effects models , 1998 .

[5]  M. Kenward,et al.  The analysis of longitudinal ordinal data with nonrandom drop-out , 1997 .

[6]  Nan M. Laird,et al.  Multivariate Logistic Models for Incomplete Binary Responses , 1996 .

[7]  R. Little,et al.  Pattern-mixture models for multivariate incomplete data with covariates. , 1996, Biometrics.

[8]  A. Gelfand,et al.  Efficient parametrizations for generalized linear mixed models, (with discussion). , 1996 .

[9]  S. Chib,et al.  Bayesian residual analysis for binary response regression models , 1995 .

[10]  J. Robins,et al.  Analysis of semiparametric regression models for repeated outcomes in the presence of missing data , 1995 .

[11]  D. Follmann,et al.  An approximate generalized linear model with random effects for informative missing data. , 1995, Biometrics.

[12]  Oliver Schabenberger.  The analysis of longitudinal ordinal data , 1995 .

[13]  Roderick J. A. Little,et al.  Modeling the Drop-Out Mechanism in Repeated-Measures Studies , 1995 .

[14]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[15]  J. Robins,et al.  Estimation of Regression Coefficients When Some Regressors are not Always Observed , 1994 .

[16]  M. Kenward,et al.  Informative Drop‐Out in Longitudinal Data Analysis , 1994 .

[17]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[18]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[19]  R. Gelber,et al.  Quality of life measures for patients receiving adjuvant therapy for breast cancer: an international trial. The International Breast Cancer Study Group. , 1992, European journal of cancer.

[20]  G. C. Wei,et al.  A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms , 1990 .

[21]  J. Ibrahim.  Incomplete Data in Generalized Linear Models , 1990 .

[22]  K. Bailey,et al.  Estimation and comparison of changes in the presence of informative right censoring: conditional linear model. , 1989, Biometrics.

[23]  P. Albert,et al.  Models for longitudinal data: a generalized estimating equation approach. , 1988, Biometrics.

[24]  Raymond J. Carroll,et al.  Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process , 1988 .

[25]  K. Bailey,et al.  Analysing changes in the presence of informative right censoring caused by death and withdrawal. , 1988, Statistics in medicine.

[26]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[27]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[28]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .