An approximate generalized linear model with random effects for informative missing data.

This paper develops a class of models to deal with missing data from longitudinal studies. We assume that separate models for the primary response and missingness (e.g., number of missed visits) are linked by a common random parameter. Such models have been developed in the econometrics (Heckman, 1979, Econometrica 47, 153-161) and biostatistics (Wu and Carroll, 1988, Biometrics 44, 175-188) literature for a Gaussian primary response. We allow the primary response, conditional on the random parameter, to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness. The resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects. An example is given to illustrate the approximate approach, and simulations are performed to critique the adequacy of the approximation for repeated binary data.

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

[2]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[3]  M. Hurd.  Estimation in truncated samples when there is heteroscedasticity , 1979 .

[4]  P. Schmidt,et al.  Limited-Dependent and Qualitative Variables in Econometrics. , 1984 .

[5]  R. Olsen,et al.  A Least Squares Correction for Selectivity Bias , 1980 .

[6]  C. Wild.  Failure time models with matched data , 1983 .

[7]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[8]  Willard G. Manning,et al.  Monte Carlo evidence on the choice between sample selection and two-part models , 1987 .

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

[10]  R F Woolson,et al.  Application of empirical Bayes inference to estimation of rate of change in the presence of informative right censoring. , 1992, Statistics in medicine.

[11]  J. Ware,et al.  Random-effects models for serial observations with binary response. , 1984, Biometrics.

[12]  P. McCullagh,et al.  Generalized Linear Models , 1992 .

[13]  B. Efron.  The jackknife, the bootstrap, and other resampling plans , 1987 .

[14]  J. Heckman.  Sample selection bias as a specification error , 1979 .

[15]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[16]  R. Schall.  Estimation in generalized linear models with random effects , 1991 .

[17]  Diane Lambert,et al.  Generalizing Logistic Regression by Nonparametric Mixing , 1989 .

[18]  S. Zeger,et al.  Longitudinal data analysis using generalized linear models , 1986 .