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

Biometrics. 1995 Mar;51(1):151-68.


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.

Publication types

  • Comparative Study

MeSH terms

  • Bayes Theorem
  • Biometry / methods
  • Buprenorphine / therapeutic use
  • Dose-Response Relationship, Drug
  • Humans
  • Longitudinal Studies
  • Mathematics
  • Methadone / therapeutic use
  • Models, Statistical*
  • Random Allocation
  • Randomized Controlled Trials as Topic / methods*
  • Substance-Related Disorders / rehabilitation
  • Time Factors


  • Buprenorphine
  • Methadone