Comments about Joint Modeling of Cluster Size and Binary and Continuous Subunit‐Specific Outcomes

In longitudinal studies and in clustered situations often binary and continuous response variables are observed and need to be modeled together. In a recent publication Dunson, Chen, and Harry (2003, Biometrics 59, 521-530) (DCH) propose a Bayesian approach for joint modeling of cluster size and binary and continuous subunit-specific outcomes and illustrate this approach with a developmental toxicity data example. In this note we demonstrate how standard software (PROC NLMIXED in SAS) can be used to obtain maximum likelihood estimates in an alternative parameterization of the model with a single cluster-level factor considered by DCH for that example. We also suggest that a more general model with additional cluster-level random effects provides a better fit to the data set. An apparent discrepancy between the estimates obtained by DCH and the estimates obtained earlier by Catalano and Ryan (1992, Journal of the American Statistical Association 87, 651-658) is also resolved. The issue of bias in inferences concerning the dose effect when cluster size is ignored is discussed. The maximum-likelihood approach considered herein is applicable to general situations with multiple clustered or longitudinally measured outcomes of different type and does not require prior specification and extensive programming.

[1]  R. Gueorguieva,et al.  A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family , 2001 .

[2]  S. Rabe-Hesketh,et al.  Generalized multilevel structural equation modeling , 2004 .

[3]  D. Dunson,et al.  Bayesian latent variable models for clustered mixed outcomes , 2000 .

[4]  A. Agresti,et al.  A Correlated Probit Model for Joint Modeling of Clustered Binary and Continuous Responses , 2001 .

[5]  J Rochon,et al.  Analyzing bivariate repeated measures for discrete and continuous outcome variables. , 1996, Biometrics.

[6]  Carla Rampichini,et al.  Alternative Specifications of Multivariate Multilevel Probit Ordinal Response Models , 2003 .

[7]  M M Regan,et al.  Likelihood Models for Clustered Binary and Continuous Out comes: Application to Developmental Toxicology , 1999, Biometrics.

[8]  Nan M. Laird,et al.  Regression Models for a Bivariate Discrete and Continuous Outcome with Clustering , 1995 .

[9]  Louise Ryan,et al.  Bivariate Latent Variable Models for Clustered Discrete and Continuous Outcomes , 1992 .

[10]  David B Dunson,et al.  A Bayesian Approach for Joint Modeling of Cluster Size and Subunit‐Specific Outcomes , 2003, Biometrics.

[11]  C J Price,et al.  The developmental toxicity of ethylene glycol in rats and mice. , 1985, Toxicology and applied pharmacology.

[12]  S. Rabe-Hesketh,et al.  Reliable Estimation of Generalized Linear Mixed Models using Adaptive Quadrature , 2002 .