A generalized estimating equation approach for modeling random length binary vector data.

A common measure in clinical trials and epidemiologic studies is the number of events such as seizures, hospitalizations, or bouts of disease. Frequently, a binary measure of severity for each event is available but is not incorporated in the analysis. This paper proposes methodology for jointly modeling the number of events and the vector of correlated binary severity measures. Our formulation exploits the notion that a given covariate may affect both outcomes in a similar way. We functionally link the regression parameters for the counts and binary means and discuss a generalized estimating equation (GEE) approach for parameter estimation. We discuss conditions under which the proposed joint modeling approach provides marked gains in efficiency relative to the common procedure of simply modeling the counts, and we illustrate the methodology with epilepsy clinical trial data.

[1]  M. Fisher,et al.  Effects of therapy with cholestyramine on progression of coronary arteriosclerosis: results of the NHLBI Type II Coronary Intervention Study. , 1984, Circulation.

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

[3]  A. Rotnitzky,et al.  A note on the bias of estimators with missing data. , 1994, Biometrics.

[4]  N. Jewell,et al.  Hypothesis testing of regression parameters in semiparametric generalized linear models for cluster correlated data , 1990 .

[5]  R. Prentice,et al.  Correlated binary regression with covariates specific to each binary observation. , 1988, Biometrics.

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

[7]  L. Zhao,et al.  Correlated binary regression using a quadratic exponential model , 1990 .

[8]  M L Terrin,et al.  Effect of hydroxyurea on the frequency of painful crises in sickle cell anemia. Investigators of the Multicenter Study of Hydroxyurea in Sickle Cell Anemia. , 1995, The New England journal of medicine.

[9]  S. Lipsitz,et al.  Generalized estimating equations for correlated binary data: Using the odds ratio as a measure of association , 1991 .

[10]  W H Theodore,et al.  Felbamate Monotherapy: Implications for Antiepileptic Drug Development , 1995, Epilepsia.

[11]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[12]  P. Diggle,et al.  Analysis of Longitudinal Data , 2003 .

[13]  J. R. Landis,et al.  The analysis of longitudinal polytomous data: generalized estimating equations and connections with weighted least squares. , 1993, Biometrics.

[14]  A. Sampson,et al.  MULTIPLE POPULATION MODELS FOR MULTIVARIATE RANDOM LENGTH DATA-WITH APPLICATIONS IN CLINICAL TRIALS , 1995 .

[15]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[16]  S. Zeger,et al.  Multivariate Regression Analyses for Categorical Data , 1992 .

[17]  R. Serfling.  Approximation Theorems of Mathematical Statistics , 1980 .