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Generalized linear mixed effects model in the analysis of longitudinal discrete data

Carrasquinha, E.; Gonçalves, M. H.; Cabral, M. S.

Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications, Springer, Berlin Heidelberg, (2013), 113-120

In many cancer studies and clinical research, repeated observations of response variables are taken over time for each subject in one or more treatment groups. Such research is commonly referred to longitudinal studies and the repeated observations of each vector response are likely to be correlated. The autocorrelation structure for the repeated data plays a significant role in the analysis of such data. The generalized linear mixed effects model (GLMM) is one of the approaches used to analyze discrete longitudinal data, where the use of random effects in the linear predictor accounts for the within-subject association. The goal of this chapter is to introduce this model in the analysis of longitudinal discrete data, taking into account the theoretical and computational difficulties as well as the problems related to parameters interpretation. The methodology is illustrated by analyzing data sets containing longitudinal measures of number of tumors in an experiment of carcinogenesis to study the influence of lipids in the development of breast cancer. The library lme4 [Bates, D., Maechler, M., Bolker, B.: lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-39. (2011)] in R software is used.