Abstract
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. http://CRAN.R-project.org/package=lme4 (2011)] in R software is used.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bates, D., Maechler, M., Bolker, B.: lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-39. http://CRAN.R-project.org/package=lme4 (2011)
Breslow, N.E., Clayton, D.G.: Approximate inference in generalized linear mixed Models. J. Am. Stat. Assoc. 88, 9–25 (1993)
Carrasquinha, E.I.: Análise de dados longitudinais discretos: uma aplicação ao estudo da influência de lípidos no adenocarcinoma mamário. Mestrado em Bioestatística. FCUL, Lisboa (2009)
Escrich, E., Solanas, M., Segura, R.: Experimental diets for the study of lipid influence on the induced mammary carcinoma in rats: I-diet definition. Int. J. in vivo Res. 8, 1099–1106 (1994)
Escrich, E., Solanas, M., Ruiz de Villa, M.C., Ribalta, T., Muntané, J., Segura, R.: Experimental diets for the study of lipid influence on the induced mammary carcinoma in rats: suitability of the diets definition. Int. J. in vivo Res. 8, 1107–1112 (1994)
Faraway, J.J.: Extending the linear Model with R. Generalized Linear, Mixed Effects and Nonparametric Regression Models. Texts in Statistical Science. Chapman and Hall/CRC, Boca Raton (2006)
Fitzmaurice, G.M., Laird, N.M., Ware, J.H.: Applied Longitudinal Analysis. Wiley, New York (2004)
Fitzmaurice, G.M., Davidian, M., Verbeke, G., Molenberghs, G.: Longitudinal Data Analysis. Chapman & Hall, Boca Raton (2008)
Mcculloch, C.E., Searle, S.R.: Generalized Linear and Mixed Models. Wiley, New York (2001)
Molenberghs, G., Verbeke, G.: Models for Discrete Longitudinal Data. Springer, New York (2005)
Self, S.G., Liang, K.Y.: Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Am. Stat. Assoc. 82, 605–610 (1987)
Acknowledgements
Research partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal—FCT under the project (PEst-OE/MAT/UI0006/2011).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carrasquinha, E., Gonçalves, M.H., Cabral, M.S. (2013). Generalized Linear Mixed Effects Model in the Analysis of Longitudinal Discrete Data. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-34904-1_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34903-4
Online ISBN: 978-3-642-34904-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)