Hybrid models were found to be very elegant to disentangle longitudinal within- and between-subject relationships

• Published in: Journal of clinical epidemiology Vol. 107; pp. 66 - 70
• Main Authors: Twisk, Jos W.R., de Vente, Wieke
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.03.2019; Elsevier Limited
• Subjects: Between-subject effect; Cholesterol; Correlation analysis; Data analysis; Data Interpretation, Statistical; Data processing; Epidemiologic Studies; Epidemiology; GEE analysis; Humans; Hybrid models; Longitudinal data analysis; Longitudinal Studies; Methods; Mixed models; Models, Statistical; Regression Analysis; Regression coefficients; Research Design; Variables; Within-subject effect; Between-subject effect; Within-subject effect; Hybrid models; Mixed models; GEE analysis; Longitudinal data analysis
• ISSN: 0895-4356; 1878-5921; 1878-5921
• DOI: 10.1016/j.jclinepi.2018.11.021

The interpretation of a regression coefficient obtained from a longitudinal data analysis is a combination of a within-subject part and a between-subject part. The hybrid model is used to disentangle the two components. The purpose of this article was to illustrate and discuss the use of the hybrid model in epidemiologic studies. In the hybrid model the between-subject part of the relationship is obtained using the individual mean value over time, whereas the within-subject part is obtained using the deviation score, that is, the differences between the observations and the individual mean value. It was shown that the regression coefficient of a standard mixed model analysis is a sort of weighted average of the between- and within-subject part of the relationship. When the outcome was continuous the separate analyses to estimate the two components of a longitudinal relationship were equal to the estimation in the hybrid model. However, for dichotomous outcome, the estimations were slightly different. The hybrid model is an elegant, easy to perform method to disentangle the within- and between-subject part of a relationship in longitudinal studies. •The between-subject part is obtained by the individual mean value over time.•The within-subject part is obtained by using the deviation score.•The deviation score is the difference between observations and individual mean.•The results of a hybrid logistic model should be interpreted with caution.