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

Abstract

Objectives: 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.

Study design and setting: 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.

Results: 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.

Conclusion: The hybrid model is an elegant, easy to perform method to disentangle the within- and between-subject part of a relationship in longitudinal studies.

Keywords: Between-subject effect; GEE analysis; Hybrid models; Longitudinal data analysis; Mixed models; Within-subject effect.