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Chapter 5 - Models to Disentangle the Between- and Within-subjects Relationship
Jos W. R. Twisk, Amsterdam University Medical Centers
Book:

Applied Longitudinal Data Analysis for Medical Science

Published online:

20 April 2023

Print publication:

27 April 2023, pp 76-91
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Summary

One of the most complicated parts of a longitudinal data analysis is the interpretation of the regression coefficient. The regression coefficient is a weighted average of the between-subjects relationship and the within-subjects relationship. In Chapter 5, first hybrid models are introduced. Hybrid models are developed to disentangle the between- and within-subjects relationship. Hybrid models can be performed by calculating: (1) the individual average value of the covariate, which is used to obtain the between-subjects part of the relationship and (2) the deviation score, which is the difference between the observed values and the individual mean value and is used to obtain the within-subjects part of the relationship. In this chapter the modelling of changes and the autoregressive model are also discussed. Both models intend to estimate only the within-subjects part of the longitudinal relationship. All methods are accompanied by extensive real-life data examples.

Application of Hybrid Models to Blood Cell Production in theBone Marrow
N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert
Journal:

Mathematical Modelling of Natural Phenomena / Volume 6 / Issue 7 / 2011

Published online by Cambridge University Press:

15 June 2011, pp. 2-12

Print publication:

2011
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A hybrid model of red blood cell production, where cells are considered as discreteobjects while intra-cellular proteins and extra-cellular biochemical substances aredescribed with continuous models, is proposed. Spatial organization and regulation of redblood cell production (erythropoiesis) are investigated. Normal erythropoiesis issimulated in two dimensions, and the influence on the output of the model of someparameters involved in cell fate (differentiation, self-renewal, and death by apoptosis)is studied.

Multiphase and Multiscale Trends in Cancer Modelling
L. Preziosi, A. Tosin
Journal:

Mathematical Modelling of Natural Phenomena / Volume 4 / Issue 3 / 2009

Published online by Cambridge University Press:

05 June 2009, pp. 1-11

Print publication:

2009
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While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models.