gms | German Medical Science

49. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie (gmds)
19. Jahrestagung der Schweizerischen Gesellschaft für Medizinische Informatik (SGMI)
Jahrestagung 2004 des Arbeitskreises Medizinische Informatik (ÖAKMI)

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie
Schweizerische Gesellschaft für Medizinische Informatik (SGMI)

26. bis 30.09.2004, Innsbruck/Tirol

The Bootstrap and Bayes for model comparison

Meeting Abstract (gmds2004)

Suche in Medline nach

  • corresponding author presenting/speaker Jens Dreyhaupt - Universität Heidelberg, Institut für Medizinische Biometrie und Informatik, Abteilung Medizinische Biometrie, Heidelberg, Deutschland
  • Ulrich Mansmann - Universität Heidelberg, Institut für Medizinische Biometrie und Informatik, Abteilung Medizinische Biometrie, Heidelberg, Deutschland

Kooperative Versorgung - Vernetzte Forschung - Ubiquitäre Information. 49. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie (gmds), 19. Jahrestagung der Schweizerischen Gesellschaft für Medizinische Informatik (SGMI) und Jahrestagung 2004 des Arbeitskreises Medizinische Informatik (ÖAKMI) der Österreichischen Computer Gesellschaft (OCG) und der Österreichischen Gesellschaft für Biomedizinische Technik (ÖGBMT). Innsbruck, 26.-30.09.2004. Düsseldorf, Köln: German Medical Science; 2004. Doc04gmds114

Die elektronische Version dieses Artikels ist vollständig und ist verfügbar unter: http://www.egms.de/de/meetings/gmds2004/04gmds114.shtml

Veröffentlicht: 14. September 2004

© 2004 Dreyhaupt et al.
Dieser Artikel ist ein Open Access-Artikel und steht unter den Creative Commons Lizenzbedingungen (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.de). Er darf vervielf&aauml;ltigt, verbreitet und &oauml;ffentlich zug&aauml;nglich gemacht werden, vorausgesetzt dass Autor und Quelle genannt werden.


Gliederung

Text

Introduction

Age-related macular degeneration (AMD) is the most common cause for the loss of central vision associated with aging. It is a complex disorder caused by a large variety of factors. The most common type of AMD is geographic atrophy (GA), which is indicated by severe destruction of the retinal cells. Pathophysiologic mechanisms underlying this atrophic processes and causes, which influence the dynamics of GA, are poorly understood at present.

We used time course data on the development of GA from 114 patients (178 eyes) recruited to the FAM-study for an investigation of the process of GA-growth. An important point of interest is to quantify the natural history of GA growth in order to decide if the natural history follows a linear or a non-linear growth process. This is helpful for planning and analysing randomised intervention trials to reduce GA growth.

Methods

We established a linear and a non-linear mixed effects model. Both models were compared to find the model adequately describing GA-growth. We used three different basic approaches to compare the non-nested mixed effects models:

1. checking model structure

2. using AIC information criteria

3. comparison of the predictive behaviour.

Approach a) is a check of model structure, i.e. a check of assumptions on within-group-errors and random effects. Graphical methods were used for these investigations.

In approach b) we used the AIC information criteria for comparison [1]. Since there is no established asymptotic theory for the AIC in the given situation, we carried out a computer - intensive wild bootstrap procedure for further explorations of both models: bootstrap samples were randomly chosen from our study population, the linear and the non-linear model was fitted for each sample and the difference in the AIC criterion was calculated. Here we extend ideas of Wahrendorf et al. [2] to linear and non-linear mixed effects models.

The third approach c) is a comparison of the predictive behaviour of both models. First, the predictive behaviour was investigated for patients with new follow up's. A parametric bootstrap using the results of the model fits was performed: bootstrap samples were created by using patient specific random effects, the fixed effects and the estimated residual variance. The linear and the non-linear model were fitted for all of these bootstrap samples and the difference of „sum of squares of difference between predicted and observed values" was calculated.

Secondly, we checked the predictive behaviour for patients newly recruited to the FAM-study. As criterion we used the „sum of squares of difference between predicted and observed values", calculated for the linear and the non-linear model. The exploration of this aspect is more difficult because specific random effects are not known for the new patients. A Bayesian procedure is used to calculate MSE's between the observed and predicted data.

Results

For an investigation of our bootstrap samples we used analytical and graphical methods. The exploration of AIC difference suggests no convincing advantage for any model. The predictive behaviour in contrast to AIC difference shows a clear advantage for the linear mixed model, however.

All analyses were carried out by using a Pentium IV Computer (2,4 GHz, 512 MB RAM) under WINDOWS 2000 with the software S-Plus 2000 (lme and nlme library) [3].

Discussion

Bootstrap methods are suitable for determining confidence intervals with more precision and are helpful in making decisions. Both, the wild and parametric bootstrap, help to handle different aspects of model assessment in mixed effects models. Because random effects estimates do not exist for a totally new test population, Bayesian techniques offer the needed extension to handle the calculation of MSE between the observed data and the model - based prediction.

Acknowledgement

Our project is supported by DFG grants: SPP AMD 1088, MA 1723/1-1.


References

1.
Davison AC, Hinkley DV. Bootstrap Methods and Their Applications. New York: Cambridge University Press, 1997.
2.
Wahrendorf J, Becher H, Brown CC. Bootstrap Comparisons of Non-nested Generalized Linear Models: Applications in Survival Analysis and Epidemiology. JRSS 1987; 36: 72-81.
3.
Pinheiro JC, Bates DM. Mixed-Effects Models in S and S-Plus. New York: Springer, 2000