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. 2018 Nov 26;18(1):152.
doi: 10.1186/s12874-018-0620-9.

Using the Beta distribution in group-based trajectory models

Jonathan Elmer  1 , Bobby L Jones  2 , Daniel S Nagin  3
Affiliations

Using the Beta distribution in group-based trajectory models

Jonathan Elmer et al. BMC Med Res Methodol. .

Abstract

Background: We demonstrate an application of Group-Based Trajectory Modeling (GBTM) based on the beta distribution. It is offered as an alternative to the normal distribution for modeling continuous longitudinal data that are poorly fit by the normal distribution even with censoring. The primary advantage of the beta distribution is the flexibility of the shape of the density function.

Methods: GBTM is a specialized application of finite mixture modeling designed to identify clusters of individuals who follow similar trajectories. Like all finite mixture models, GBTM requires that the distribution of the data composing the mixture be specified. To our knowledge this is the first demonstration of the use of the beta distribution in GBTM. A case study of a beta-based GBTM analyzes data on the neurological activity of comatose cardiac arrest patients.

Results: The case study shows that the summary measure of neurological activity, the suppression ratio, is not well fit by the normal distribution but due to the flexibility of the shape of the beta density function, the distribution of the suppression ratio by trajectory appears to be well matched by the estimated beta distribution by group.

Conclusions: The addition of the beta distribution to the already available distributional alternatives in software for estimating GBTM is a valuable augmentation to extant distributional alternatives.

Keywords: Beta distribution; Cardiac arrest; Group-based trajectory modeling.

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Conflict of interest statement

Ethics approval and consent to participate

The University of Pittsburgh Institutional Review Board approved all aspects of this study. Consent to participate is not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures

Fig. 1
Fig. 1
The Distribution of Hour 12 Suppression Ratio Data with the Best Fitting Beta Distribution. *The sum of the heights of the relative frequency density bars multiplied by their width sum to 1.0 so as to conform the with estimated beta density
Fig. 2
Fig. 2
Three Group Trajectory Model with Beta Distributed Suppression Ratio
Fig. 3
Fig. 3
Distribution of 24 h suppression ratio data with the best-fitting data distribution for Group 1 (a), Group 2 (b) and Group 3 (c). *The sum of the heights of the relative frequency density bars multiplied by their width sum to 1.0 so as to conform the with estimated beta density
See this image and copyright information in PMC

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