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BMC Medical Research Methodology
Published in: BMC Medical Research Methodology 1/2018

Open Access 01-12-2018 | Technical advance

Using the Beta distribution in group-based trajectory models

Authors: Jonathan Elmer, Bobby L. Jones, Daniel S. Nagin

Published in: BMC Medical Research Methodology | Issue 1/2018

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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.
Footnotes
1
Up to 5th order polynomials can be estimated in the software used to estimate the models reported in the case study.
 
2
The call to the Stata-based trajectory estimation used to estimate this model was as follows:
traj, var.(srt1-srt48) indep(t1-t48) model(beta) order(3 2 2) dropout(0 0 0) where srt* is the median supression ratio at hour * and t* is the hour of measurement from 1 to 48 and the “dropout” component of the call activates the generalization of GBTM to account for nonrandom subject attrition.
 
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Metadata
Title
Using the Beta distribution in group-based trajectory models
Authors
Jonathan Elmer
Bobby L. Jones
Daniel S. Nagin
Publication date
01-12-2018
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2018
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/s12874-018-0620-9

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