JSM 2005 - Toronto

Abstract #303603

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Activity Number: 481
Type: Contributed
Date/Time: Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract - #303603
Title: Nonlinear Hyperbolastic Models and Applications in Craniofacial and Stem Cell Growth
Author(s): Zoran Bursac*+ and Mohammad Tabatabai and David K. Williams
Companies: University of Arkansas for Medical Sciences and Cameron University and University of Arkansas for Medical Sciences
Address: 4301 W Markham Slot 781, Little Rock, AR, 72205, United States
Keywords: hyperbolastic models ; non-linear models ; growth models
Abstract:

Mathematical models describing growth kinetics are important for predicting many biological phenomena such as tumor volume, number of stem cells, and/or cranofacial growth. Growth models such as logistic, Gompertz, Richards, and Weibull have been extensively studied and applied in a range of medical and biological studies. We introduce a class of three and four parameter models called "hyperbolastic models" for accurately predicting and analyzing self-limited growth behavior. To illustrate the application and utility of these models, we apply them to two previously published sets of data. In both applications, based on several accuracy measures, at least one of newly proposed models provides a better fit to the data than the four classic models. Newly proposed H3 model performs the best in both instances. We strongly believe the family of hyperbolastic models can be a valuable predictive tool in many areas of biomedical and epidemiologic research. Practitioners should test and compare the fit and prediction of these models to the standard ones before making a decision on the most appropriate.

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