Bayesian non-linear models for the bactericidal activity of tuberculosis drugs
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Date
2015-05
Authors
Burger, Divan Aristo
Journal Title
Journal ISSN
Volume Title
Publisher
University of the Free State
Abstract
Trials of the early bactericidal activity (EBA) of tuberculosis (TB) treatments assess
the decline, during the first few days to weeks of treatment, in colony forming
unit (CFU) count of Mycobacterium tuberculosis in the sputum of patients with
smear-microscopy-positive pulmonary TB. Profiles over time of CFU data have
conventionally been modeled using linear, bilinear or bi-exponential regression.
This thesis proposes a new biphasic nonlinear regression model for CFU data that
comprises linear and bilinear regression models as special cases, and is more
exible
than bi-exponential regression models. A Bayesian nonlinear mixed effects
(NLME) regression model is fitted jointly to the data of all patients from clinical
trials, and statistical inference about the mean EBA of TB treatments is based
on the Bayesian NLME regression model. The posterior predictive distribution
of relevant slope parameters of the Bayesian NLME regression model provides
insight into the nature of the EBA of TB treatments; specifically, the posterior
predictive distribution allows one to judge whether treatments are associated with
mono-linear or bilinear decline of log(CFU) count, and whether CFU count initially
decreases fast, followed by a slower rate of decrease, or vice versa. The fit
of alternative specifications of residuals, random effects and prior distributions is
explored. In particular, the conventional normal regression models for log(CFU)
count versus time profiles are extended to provide a robust approach which accommodates
outliers and potential skewness in the data. The deviance information
criterion and compound Laplace-Metropolis Bayes factors are calculated to discriminate
between models. The biphasic model is fitted to time to positivity data
in the same way as for CFU data.
Description
Keywords
Thesis (Ph.D. (Mathematical Statistics and Actuarial Sciences))--University of the Free State, 2015, Bayesian statistical decision theory, Antitubercular agents