Bayesian non-linear models for the bactericidal activity of tuberculosis drugs
Burger, Divan Aristo
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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.