A Bayesian Nonlinear Mixed-Effects Regression Model for the Characterization of Early Bactericidal Activity of Tuberculosis Drugs

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. We propose a new biphasic nonlinear regression model for CFU data that comprises linear and bilinear regression models as special cases and is more flexible than bi-exponential regression models. A Bayesian nonlinear mixed-effects (NLME) regression model is fitted jointly to the data of all patients from a trial, 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 monolinear or bilinear decline of log(CFU) count, and whether CFU count initially decreases fast, followed by a slower rate of decrease, or vice versa.