Bayesian non-linear models for the bactericidal activity of tuberculosis drugs

[摘要] Trials of the early bactericidal activity (EBA) of tuberculosis (TB) treatments assessthe decline, during the first few days to weeks of treatment, in colony formingunit (CFU) count of Mycobacterium tuberculosis in the sputum of patients withsmear-microscopy-positive pulmonary TB. Profiles over time of CFU data haveconventionally been modeled using linear, bilinear or bi-exponential regression.This thesis proposes a new biphasic nonlinear regression model for CFU data thatcomprises linear and bilinear regression models as special cases, and is more exiblethan bi-exponential regression models. A Bayesian nonlinear mixed effects(NLME) regression model is fitted jointly to the data of all patients from clinicaltrials, and statistical inference about the mean EBA of TB treatments is basedon the Bayesian NLME regression model. The posterior predictive distributionof relevant slope parameters of the Bayesian NLME regression model providesinsight into the nature of the EBA of TB treatments; specifically, the posteriorpredictive distribution allows one to judge whether treatments are associated withmono-linear or bilinear decline of log(CFU) count, and whether CFU count initiallydecreases fast, followed by a slower rate of decrease, or vice versa. The fitof alternative specifications of residuals, random effects and prior distributions isexplored. In particular, the conventional normal regression models for log(CFU)count versus time profiles are extended to provide a robust approach which accommodatesoutliers and potential skewness in the data. The deviance informationcriterion and compound Laplace-Metropolis Bayes factors are calculated to discriminatebetween models. The biphasic model is fitted to time to positivity datain the same way as for CFU data.

[发布机构] University of the Free State