Bayesian nonlinear models

Short Title: Robust Nonlinear Mixed Effects Regression Models in Tuberculosis Research

Short Description:   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 count have conventionally been modeled using linear, bilinear or bi-exponential regression. Recent research proposes a biphasic nonlinear regression model for CFU count that comprises linear and bilinear regression models as special cases, and is more flexible than bi-exponential regression models. Bayesian nonlinear mixed effects (NLME) regression models are fitted jointly to the data of all patients from various 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 research primarily includes the investigation of heavy tailed and skew distributions to develop models that are robust to occasional outliers seen in data.

People Involved: Divan Burger (University of Pretoria) and Robert Schall (University of the Free State).

Short Title: Statistical Inference for Ectoparasiticide Efficacy in Animal Trials

Short Description:   In controlled animal trials of ectoparasiticides the efficacy of treatments is estimated based on the number of surviving parasites with which experimental animals have been infested. Guidelines for the conduct and analysis of animals trials published by international regulatory authorities require that the estimated efficacy of a test treatment (as determined by the Abbott estimator) should at least be 90%, for the treatment to be declared efficacious. This decision rule, therefore, is simply based on a point estimate of efficacy, and does not take into account the precision of the estimate; specifically, proper statistical inference on the efficacy of the test treatment in question is not required. As a consequence, the Type I error probability of falsely declaring a truly non-efficacious product to be efficacious can be as high as 50%. In the proposed research project we investigate the use of appropriate statistical decision rules for the efficacy which control the Type 1 error at a specified low level, say the conventional 5%. The statistical model for the data assumes a Beta-Binomial distribution which can accommodate the binomial over-dispersion typically associated with such data. A Bayesian approach for implementing the analysis of ectoparasiticide efficacy data will be explored, and appropriate prior distributions will be investigated.

People Involved: Divan Burger (University of Pretoria), Chandré Teise (University of the Free State) and Robert Schall (University of the Free State).