Robust Bayesian nonlinear mixed‐effects modeling of time to positivity in tuberculosis trials

Abstract

Early phase 2 tuberculosis (TB) trials are conducted to characterize the early bactericidal activity (EBA) of anti-TB drugs. The EBA of anti-TB drugs has conventionally been calculated as the rate of decline in colony forming unit (CFU) count during the first 14 days of treatment. The measurement of CFU count, however, is expensive and prone to contamination. Alternatively to CFU count, time to positivity (TTP), which is a potential biomarker for long-term efficacy of anti-TB drugs, can be used to characterize EBA. The current Bayesian nonlinear mixed-effects (NLME) regression model for TTP data, however, lacks robustness to gross outliers that often are present in the data. The conventional way of handling such outliers involves their identification by visual inspection and subsequent exclusion from the analysis. However, this process can be questioned because of its subjective nature. For this reason, we fitted robust versions of the Bayesian nonlinear mixed-effects regression model to a wide range of TTP datasets. The performance of the explored models was assessed through model comparison statistics and a simulation study. We conclude that fitting a robust model to TTP data obviates the need for explicit identification and subsequent "deletion" of outliers but ensures that gross outliers exert no undue influence on model fits. We recommend that the current practice of fitting conventional normal theory models be abandoned in favor of fitting robust models to TTP data.

Bedaquiline, moxifloxacin, pretomanid, and pyrazinamide during the first 8 weeks of treatment of patients with drug-susceptible or drug-resistant pulmonary tuberculosis: a multicentre, open-label, partially randomised, phase 2b trial

“…We estimated the bactericidal activity parameters by the fit of a Bayesian non-linear mixed-effects regression model to log 10 (TTP) 18 and log 10 (CFU) count 19,20 of all patients with drug-susceptible tuberculosis jointly. The bactericidal activity was characterised by the daily percentage change in time to positive signal, and the daily change in log(CFU) of overnight sputum samples.…”

Fourteen-Day Bactericidal Activity, Safety, and Pharmacokinetics of Linezolid in Adults with Drug-Sensitive Pulmonary Tuberculosis

“…This was an observational study with no prespecified hypothesis testing. Bactericidal activity was characterized by the daily percentage change in TTP and the daily rate of change in log 10 (CFU) count over 14 treatment days using Bayesian nonlinear mixed effects regression modeling (25,26). This model was designed specifically for this type of data and can handle missing data due to contamination, early participant withdrawal, or culture conversion.…”

A generalized Bayesian nonlinear mixed‐effects regression model for zero‐inflated longitudinal count data in tuberculosis trials

“…However, the biexponential regression model is not appropriate for log 10 (CFU) versus time profiles that are decreasing slowly during the early phase of treatment, followed by a faster decline. The NLME regression model of Burger and Schall() has recently been introduced for the modeling of log 10 (CFU) count versus time profiles and was shown to be more flexible than biexponential regression models in the sense that they allow for terminal rates of decline to be greater than initial rates of decline and vice versa. Burger and Schall() proposed a Bayesian method for fitting the required hierarchical nonlinear regression models, for estimation of the model parameters and for inference about relevant parameter contrasts.…”