A time-to-event pharmacodynamic model describing treatment response in patients with pulmonary tuberculosis using days to positivity in automated liquid mycobacterial culture

Abstract

Days to positivity in automated liquid mycobacterial culture have been shown to correlate with mycobacterial load and have been proposed as a useful biomarker for treatment responses in tuberculosis. However, there is currently no quantitative method or model to analyze the change in days to positivity with time on treatment. The objectives of this study were to describe the decline in numbers of mycobacteria in sputum collected once weekly for 8 weeks from patients on treatment for tuberculosis using days to positivity in liquid culture. One hundred forty-four patients with smear-positive pulmonary tuberculosis were recruited from a tuberculosis clinic in Cape Town, South Africa. A nonlinear mixed-effects repeated-time-to-event modeling approach was used to analyze the time-to-positivity data. A biexponential model described the decline in the estimated number of bacteria in patients' sputum samples, while a logistic model with a lag time described the growth of the bacteria in liquid culture. At baseline, the estimated number of rapidly killed bacteria is typically 41 times higher than that of those that are killed slowly. The time to kill half of the rapidly killed bacteria was about 1.8 days, while it was 39 days for slowly killed bacteria. Patients with lung cavitation had higher bacterial loads than patients without lung cavitation. The model successfully described the increase in days to positivity as treatment progressed, differentiating between bacteria that are killed rapidly and those that are killed slowly. Our model can be used to analyze similar data from studies testing new drug regimens.

Figures

Fig 1

Box-and-whisker plots of days to positivity for each week of treatment.

Fig 2

Visual predictive check from 100 simulations using the final model stratified into each week of treatment. The continuous line is a Kaplan-Meier plot for the real data. A positive sputum result was regarded as an event and will result in a step on the staircase plot. The shaded area is a 90% prediction interval based on the simulated data from the model.

Fig 3

Typical relative amount of Mycobacterium tuberculosis bacteria processed from patients' weekly sputum samples and inoculated into the MGIT.

Fig 4

Maximum growth rate of mycobacteria in MGIT culture for the logistic growth model as weeks on treatment progress.

Fig 5

Probability of obtaining a positive MGIT culture result upon incubation for up to 42 days as weeks on treatment progress.

Fig 6

Schematic of the final model and equations.