A Reiterative Method for Calculating the Early Bactericidal Activity of Antituberculosis Drugs

Abstract

Studies of early bactericidal activity (EBA) are important in the rapid evaluation of new antituberculosis drugs. Historically, these have concentrated on the log fall in the viable count in sputum during the first 48 hours of therapy. In this paper, we provide a mathematical model that suggests that the viable count in sputum follows an exponential decay curve with the equation V = S + Me(-kt) (where V is the viable count, M the population of bacteria susceptible to the test drug, S the population susceptible only to sterilizing agents, t the day of sputum collection as related to start of therapy, k the rate constant for the bacteria killed each day, and e the Napierian constant). We demonstrate that data from clinical trials fits the exponential decay model. We propose that future EBA studies should be performed by measuring daily quantitative counts for at least 5 days. We also propose that the comparison of the early bactericidal activity of antituberculosis drugs should be evaluated using the time taken to reduce the viable count by 50% (vt(50)). A further reiterative refinement following a rule set based on statistically the best fit to the exponential decay model is described that will allow investigators to identify anomalous results and thus enhance the accuracy in measuring early bactericidal activity.