© 2003 American Thoracic Society
A reiterative method for calculating bactericidal activityTo the Editor:Gillespie and colleagues (1) propose that the early bactericidal activity (EBA) of drugs should be calculated from daily counts of colony forming units of Mycobacterium tuberculosis in sputum over a 5-day period by iterative fitting to an exponential model, V = S + Me-kt. This model is mathematically equivalent to the usual procedure of fitting linear regression lines to log viable counts on days of treatment, during the period when population M is being killed. To examine the model, separate regression lines during Days 0–2 and during Days 2, 4, and 6 have been fitted to the Jindani data (2) on each of 107 individual patients within 23 groups, usually consisting of 4 patients, treated with isoniazid, streptomycin, rifampin, ethambutol, pyrazinamide, p-aminosalicylic acid, or thiacetazone in monotherapy or in combinations (Table 1) . Two-sample t tests with unequal variances show that the fall in counts during the first 2 days was significantly greater than those in the subsequent days except for drugs that had very low initial EBAs, in agreement with similar conclusions obtained elsewhere (3). This slowing of the exponential fall may not have been apparent in the data used by Gillespie and colleagues because of technical faults in sputum processing among 10 of their 16 patients (4). Because k is variable, it is therefore inappropriate to use their suggested single rate constant, Vt. Iterative discarding of data points because they do not fit an incorrect model is a source of bias rather than a help in discarding "discrepant" results. Furthermore, almost all of the ability to discriminate between the EBAs of different drugs and different dose sizes occurs during the first 2 days. Thus, the value of F[22, 84] (the variance ratio), the best measure of discrimination between regression coefficients in the 23 regimens, is 5.45 over the first 2 days, and drops to 3.85 over the entire 0–6-day period (Gillespie proposal) because it includes Days 2–6 with F = 1.61. Prolonging the period of study therefore causes lowered efficiency. The question of whether the sterilizing activity of drugs can be measured requires separate regression analyses starting at Day 2 or later (3, 5). In summary, the proposed method should be rejected since it uses an incorrect model, is potentially biased, and is inefficient. Further, values of Vt, measured over 5 days, could not be compared with the considerable body of EBA results already obtained for most drugs over the first 2 days only.
St George's Hospital Medical School London, United Kingdom REFERENCES
From the Authors:It is erroneous to suggest that our model is "mathematically equivalent to the usual procedure." The older method does not use linear regression, as only two points are used, not the minimum of three required. Rather, the equation represents EBA as half of the ratio between the Day 0 and Day 2 viable counts expressed as a log (1). It is important to recognize that EBA is a ratio: variation in either the initial or final value will have profound effects on the result, affecting less bactericidal drugs more than highly bactericidal drugs. This phenomenon has been recognized in studies of forced expiratory volume in patients with chronic obstructive pulmonary disease, where variability inherent in the measurement method may have obscured biological variation (2). Thus, the failure of "standard" EBA to identify the activity of important antituberculosis agents, like pyrazinamide, can be explained (3).Sodium hydroxide does not appear to alter the way in which the sputum viable count declines. It does reduce the sputum viable count by approximately one log but specimen series follow an exponential decay curve with an r2 of 1.0 whether decontaminated with sodium hydroxide or inoculated onto selective medium. The values for vt50 for two patients were as follows: Patient A, 0.31 days (r2 1.0), and 0.39 days (r2 1.0); and Patient B, 0.4 days (r2 1.0), and 0.5 days (r2 1.0) with and without sodium hydroxide decontamination, respectively. The use of the term "k" in Mitchison's letter is confusing as he employs it to refer to the slope of the two lines that he draws; in our model "k" refers to the exponential decay constant calculated by computer. We believe that the purpose of early bactericidal activity studies in Phase II of a drug's development should not be to distinguish between regimens but to determine whether an agent has activity against M. tuberculosis in the human host. Thus, the difference between the initial and final sputum count is the most important measure. A range of different methods has been proposed to deal with the variation found in previously reported studies (1, 3, 4). The data that we have analyzed fits our model closely, giving confidence that it is valid and may be used to analyze data in new studies (5). Whether our reiterative exponential decay model is useful will be determined by future clinical investigators who test it with new data in comparison with older methods.
University College London, Royal Free Campus London, United Kingdom REFERENCES
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