© 2003 American Thoracic Society
Bactericidal activity of antituberculosis drugsTo the Editor:Gillespie and colleagues (1) propose a new method of assessing the early bactericidal activity of antituberculosis drugs. They recommend that sputum samples are collected daily for at least 5 days and a reiterative single exponential decay model used to model the daily bacterial counts. There are several problems with their approach. For example, for Patient I4 they have counts on 6 days (Day 0, 1, 2, 3, 5, and 7), and the counts on Days 5 and 7 are both zero. Using their reiterative refinement to fit the exponential model, they omit the data for Days 0 and 1, leaving two non zero counts, and fit a 3 parameter exponential curve to the remaining data. As the number of observations equals the number of parameters, the fitted curve goes through all the observed data. Instead of fitting a model to their data they have fitted the data to their model. The model obtained after omitting half the observed non zero counts serves no useful purpose since it does not reflect the observed changes in bacterial counts with time. Far more data points would be required in order to reliably fit an exponential curve to the complete data for each patient. A five-parameter model with two exponential terms and a non zero asymptote would better reflect the underlying biological model of an initial rapid bactericidal phase, followed by a slower sterilizing phase. However, in order to reliably fit a double exponential model, daily sputum samples would be required from each patient for 2 or 3 weeks. Using the changes in the log10 counts over Days 0 to 2 (EBA) and Days 2 to 14 as summary measures (2) is a pragmatic and realistic approach. Finally, the acknowledgment of a statistician does not guarantee that their advice has been followed or that they have seen the paper before submission.
British Medical Research Council Clinical Trials Unit London, United Kingdom REFERENCES
From the Authors:An essential requirement for the reiterative exponential decay model for evaluating early bactericidal data is the need to have a minimum of four data points to fit a curve (1). Data points with zero values cannot be accepted for two reasons. First, the limit of detection of quantitative culture is between 102 and 103 cfu/mL. Thus negative cultures may represent samples in which there are less than 1,000 cfu/mL, true negative cultures or a failure of the culture medium to support the growth of small numbers of organisms. Secondly, as Doré and Nunn point out, to use only two points would be fitting the data to the model. The two points in question are not zero as the authors speculate but 5 x 103 cfu/ml and 2 x 104, giving four valid points with which the curve fitting program can calculate a valid curve.The new model does require further testing ideally using data over 14 days to confirm our preliminary observation that a model with two exponential terms does not describe the data significantly better than a model with one exponential term. We have now examined such data and confirmed our earlier result (1). We chose not to use linear regression because log transforming data assumes that the variation around each point follows a Gaussian distribution and that the standard deviation is the same at each value of x (2). Experience shows that this is not the case for EBA data and thus we believe that log transformation of early bactericidal data is inappropriate (3, 4). Although adding log10 counts over Days 0 to 2 and Days 2 to 14 has been used as a pragmatic approach for some years the shortcomings of this method have been recognized by many in the field (4, 5). We believe that the reiterative exponential decay model is a useful new tool for clinical researchers and we hope that others will evaluate it. From their experience we hope that the model can be improved so that we can speed the evaluation of new drugs for tuberculosis (5, 6).
University College London, Royal Free Campus London, United Kingdom REFERENCES
This article has been cited by other articles:
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
