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Centre for Child Health, Institute of Community Health Sciences, Queen Mary's Barts and the London School of Medicine and Dentistry, University of London
Department of Medical Microbiology, Barts and The London NHS Trust, London, United Kingdom
We write to comment on the article by Cespedes et al. [1] regarding the nasal carriage of >1 strain of Staphylococcus aureus. In particular, we challenge the usefulness of the mathematical model presented in their article.
The article reports on the prevalence of colonization with multiple strains (defined as "discordant") of S. aureus in 2 populations: one consisting of subjects in a methadone maintenance program, and the other consisting of patients admitted to the Montefiore Medical Center (MMC). The presence of this discordance was detected by the analysis of 3 colonies from the initial sample.
What was the rationale for the choice of 3 colonies for subsequent analysis This is clearly an important decision that determines the power of the study to detect carriage of >1 strain and, thus, to determine the level of discordance. Oddly, in one case (table 1, sample 1503), which was one of the initial 4 discordant samples, 4 colonies were selected for analysis. Why Had only 3 colonies been tested from this sample, this might well have excluded the single discordant isolate, and the number of observed discordant events thus would have been reduced to 3 instead of 4. It is not clear to us why samples 1117, 1490, and 0783 are not defined as discordant, since they contain S. aureus isolates that differ by >3 bands on pulsed-field gel electrophoresis and that are of >1 spa or multilocus sequence typing type. It is unfortunate that the data from the results of resampling are not shown in full. Finally, why are the MMC data not used in the mathematical model exercise
The content of the article is clinically very relevant to the problem of nosocomial infection. Competition for colonization space between methicillin-resistant and -sensitive S. aureus (MRSA and MSSA, respectively) would lead to a lower frequency of simultaneous cocolonization than that expected by chance [2]. If these strains compete, broad-spectrum antimicrobial administration, which asymmetrically affects MSSA and MRSA, would select in favor of MRSA infection of hospital inpatients. Although Cespedes et al. did not directly address this question, since this was not the main point of their study, the data they have collected have the potential to shed light on this related area, and we urge them to publish it.
The reasons for using the probabilistic model are not clear. One possible reason is that, on resampling the 4 true originally discordant samples, only 2 were confirmed as discordant, whereas, of the 18 originally concordant samples, 16 were confirmed as concordant (2 failed to grow). Cespedes et al. may be suggestingon the basis of this small samplethat direct observation of the proportion discordant cannot be trusted as a true measure of discordance in the S. aureuscolonized population. This fraction is defined as the probability originally discordant, P(OD), or, alternatively, as the symbol . If we define SC, OC, and OD as "sample concordant," "originally concordant," and "originally discordant," respectively, it would be possible to estimate indirectly from the knowledge of the proportion of concordant samples (which Cespedes et al. trust much more) from the equation
which is a standard result of probability theory. In other words, this is equal to the probability of being originally concordant and sample concordant plus the probability of being originally discordant but sample concordant. The laws of probability do the rest:
where P(SC|OC) is the probability of being sample concordant in those originally concordant, etc. This is equivalent to
Cespedes et al. then enter the numbers in place of probability symbols:
On rearranging, we obtain
rearranging again, we obtain = 2 × [1-(117/121)] = 0.066, or 6.6%. The alarming finding would be that the proportion discordant is neither 3.3% (as expected from the original sample: 100 × 4/121) nor 1.7% (as expected from the resampling results: 100 × 2/121), but 6.6%! The flaw in this argument is that P(SC) is not 117/121 but 119/121, as equation (1) would suggest. This is because, if it is assumed that all 117 samples that were originally concordant remain concordant on resampling (as Cespedes et al. implicitly assume from a resampling of 18 samples), P(SC) in equation (1) equals 117/121 + 2/121 = 119/121. When we replace this number in equation (2), we obtain = 3.3%, which is exactly the same as the result obtained by the simple mathematical calculation 4/121 × 100, and the mathematical model would become redundant. We would accept 3.3% as the proportion discordant, although the binomial 95% confidence interval is 1.3%8.2%. Nonetheless, had the authors chosen to test >3 colonies per sample, they might have observed a larger number of discordant samples.
References
1. Cespedes C, Sad-Salim B, Miller M, et al. The clonality of Staphylococcus aureus nasal carriage. J Infect Dis 2005; 191:44452. First citation in article
2. Dall'Antonia M, Coen PG, Wilks M, Whiley A, Millar M. Interference between methicillin-sensitive and -resistant Staphylococcus aureus in the anterior nares. J Hospital Infect (in press). First citation in article