Probability of Eradication Using Vancomycin Alone or in Combination for Methicillin-Resistant Staphylococcus aureus Bacteremia

LETTER

I read with interest the paper of Dilworth et al. (1), entitled “β-Lactams Enhance Vancomycin Activity against Methicillin-Resistant Staphylococcus aureus Bacteremia Compared to Vancomycin Alone.” The results are intriguing, but important misstatements merit attention. It is stated on page 104 that based on adjusted odds ratios, “Combo” patients were 11.24 times more likely than “Van-alone” patients to achieve microbiologic eradication and hemodialysis patients were 24 times less likely to achieve eradication than nonhemodialysis patients. Neither statement is correct. The odds ratio is exactly that: a ratio of two odds, which in this particular case is the odds of eradication (ratio of number of eradications to number of failed eradications) for the Combo or hemodialysis group divided by the odds of eradication for the Van-alone or nonhemodialysis group, respectively. The likelihood or risk of an occurrence based on an exposure, which is what the statements actually refer to, is relative risk, the ratio of the probability of eradication for the Combo or hemodialysis group to the probability of eradication in the respective nonexposed group. The importance of this distinction is shown by calculating the unadjusted odds ratio for the Combo compared to Van-alone (Table 3 of the paper). The odds ratio is 48/2 (ratio of number of eradications to number of eradication failures for the Combo) divided by 24/6 (ratio of number of eradications to the number of eradication failures for Van-alone), which equals 6 (comparable to the adjusted value of 5.15 in Table 4). The relative risk, however, is 48/50 (96%) (probability of eradication in the Combo group) divided by 24/30 (80%) (probability of eradication in the Van-alone group), which equals 1.20, a 20% greater likelihood of eradication in the Combo group than the Van-alone group, not 6 times. It can be estimated from the adjusted odds ratio of 11.24 (Table 5) for the Combo group that this corresponds to a 27% greater likelihood of eradication than for the Van-alone group, not 11.24 times.

Raw data for hemodialysis are not provided but can be estimated from the odds ratio of 0.07 (Table 4). There are 8 failed eradications, 72 eradications, and 12 hemodialysis cases; thus, eradication occurred in 7 of 12 (58%) hemodialysis cases versus 65 of 68 (96%) nonhemodialysis cases. The relative risk is 0.60, a 40% (not 24 times) lower likelihood of eradiation for hemodialysis compared to nonhemodialysis. These points are critical for proper understanding of the magnitude of the benefit of the vancomycin combination and the risk of hemodialysis (the strongest predictor of failed eradication) for failed eradication, and the erroneous conclusions in the discussion should be corrected in an erratum. Moreover, although the numbers of hemodialysis cases are the same in the Combo and Van-alone groups, these make up 12% of the former and 20% of the latter. At least 3 and possibly all 5 failed eradications with hemodialysis occurred in the Van-alone group, raising the strong possibility that confounding factors related to hemodialysis and not use of the Combo could account for the results.