A simple mathematical model to determine the ideal empirical antibiotic therapy for bacteremic patients.

Background: Local epidemiological data are always helpful when choosing the best antibiotic regimen, but it is more complex than it seems as it may require the analysis of multiple combinations. The aim of this study was to demonstrate a simplified mathematical calculation to determine the most appropriate antibiotic combination in a scenario where monotherapy is doomed to failure.

Methods: The susceptibility pattern of 11 antibiotics from 216 positive blood cultures from January 2012 to January 2013 was analyzed based on local policy. The length of hospitalization before bacteremia and the unit (ward or intensive care unit) were the analyzed variables. Bacteremia was classified as early, intermediate or late. The antibiotics were combined according to the combination model presented herein.

Results: A total of 55 possible mathematical associations were found combining 2 by 2, 165 associations with 3 by 3 and 330 combinations with 4 by 4. In the intensive care unit, monotherapy never reached 80% of susceptibility. In the ward, only carbapenems covered more than 90% of early bacteremia. Only three drugs combined reached a susceptibility rate higher than 90% anywhere in the hospital. Several regimens using four drugs combined reached 100% of susceptibility.

Conclusions: Association of three drugs is necessary for adequate coverage of empirical treatment of bacteremia in both the intensive care unit and the ward.