Infections due to antibiotic-resistant Gram-negative rods (GNRs) result in high associated mortality and frequently have poor treatment options. To determine risk factors for recovery on culture of antibiotic resistant GNRs, cases were retrospectively analyzed at a major academic hospital system from 2011-2016. Three separate classes of antibiotics were studied - colistin (analyzed separately for GNRs and for Klebsiella Pneumoniae), carbapenems (analyzed separately for ertapenem and anti-Pseudomonal carbapenems), and aminoglycosides (analyzed separately for gentamicin/tobramycin and amikacin). In each case, bivariate associations were determined and used to develop multivariate models predicting the presence of resistance to the chosen antibiotic. Models had c-statistics ranging from 0.63 to 0.89. Common predictors included male gender, medical comorbidities, transfer from another healthcare facility, indicators of mechanical ventilation or tracheostomy, and recent antibiotic exposure. We then compared two strategies of treating empirically with either meropenem or colistin and performed sensitivity analyses to determine which strategy was preferable in terms of cost (low acuity) and avoidance of mortality (high acuity strategy) under several willingness-to-pay thresholds. Under base case assumptions, the meropenem-first strategy dominated in low acuity patients at a meropenem resistance rate of up to 10.9%. In high acuity patients, the colistin strategy was preferable with a willingness-to- pay per avoided death as low as $46,231; at $468,750 per avoided death, the colistin- first strategy was preferable with meropenem resistance rates as low as 5.5%. The model predicting likelihood of resistance to anti-Pseudomonal carbapenems can provide critical information in determining the optimal initial empiric antibiotic strategy.