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We asked if the factors that predict overall mortality following two common surgical procedures are different from those that predict adverse occurrences (complications) during the hospitalization or death after an adverse occurrence, which we refer to as “failure to rescue.” We examined 5,972 Medicare patients undergoing elective cholecystectomy or transurethral prostatectomy using three outcome measures: 1) the death rate (number of deaths/number of patients); 2) the adverse occurrence rate (number of patients who developed an adverse occurrence/number of patients); and 3) the failure rate (number of deaths in patients who developed an adverse occurrence/number of patients with an adverse occurrence). The death rate was associated with both hospital and patient characteristics. The adverse occurrence rate was associated primarily with patient characteristics. In contrast, failure to rescue was associated more with hospital characteristics, and was less influenced by patient admission severity of illness as measured by the MedisGroups score. We concluded that factors associated with hospital failure to rescue are different from factors associated with adverse occurrences or death. Understanding the reasons behind variation in mortality rates across hospitals should improve our ability to use mortality statistics to help hospitals upgrade the quality of care.