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It is naive and incorrect to use the proportions of successful operations to compare the performance of surgeons because the patients‘‘ risk profiles are different. In this paper, we explore the use of risk‐adjusted procedures to compare the performance of surgeons. One such risk‐adjusted statistic is the standardized mortality ratio （SMR）, which measures the performance of a surgeon adjusted for the risks of patients assuming the average performance of a group of surgeons. Unlike the traditional SMR which is defined based on a population, this SMR is a random variable. Thus, all existing results for the traditional SMR are not valid unless the sample is large enough to be considered a population. In this paper, we develop two risk‐adjusted procedures for comparing the performance of surgeons. The asymptotic distributions of the test statistics are derived. We also use the bootstrap procedure to estimate finite‐sample distributions. Both probability of type I error and power of these procedures are investigated. Copyright ? 2017 John Wiley And Sons, Ltd.
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