Modeling the uncertainty of surgical procedure times - Comparison of log-normal and normal models

Background: Medical institutions are under increased economic pressure to s chedule elective surgeries efficiently to contain the costs of surgical ser vices. Surgical scheduling is complicated by variability inherent in the du ration of surgical procedures. Modeling that variability, in turn, provides a mechanism to generate accurate time estimates. Accurate time estimates a re important operationally to improve operating room utilization and strate gically to identify surgeons, procedures, or patients whose duration of sur geries differ from what might he expected. Methods: The authors retrospectively studied 40,076 surgical cases (1,580 C urrent Procedural Terminology-anesthesia combinations, each with a case fre quency of five or more) from a large teaching hospital, and attempted to de termine whether the distribution of surgical procedure times more closely f it a normal or a log-normal distribution. The authors tested goodness-of-fi t to these data for both models using the Shapiro-Wilk test. Reasons, in pr actice, the Shapiro-Wilk test may reject the fit of a log-normal model when in fact it should be retained were also evaluated. Results: The Shapiro-Wilk test indicates that the log-normal model is super ior to the normal model for a large and diverse set of surgeries. Goodness- of-fit tests may falsely reject the lognormal model during certain conditio ns that include rounding errors in procedure times, large sample sizes, unt rimmed outli ers, and heterogeneous mixed populations of surgical procedure times. Conclusions: The authors recommend use of the log-normal model for predicti ng surgical procedure times for Current Procedural Terminology-anesthesia c ombinations, The results help to legitimize the use of log transforms to no rmalize surgical procedure times before hypothesis testing using linear sta tistical models or other parametric statistical tests to Investigate factor s affecting the duration of surgeries.