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

Medical institutions are under increased economic pressure to schedule elective surgeries efficiently to contain the costs of surgical services. Surgical scheduling is complicated by variability inherent in the duration of surgical procedures. Modeling that variability, in turn, provides a mechanism to generate accurate time estimates. Accurate time estimates are important operationally to improve operating room utilization and strategically to identify surgeons, procedures, or patients whose duration of surgeries differ from what might be expected.

The authors retrospectively studied 40,076 surgical cases (1,580 Current Procedural Terminology-anesthesia combinations, each with a case frequency of five or more) from a large teaching hospital, and attempted to determine whether the distribution of surgical procedure times more closely fit a normal or a log-normal distribution. The authors tested goodness-of-fit to these data for both models using the Shapiro-Wilk test. Reasons, in practice, the Shapiro-Wilk test may reject the fit of a log-normal model when in fact it should be retained were also evaluated.

The Shapiro-Wilk test indicates that the log-normal model is superior to the normal model for a large and diverse set of surgeries. Goodness-of-fit tests may falsely reject the log-normal model during certain conditions that include rounding errors in procedure times, large sample sizes, untrimmed outliers, and heterogeneous mixed populations of surgical procedure times.

The authors recommend use of the log-normal model for predicting surgical procedure times for Current Procedural Terminology-anesthesia combinations. The results help to legitimize the use of log transforms to normalize surgical procedure times before hypothesis testing using linear statistical models or other parametric statistical tests to investigate factors affecting the duration of surgeries.