SURGICAL PROCEDURE TIMES ARE WELL MODELED BY THE LOGNORMAL DISTRIBUTION

Abstract

S47 INTRODUCTION: Efficient scheduling of elective surgeries in a hospital is complicated by the variability inherent in surgical procedures, so that accurate modeling of time distributions is the essential first step in constructing a scheduling system. In the literature, both normal [1] and lognormal [2] distributions have been proposed for describing surgical times. In this study, we fitted lognormal distributions to surgeries characterized by single Current Procedural Terminology (CPT) codes and tested the goodness of those fits statistically to determine whether the lognormal is a suitable model for predicting the duration of surgical procedures. METHODS: We reviewed all surgical cases performed at a large teaching hospital over a 6 year period (46,317 surgical cases and 5,122 different procedures). Each procedure was categorized by CPT code and type of anesthesia and then fitted to a lognormal distribution. 1956 procedures were omitted due to insufficient surgical cases. Closeness of fit to a lognormal distribution was tested using Lilliefors tests and the results categorized as no fit (P <0.01), poor fit (0.01 <or=to P <0.1), and good fit (P >or=to 0.1). To examine the effect of sample size on goodness of fit, the data were further segmented by sample size into small (n < 30), medium (30 <or=to n < 200), and large (n >or=to 200) groups. Chi-square tests were used to determine whether goodness of fit was independent of sample size by category. We analyzed both surgical times (ST) and total times (TT) with similar results. RESULTS: Good fits were obtained for lognormal distributions for the majority of procedures for ST and TT. The goodness of fit to lognormals was dependent on sample size with good fits for 91% of small and 60% of medium sized samples. Only 21% of samples with n > 200 fit for ST. Chi-square tests for independence showed dependence of the fit on sample size by category (P < 0.00). CONCLUSIONS: ST and TT data were best fit to the lognormal model for the majority of procedures with small and medium sized samples. Procedures with large sample sizes were not as well modeled as smaller samples. Our findings are important because they confirm that a lognormal model, supported by adequate data could be used to model surgical time durations. Good models of time durations are essential for better scheduling systems. Better scheduling systems can increase operational efficiency. (Table 1)Table 1: Goodness of Fit versus Category Size for ST (Count, Row %)