To the Editor
Glance et al1 compared anesthesia times among hospitals using Anesthesia Quality Institute (AQI) data. They appear not to have considered our 2013 Statistical Grand Rounds in the Journal on how to validly compare anesthesia times among hospitals.2
Weibull and log-normal distributions for modeling durations have 2 parameters. The authors’ survival analysis may have compared only one of the parameters and assumed homogeneity of the second (“ancillary”) parameter among hospitals. Appropriate managerial decision making to reduce the hours that anesthesiologists work late causes heterogeneity among facilities in both parameters.2 This is especially relevant for the current study, because anesthesia billing times were used as surrogates for surgical times, the latter generally absent in AQI data.3 Anesthesiology groups vary in what periods they include for anesthesia time-unit billing. For example, the in-room to out-of-room time is used as the anesthesia start and end times at 1 institution where R.H.E. is affiliated; some preoperative and postoperative activities are included at the other (26.5 [11.8] [standard deviation] minutes per case).
We raise 2 questions. What are the 6 P values for each of the authors’ 6 studied procedures for heterogeneity of the ancillary parameter among facilities? If statistically significant, would this be inconsistent with the assumptions of the authors’ analyses? Knowing more about the mixed-effects survival analysis used by the authors is important because there are at least 2 other published ways to compare duration data among hospitals.2,4
First, generalized pivotal methods can be used for comparisons of durations among groups, as reviewed in the Journal’s Statistical Grand Rounds series.2,5 Such methods permit comparison not only of medians, as the authors did, but also average times (ie, costs) and the longest durations that cases might take (ie, maximum expected costs).2,5 Generalized pivotal methods are suitable both for log-normal distributions, as in our articles, and for Weibull distributions, as assumed by the authors.2–5
Second, because the authors compared only medians among facilities, they could have used batching (binning), which was how we previously compared AQI data anesthesia times.4,5 The absence of risk adjustment for uncommon patient characteristics (eg, “emergent” surgery for knee replacement) is irrelevant for such analyses because the median is uninfluenced by outliers. The process is as follows. For each 4-week period during the studied year (or month), calculate each hospital’s median duration among cases as a summary measure. Use the N = 13 four-week periods (or N = 12 months) to calculate the mean and standard error of the period’s median. From the Central Limit Theorem, simple analysis of variance can then be used to compare facilities. In the Appendix of our article, sensitivity analysis showed validity of this method for comparing durations among facilities.4 Not only did median durations differ >2-fold among hospitals, so did the coefficients of variation.4 The implication is the importance of statistical analyses to take variability of both Weibull/lognormal/gamma parameters into account. We are concerned that such considerations of this variability may not have been incorporated in the analyses performed by Glance et al,1 affecting their results.
Franklin Dexter, MD, PhD, FASA
Department of Anesthesia
University of Iowa
Iowa City, Iowa
Richard H. Epstein, MD
Department of Anesthesiology, Perioperative Medicine and Pain Management
University of Miami
Department of Anesthesiology
Sidney Kimmel Medical College at Thomas Jefferson University
1. Glance LG, Dutton RP, Feng C, Li Y, Lustik SJ, Dick AW. In response. Anesth Analg. 2018;127:e34–35.
2. Dexter F, Epstein RH, Bayman EO, Ledolter J. Estimating surgical case durations and making comparisons among facilities: identifying facilities with lower anesthesia professional fees. Anesth Analg. 2013;116:1103–1115.
3. Epstein RH. Quality improvement demands quality data. Anesth Analg. 2015;121:1425–1427.
4. Flood P, Dexter F, Ledolter J, Dutton RP. Large heterogeneity in mean durations of labor analgesia among hospitals reporting to the American Society of Anesthesiologists’ Anesthesia Quality Institute. Anesth Analg. 2015;121:1283–1289.
5. Ledolter J, Dexter F, Epstein RH. Analysis of variance of communication latencies in anesthesia: comparing means of multiple log-normal distributions. Anesth Analg. 2011;113:888–896.