title: Analyzing intensive care unit length of stay data: problems and possible solutions.
abstract: OBJECTIVE
  To explore methods of evaluating the length of stay patterns of intensive care unit (ICU) patients. It was hypothesized that the mean does not adequately describe the typical length of stay (central tendency) because distribution patterns are often markedly skewed by patients with extended stays. Therefore, other descriptors are needed. In addition, ways are needed to identify outliers-patients with stays longer or shorter than the bulk of the data.
  
  
  METHODS
  Review of retrospective data.
  
  
  METHODS
  University hospital surgical ICU.
  
  
  METHODS
  Representative data included all (4,499) patients admitted over a 6-yr period. Each was assigned to a diagnostic group that represented either a frequently performed surgical procedure (e.g., thymectomy) or in cases where there was no predominant procedure, a surgical discipline (e.g., otolaryngology).
  
  
  METHODS
  None.
  
  
  RESULTS
  The frequency distributions were usually skewed to the right and included two populations of interest: The portion with the majority of observations ("body"), which described "typical" behavior, and the "tail", which provided information on outliers. The average of the mean lengths of stay of all diagnostic groups was higher than the average of the medians (3.9 +/- 1.8 [SD] vs. 2.7 +/- 1.1 days, p < .001) and modes (2.1 +/- 1.2 days, p < .001), reflecting the rightward skewness of the length of stay frequency distributions. The median +/- 1 day included 75 +/- 13% of the patients, thus confirming that the median was the most useful descriptor of central tendency. Various methods were used to identify outliers. Histograms of the frequency distributions were examined and outliers visually identified. Conventional outlier analysis labeled as outliers patients staying greater than two standard deviations from the mean stay. This method underestimated the number of outliers when the distributions were skewed to the right. Another method involved designating a specific length of stay (e.g., 7 or 10 days) or percentage of patients as the outlier threshold. Each method designated different numbers of patients as outliers.
  
  
  CONCLUSIONS
  When analyzing length of stay data it is important to visually examine the frequency distribution because it is often skewed to the right. This skewness renders traditional parameters such as the mean and standard deviation less useful for describing the typical length of stay. Instead, the median, mode, and harmonic mean should be used. When reporting length of stay, some indication of the characteristics of the data should be presented. A graph of the frequency distribution rapidly allows the reader to determine its shape. A simple method is to report the mean, median, and range.
authors.affiliation: Department of Anesthesiology, College of Physicians and Surgeons, Columbia University, New York, NY, USA.
authors.forename: C
authors.initials: C
authors.lastname: Weissman
mesh_terms: D015982:Bias; D003627:Data Interpretation, Statistical; D006302:Health Services Research / Q000379:methods* / Q000592:standards; D006801:Humans; D007362:Intensive Care Units; D007902:Length of Stay / Q000706:statistics & numerical data*; D016311:Outliers, DRG; D015203:Reproducibility of Results; D012189:Retrospective Studies