title: Patient result median monitoring for clinical laboratory quality control.
abstract: BACKGROUND
  Statistical process control is foundational in laboratory medicine. It typically uses artificial control specimens and can detect some, but not all, analytical defects. A practical, robust method to more directly detect trends in patient results, such as monitoring mean or median patient results, is desirable.
  
  
  METHODS
  We generated a simulated set of laboratory results from a normal distribution, and also downloaded sequential patient results for serum sodium and CA 19-9. For each of the three data sets we calculated the standard error of the mean and estimated the standard error of the median by bootstrapping.
  
  
  RESULTS
  The standard error of the mean is a practical, easily calculated summary statistic that can be used to construct control charts. The standard error of the median, cannot be reliably estimated without using bootstrap methods, but is more resistant to outliers. Our study confirms a simple relationship between the variance of the median and the variance of the mean, i.e., for Gaussian distributions, Var[Median]/Var[Mean]=π/2. We also confirm that for skewed distributions, the median is more stable than the mean, implying Var[Median]/Var[Mean]<1. Finally, we establish a sample size of 200 individual patient results as sufficient for monitoring medians for data from approximately Gaussian distributions.
  
  
  CONCLUSIONS
  Monitoring patient result medians represents a practical, statistically self-consistent approach to laboratory quality control.
authors.affiliation: ARUP Laboratories, Institute of Clinical and Experimental Pathology, Salt Lake City, UT 84108, USA. Andrew.wilson@aruplab.com
authors.forename: Andrew
authors.initials: A
authors.lastname: Wilson
authors.forename: William L
authors.initials: WL
authors.lastname: Roberts
authors.forename: Igor
authors.initials: I
authors.lastname: Pavlov
authors.forename: Jo
authors.initials: J
authors.lastname: Fontenot
authors.forename: Brian
authors.initials: B
authors.lastname: Jackson
mesh_terms: D019411:Clinical Laboratory Techniques / Q000592:standards*; D006801:Humans; D011786:Quality Control; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity