Patient result median monitoring for clinical laboratory quality control

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]