Reference Interval Estimation from Mixed Distributions using Truncation Points and the Kolmogorov-Smirnov Distance (kosmic)

Abstract

Appropriate reference intervals are essential when using laboratory test results to guide medical decisions. Conventional approaches for the establishment of reference intervals rely on large samples from healthy and homogenous reference populations. However, this approach is associated with substantial financial and logistic challenges, subject to ethical restrictions in children, and limited in older individuals due to the high prevalence of chronic morbidities and medication. We implemented an indirect method for reference interval estimation, which uses mixed physiological and abnormal test results from clinical information systems, to overcome these restrictions. The algorithm minimizes the difference between an estimated parametrical distribution and a truncated part of the observed distribution, specifically, the Kolmogorov-Smirnov-distance between a hypothetical Gaussian distribution and the observed distribution of test results after Box-Cox-transformation. Simulations of common laboratory tests with increasing proportions of abnormal test results show reliable reference interval estimations even in challenging simulation scenarios, when <20% test results are abnormal. Additionally, reference intervals generated using samples from a university hospital's laboratory information system, with a gradually increasing proportion of abnormal test results remained stable, even if samples from units with a substantial prevalence of pathologies were included. A highperformance open-source c++ implementation is available at https://gitlab.miracum.org/kosmic.

A Framework for Criteria-Based Selection and Processing of Fast Healthcare Interoperability Resources (FHIR) Data for Statistical Analysis: Design and Implementation Study

“…Here, we demonstrate how reference intervals for a very common laboratory test (hemoglobin) can be established using the tools developed in this study and the open source kosmic [ 25 ] algorithm, despite a very high proportion of abnormal findings in the analyzed data set (ie, in-patient laboratory findings from a tertiary care center). To reduce the number of abnormal findings, we excluded all patients with cancer diagnoses (defined by ICD codes starting with C ) and those who received transfusions (defined using OPS codes starting with 8-80 ) at any time.…”

Establishment of PIVKA-Ⅱ Reference Intervals From Hospital-stored Data: A Comparison Analysis

“…The parameters of the normal distribution (µ, σ), the Box-Cox-transformation parameter (λ), and the truncation interval T are optimized numerically, consistent with previous work 17 . To provide confidence intervals, the authors used bootstrapping of the original dataset (random sampling with replacement).…”

Influence of Turkish origin on hematology reference intervals in the German population

“…To calculate reference intervals and corresponding confidence intervals, we used an indirect data mining approach 29 . The applied kosmic algorithm assumes that a dataset obtained as explained above is composed of a major fraction of physiological test results and a minor fraction of pathological test results.…”

“…The estimated normal distribution of the remaining central part is used to calculate the 2.5th and 97.5th percentiles, which are defined as the limits of the reference interval. Additionally, the algorithm offers a quantitative measurement of the precision of the reference limits by calculating confidence intervals using a bootstrapping procedure (repeated random sampling with replacement) 29 . The algorithm has been applied in various publications and has proven to provide valid results even if the input dataset contains up to 20–30% pathological test results (e.g.…”

“…The algorithm has been applied in various publications and has proven to provide valid results even if the input dataset contains up to 20–30% pathological test results (e.g. of patients from intensive care units) 20 , 29 , 30 . We used a Python binding to the kosmic algorithm and calculated the 90% confidence interval for each reference limit with n = 100 bootstrap samples.…”