Calculation of limits for significant unidirectional changes in two or more serial results of a biomarker based on a computer simulation model

Abstract

Background: Reference change values (RCVs) were introduced more than 30 years ago and provide objective tools for assessment of the significance of differences in two consecutive results from an individual. However, in practice, more results are usually available for monitoring, and using the RCV concept on more than two results will increase the number of false-positive results. Therefore, a simple method is needed to interpret the significance of a difference when all available serial biomarker results are considered.

Methods: A computer simulation model using Excel was developed. Based on 10,000 simulated data from healthy individuals, a series of up to 20 results from an individual was generated using different values for the within-subject biological variation plus the analytical variation. Each new result in this series was compared to the initial measurement result. These successive serial relative differences were computed to give limits for significant unidirectional differences with a constant cumulated maximum probability of both 95% (P < 0.05) and 99% (P < 0.01).

Results: Factors used to multiply the first result from an individual were calculated to create the limits for constant cumulated significant differences. The factors were shown to become a simple function of the number of results and the total coefficient of variation.

Conclusions: To interpret unidirectional differences in two or more serial results of a biomarker, the limits for significances are easily calculated using the presented factors. The first result is multiplied by the appropriate factor for increase or decrease, which gives the limits for a significant difference.

Keywords: Simulation models; biological variation; log-normal (Gaussian) distribution; monitoring; normal (Gaussian) distribution; reference change value; unidirectional differences.