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.

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

“…As also previously found 9 we have shown that the practical use of traditional RCV calculations applied on normally distributed data will produce too many false positive results especially for high values of CV T , compared to theoretical RCV calculations. On the other hand, the calculated RCF up factors are comparable for both normal and ln-normal distributions up to CV T ¼ 20.0% (Table 1), but not for RCF down factors The RCF down factor is < 0 (negative) and therefore the significant limit is zero (0) because a negative concentration makes no sense.…”

“…The method has been described in detail in a previous publication associated with significant unidirectional changes in serial results. 9 Briefly, the method is described here with the modifications associated with significant bidirectional changes in serial results.…”

“…The RCF up and RCF down factors were determined based on 10,000 simulated normally distributed results and 10,000 ln-normally distributed results. The RCF factors were calculated for different sets of results (consisting of 2, 3,4,5,6,7,8,9,10,15 and 20 serial results) and for different percentages of CV T (10.0, 20.0, 30.0 and 40.0%). When significant limits for bidirectional changes are calculated with a probability of 95% (p < 0.05), the total false positive rate is 5%.…”

A note on the calculation of reference change values for two consecutive normally distributed laboratory results

“…[6]. Several manuscripts can be found in this field, for example [3,[9][10][11]. The approach defines criteria for normal variation in two sequential measurements, which mathematically are often defined as…”

“…[6]. Several manuscripts can be found in this field, for example [3,[9][10][11]. The approach defines criteria for normal variation in two sequential measurements, which mathematically are often defined as The calculation of RCVs for many different laboratory outcomes is quite simple since all laboratories know approximately the analytical and intra-individual variabilities for medical laboratory results from samples from the healthy population.…”