Three types of biological variation (CV_{B}) have been described: (1) intra-individual variation (CV_{I}), (2) inter-individual variation (CV_{G}), and (3) combined CV_{B} (combined CV_{I} and CV_{G}). As a surrogate for the biological variation [2], the empirical (biological) coefficient of variation (CV_{E}) has been proposed [1, 2]. According to Simundic et al. [4], CV_{E} could be termed CV_{A+I+G}.

The empirical biological variation CV_{E} derived from the reference interval (RI) was proposed because laboratories are obliged to provide RI for all measurands, must check their transferability (if taken from external sources), and should review the RI periodically as required by ISO 15189 [5]. Furthermore, reference limits (RL) usually vary less than data on biological variation in the literature and often are from consensus groups.

RLs reflect the biological variations, including the analytical variation. If values are normally distributed, the empirical (biological) standard deviation, s_{E}, can be estimated by (upper RL–lower RL)/3.92 [2]. However, a “true” empirical normal distribution does not exist in laboratory medicine. For small reference ranges and relatively high mean values (e.g., sodium and chloride concentrations in plasma or hematological quantities), the distribution usually looks close to “normal”, but a log-normal distribution has the same shape under these conditions. For relatively large reference ranges (e.g., thyreotropin, triglycerides, enzymes in plasma), it is obvious that the data are not normally distributed. Generally, it may be assumed that laboratory data follow a power normal distribution, i.e., (x^{λ}–1)/λ has a normal distribution, where the coefficient λ controls the shape of the distribution. Important special cases are λ=1, indicating a normal distribution, and λ=0, the lognormal distribution. The λ value for a specific data set can be estimated by numerical methods.

If λ is unknown and cannot be estimated from data, e.g., because only RLs are given, but there are no individual values, the assumption of a logarithmic distribution was recommended [6]. Assuming a lognormal distribution, the empirical standard deviation (s_{E}) is calculated from the lower reference limit (RL_{1}) and the upper reference limit (RL_{2}) by Eq. (1), as recently explained [2]:

$${\text{s}}_{\text{E},\mathrm{ln}}=\mathrm{(}lnR{L}_{2}-lnR{L}_{1}\mathrm{)}/\mathrm{3.92.}\text{\hspace{1em}(1)}$$(1)

Then, the CV_{E} of a logarithmic normal distribution expressed on the linear scale (CV_{E}*) can be calculated from Eq. (1), as explained in the Appendix:

$${\text{CV}}_{\text{E}}{}^{\ast}={\mathrm{(}\mathrm{exp}\mathrm{(}{s}_{E,ln}{}^{2}\mathrm{)}-1\mathrm{)}}^{0.5}\cdot 100.\text{\hspace{1em}(2)}$$(2)

CV_{E}* can be considered as a surrogate for the conventional biological variation (CV_{B}), although it also contains the analytical variation. The CV_{E}* values were compared (Figure 1) with the combined CV_{B} values [CV_{B}=(CV_{I}^{2}+CV_{G}^{2})^{0.5}] for 64 quantities (in blood, serum, and plasma) listed in the RiliBÄK [8]. The CV_{B} data were taken from Ricos et al. [7]. Although this list is already very comprehensive, CV_{B} data are available for only 80% of the RiliBÄK measurands. As shown in Figure 1, CV_{B} and CV_{E}* correlate quite well. The greatest divergences (above the regression line=black line in Figure 1) are obtained with C-reactive protein, CA 19-9, and prostate-specific antigen (PSA). In the Ricos et al. [7] list, a relatively high CV_{G} value of 130% is presented for CA 19-9. Erden et al. [9] more recently published a CV_{G}=64.2%, a value that appears more realistic. In , the intra-individual biological variation (CV_{I}) of PSA is compared from several reports. The most comprehensive survey was published by Söletormos et al. [10] on behalf of the European Group on Tumor Markers. The CV_{I} values from 13 studies varied between 2.1% and 22.9%. These large differences between studies make a choice of the correct CV_{B} value difficult. Ricos et al. [7] selected a CV_{I}=18.1, whereas a CV_{I} of about 13% (close to the mean of the reported span) would correlate with the CV_{E}* quite well.

Figure 1: Comparison of CV_{E}* values with combined CV_{B} values taken from Ricos et al. [7].

PSA, prostate-specific antigen; CRP, C-reactive protein.

Table 1: The intra-individual variability of plasma PSA reported by several researchers.

The empirical biological variation CV_{E}* derived from the reference range can be applied to derive permissible analytical uncertainty and to determine quantity quotients standardizing reporting laboratory results.

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