Gross Overestimation of Total Allowable Error Based on Biological Variation

To the Editor: The factor 1.65 implies that 95% of the results (1-sided) will fall within the TE limit, given a gaussian distribution. Values for CVb, CVw, and TEa are easily available (1), but where does this expression for TEa come from? The allowable imprecision has been derived with different methods (2). As Stöckl et al. (2) stated, “A striking feature is the fact that all of the individual approaches described above [in Stockel et al.'s text] recommend numbers for analytical standard deviation near or equal to 0.5 times the biological standard deviation.” This maximum analytical imprecision can easily be shown to add 12% to the biological variation. The bias in the TEa expression was derived by Gowans et al. (3). The analytical goals were calculated for the successful transfer of reference intervals between laboratories. A maximum of 4.6% of a normal population outside a reference limit (as opposed to 2.5% with zero bias and imprecision) was considered the maximum acceptable level on the basis of the IFCC guideline on the calculation of reference values with n = 120 (4). The maximum bias in the expression is valid only in cases when the imprecision equals zero. Fraser and Hyltoft Petersen were the first—to my knowledge—to combine these 2 criteria in a single expression (5). This expression was a quality goal and was meant for use in External Quality Assessment Service reports. For this expression, however, no theoretical basis was presented. Fraser and Hyltoft Petersen indicated, “However, when only a single determination of each survey material is used or allowed, the 95% acceptance range (for total error) for each laboratory from the target value is:” ± 1.65(0.5 × CVw) + 0.25 × (CVw2+ CVb2)1/2 {published version in (5):“ ± [1.65(12CV1) + 14(CV12+ CVG2)1/2]” As an example, the calculations for creatine kinase displayed in Fig. 1 are as follows (1): CVw = 22.8%, CVb = 40.0%, the maximum bias (SE) = 0.25 × (CVw2 + CVb2)1/2 = 11.5%, and the maximum analytical imprecision (CVa) = 0.5 × CVw = 11.4%. In the first model, analytical imprecision (CVa) and bias (SE) are related, as indicated by line SE (solid line). Curve TEa1 (dashed line) indicates the maximum combined bias and imprecision that fulfill the assumptions of the Gowans et al. model based on reference limits, with a maximum close to 1.65 × CVa(max). Conventional model TEa2 (dotted line) is indicated as a constant that combines the maximum values of bias and imprecision. As Gowans et al. showed (3), the maximum allowable bias and imprecision are interrelated, and they can be described in the curve presented in Fig. 1 for CK (the CVa–SE curve). The values for maximum bias and imprecision calculated above can be found in tables (1) and are the extremes in the CVa–SE curve. The maximum value of TEa in the curve (determined by inspection) is 18.9% (TEa1). This value is very close to 1.65 × CVa(max). In the conventional model, 2 maximum values for bias and imprecision, at the extremes of the curve, are added together to give the TEa2 estimate. This estimated TEa2 is a fixed number: TEa2=1.65 × (0.5 × CVw) + 0.25 × (CVw2 + CVb2)1/2)=30.3% Comparing 18.9% with 30.3%, we see that TEa is overestimated in the latter model. For different purposes, the maximum allowable imprecision and bias have been derived separately from data on biological variation. To combine these maximum values into a single expression has no theoretical basis and leads to gross overestimation of TEa. total error systematic error total allowable error interindividual imprecision intraindividual imprecision analytical imprecision