Documenting the linearity of an assay method has become a required practice in the clinical laboratory. Approaches to this procedure may present with extensive calculations and some ambiguities in interpretation. On the other hand, we know that the precision of most automated and semi-automated methods is very high, and that significant deviations of the squared correlation coefficient from 1.000 are usually the result of non-linearity of those methods. Because of this, we evaluated the use of the squared correlation coefficient as a screening method for linearity of automated and semi-automated assays in two different laboratories.

Fifty-one different automated and semi-automated assays were evaluated at the University of Pittsburgh Medical Center and twenty-eight at the Magee-Women's Hospital. The squared correlation coefficients were calculated using spread sheet regression function, and the linearity plots were evaluated by three clinical pathologists as clinically acceptable or non-acceptable. The coefficients were then ranked in ascending order and plotted against this evaluation. A clear breakpoint at an R2 value of 0.9970 was found, with values above this considered acceptable and below this as non-acceptable.

We propose that the squared correlation coefficient can be used as a screening test for evaluating the linearity of all the automated and semi-automated tests. It is readily available in spread sheet functions, easy to calculate, and conceptually simple. Using this screen approximately 90 % of all tests in our laboratories can be shown to be sufficiently linear for clinical use. We also suggest an algorithm which we have found useful for evaluation of methods that do not meet this screening criterion.

CAP-provided material for linearity studies was used for most of the studies (CAP, Northfield, IL). Commercially-available material was used in some instances (Document TDM I Set, Casco Standards, Portland, ME). When purchased materials were not available, we used high and low patient samples diluted appropriately. An example of this dilution scheme has been outlined by Emancipator and Kroll. Most linearity samples were analyzed at five concentrations in duplicate, resulting in an R2 with eight degrees of freedom. In some cases four concentrations were used, but the specimens were analyzed in triplicate, giving an R2 with 10 degrees of freedom. In instances where Document TDM I Set were used, manufacturer's instructions were followed, with duplicate values obtained for at least 7 different concentrations.

The assayed results in each case were placed in a spread sheet (QuatroPro, Borland), placing the concentration obtained from the analysis on the Y axis and the proportion of the highest linearity sample on the X axis. For example a linearity standard prepared with 3 parts of the low standard and 2 parts of the high standard was plotted as 0.4. For each set of data we obtained the squared correlation coefficient, provided as part of the programmed regression calculation in the program. The plots of these data were presented to three chemical pathologists for their clinical evaluation of the linearity of each curve over the specified range for each assay. The correlation coefficients were not made available to the reviewers at this time. The reviewers were asked to judge each curve as either clinically acceptable linearity or clinically unacceptable linearity. If professional judgment were not in full agreement, we classified the curves as borderline acceptable.

We have ranked 51 methods by ascending squared correlation coefficients in Table 1, along with the ranges evaluated for linearity, and the classification by the reviewing pathologists. The squared correlation coefficients were plotted against rank in Fig.2a. A clear break in this plot can be seen at an R2 of 0.9970, with values below this point associated with curves that were considered nonlinear by the reviewers. To ascertain whether this specific breakpoint could be a relevant indicator in other laboratories, we repeated the study in a different hospital (Table 2 and Fig. 2b). The breakpoint of 0.9970 appeared to be valid for this laboratory as well.

Those methods deemed "non-acceptable" indicate that further work and professional input is needed to define acceptable and useful range. This does not necessarily mean that the method is not useful in the clinical laboratory.

- First, check the precision of the method. Poor precision can potentially be a problem with an automated method, although this
- must be relatively rare from our experience. The precision error can be minimized by doing the linearity checks with the same samples on the same day on the same instrument.
- Second, check the quality of the linearity specimens. We found in some instances that the commercially-prepared materials did not dilute down accurately. For example, our bilirubin linearity samples showed marked curvature above 14 mg/dL, yet were acceptably linear well beyond the 20 mg/dL when prepared from patient specimens.
- Third, if R2 is still low, the method requires further evaluation. It should be kept in mind that some methods may show some nonlinearity in ranges where clinical decisions are not likely to be affected, e.g.., glucose below 30 mg/dL. In such instances the rapid turnaround time is more critical to the physician than the exact concentration of glucose.
- As a general precaution, however, any time nonlinear curves are used for analyses the nonlinearity should be documented in the procedure and the rules for using this curve in the linear and nonlinear portions should be carefully defined.

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