## BACKGROUND

Once upon a time, routine laboratories had the competence and capacity to develop new principles and methods of measurements; for example, blood gases by Paul Astrup in Copenhagen and immunological methods for minute hormone concentrations by Leif Wide in Stockholm and Roger Ekins in London. Also, principles developed in basic science were earlier explored, for example, mass spectrometry using isotope dilutions by Ingemar Björkhem in Stockholm in the search for reference methods. Nowadays, resources of industry are usually required to develop methods for the routine laboratory. However, discovery of new diagnostic markers and techniques to measure their concentration can be traced to a hospital laboratory, for example, cystatine C by Anders Grubb in Malmö. In some cases, new techniques have led to the establishment of thriving industries, for example, Hemocue in Ängelholm.

All IVD instruments and reagents that will be “put on the market” must be documented and approved by an official agency. In Europe, the documentation must get a CE mark,^{1} and in the United States, an approval procedure by FDA is mandated. The approval focuses on risks associated with the use of the devices and documentation of their performance. Much of the responsibility of the IVD performance is hereby transferred from the laboratories to the manufacturers.

The approval procedure requires a thorough validation of the products to show that the device/reagent is fit for its purpose. For measurements, this includes, but is not limited to, trueness and precision, linearity, chemical interferences, carryover, and risk appraisal. The laboratories must verify that the procedures can be performed at least equally well in-house before they are commissioned to routine investigations.

Laboratories usually limit the verification to compare claims regarding trueness and precision, whereas the other criteria may be regarded as inherent to the method/instrument and left to the manufacturer to investigate and bring under control.

Validation and verification are based on statistical procedures. The outcome and interpretation of these depend on the model and what it is designed to illustrate. Thus, the number of samples, repeats, calibrators, sample material, and batch-to-batch variation appraisal are input variables that need consideration. Industry and users should agree on these procedures to make the manufacturers’ claims and the verification results of the laboratories comparable.

For this purpose, international standards and recommendations are available. They may be mandatory but are mostly voluntary, for example, the ISO standards. Standards rarely give concrete instructions or worked examples. However, guidance documents or recommendations provide exactly that.

Recommendations and standards will not be widely accepted and applied unless they capture the users’ different needs and expectations. Although electronic communications have simplified and shortened the consensus procedure, it may still take several years for a document to become accepted.

Besides ISO and CEN, the International Federation of Clinical Chemistry and Laboratory Medicine, the Joint Committee for Traceability in Laboratory Medicine (an international consortium sponsored by the Bureau International des Poids et Mesures), and the Clinical and Laboratory Standards Institute (CLSI) produce standards and recommendations. Briefly, the International Federation of Clinical Chemistry and Laboratory Medicine represents national professional societies, and the Joint Committee for Traceability in Laboratory Medicine has several stakeholders from the profession, industry, and metrology. The CLSI is a nonprofit organization that coordinates volunteer contributions from representatives of the profession, the regulatory agencies, and industry.

The CLSI has published a series of documents on the evaluation of laboratory methods, that is, the evaluation protocols (EPs). Recently, the Association for Clinical Biochemistry (ACB) in the United Kingdom published free downloadable documents and software,^{2} which describe minimal, yet powerful verification procedures in the laboratory.

## IMPRECISION FROM PATIENT SAMPLES OR REFERENCE MATERIALS

Imprecision is the numerical expression of precision and is reported as the SD or coefficient of variation. The SD is the square root of the variance, and the coefficient is the SD relative to the mean of the measurements. When the SD is calculated from repeated measurements of the same sample and unchanged conditions, the repeatability or within-series variation is obtained. The mean of the SD is underestimated, for mathematical reasons, if only few observations are considered; for example, if based on 2 observations, the mean underestimate is approximately 20% with a considerable dispersion. Therefore, it is imperative that any estimation of the SD is based on a sufficient number of observations (Fig. 1).

If conditions change between estimating the imprecision, for example, from one day to another or after recalibration of the measurement procedure, the imprecision is characterized as between-series imprecision. The end user is more interested in the combined imprecision or the intralaboratory imprecision, which can be estimated from the repeatability and the between-series imprecision. The laboratory needs to establish efficient methods to estimate all 3 types of imprecision.

The between-run variation is best estimated using a statistical procedure, the ANOVA, that is, analysis of variance. The ANOVA may be best known from estimating if there is a statistical difference between several series of measurements and its results are presented to answer that question in a standardized manner in most statistical packages and spreadsheet programs. The standard output is shown in Table 1.

An ANOVA can also be used to estimate the within- and between-series variation and provides a method to estimate the within-laboratory variation. The MS_{w} is the mean sum of square and is equal to the within-series variance. The MS_{b} includes the within-series variation and needs to be compensated:

where *n* is the mean number of observations in the series. The *s* _{b} ^{2} is the “purified between-series variance,” also called the “unbiased between-series variance” in statistical literature. The total, combined, or intralaboratory variance is

If the above correction is not made and the within-laboratory variance was estimated as the sum of MS_{b} and MS_{w}, it would be grossly overestimated.

At least 5 observations during 5 runs are suggested in the ACB software, but up to 10 observations in up to 10 series can be accommodated in the program; the more observations, the more reliable the results will be. The program will make all the calculations and display the outcome in a table and graph (Fig. 2 and Table 2).

If in measurements the MS_{b} were smaller than the MS_{w}, a negative *s* _{b} ^{2} would result.^{1} By convention, the MS_{b} is then set to 0, and the intralaboratory variance is equal to the within-series variance.

An estimate of the intralaboratory variation can be made either as a particular study according to the ACB protocol or by using data collected during weeks. Routinely obtained IQC data accumulated during a month with 2 to 3 daily replicate measurements can be used. There will be 30 series in the ANOVA, each with 2 to 3 observations. Despite the few within-day observations, the within-series degrees of freedom will be large and the estimates quite will be reliable. The program is not designed for this model, but the calculations can easily be performed in a spreadsheet using the ANOVA function and the formulas above for the calculation of the between-series variance^{1} and intralaboratory variation.^{2}

If the variances were estimated from all observations as if they belonged to one homogeneous data set, this would lead to an underestimate of the intralaboratory variance because the between-series variation is not taken into account. The magnitude of the underestimate cannot be stated in general terms. If such a value is used to establish IQC limits, the risk of “false alarms” will increase, which may affect the cost of quality management and increase the turnaround time.

The ANOVA approach can also be used to establish the total variation with several instruments involved. It will then be important to use more than 5 observations in each series to ascertain a reasonable within-series variance.

These procedures can be carried out with patient material, provided there is enough for the entire series, but equally well with reference materials. The advantage of using material with a known concentration is that the bias can be estimated in the same procedure.

## ESTIMATION OF BIAS FROM PATIENT MATERIAL

Traditionally, laboratories compare a new measurement procedure with previous ones by splitting samples into aliquots that are measured by the new (test) and a comparative method as close in time as possible. This procedure has been described in both the CLSI EP9 and EP15. The ACB provides a flexible program that easily handles this situation. The program allows single or duplicate measurements and estimates a number of statistics that will assist the laboratory to evaluate the performance. There are not too many reference methods available, and this approach will therefore not address the bias as defined metrologically but rather the difference between the selected methods.

It is important that the chosen samples are representative and that they cover the entire measuring interval. Outliers in the central part of the measuring interval tend to have little impact on the regression, whereas outliers at the ends of the interval may have a large impact. Any outlier will affect the correlation coefficient (*r*).

In the next paragraphs, functions that are included in the ACB software will be discussed, and the figures are copied from those spreadsheets. There is much more information available than the regression and bias if samples have been properly selected and carefully measured. Therefore, the philosophy of the software is to allow as much flexibility as possible and leave it to the user to pick and choose and evaluate the results guided by some instructions. The software allows the input of up to 100 samples, as single measurements or duplicates.

Before the statistical evaluation is performed, the scatterplot (Fig. 3) and difference plots should be carefully studied to identify outliers that may be candidates for deletion, and at least, they indicate possible problems with the measuring system. To assist this procedure, the difference between individual measurements is shown and the maximal is flagged.

Basic statistics are calculated for the data sets, for example, mean and SD, to characterize the sample population.

The significance of the difference between the methods is evaluated by the Student *t* test of dependent variables *t* _{dep}. This test requires that the differences are normally distributed. The data set and the distribution of the data set can therefore be truncated, which is described in more detail in the next paragraphs.

Data are used for various more advanced calculations, for example, the regression function, that is, the slope and intercept, and the correlation coefficient. The ordinary linear regression (OLR) requires that the analytical variance of the dependent variable (*y*) is much larger than that of the independent variable (*x*). If that is not the case, a better regression would be an orthogonal regression and the choice is the Deming regression. Both options are available and either can be displayed in the scattergram. However, the Deming regression requires that the variance of the method is defined. The ACB program allows input of results as singles or duplicates. If duplicates have been entered, then the analytical imprecision of the methods is calculated and will be input to the Deming regression. In any case, the operator can define the analytical imprecision of the dependent and independent variables and enter them independently—it may be that the imprecision of the methods has been carefully established in separate experiments. As the analytical variance of the dependent variable increases relative to that of the independent one, the Deming regression function approaches that of the OLR.

The Passing-Bablok regression has the advantage of being less sensitive to outliers and has no requirements to the distribution of the data. The calculation of the Passing-Bablok requires a special program.

The regression function may differ in different parts of the measuring interval, which means that the data sets are not linearly correlated. It is therefore valuable to consider partitioning the data set, and the program allows up to 3 partitions. The average bias and the Student *t* _{dep} are then displayed for each partition. The partitioning also allows truncating the data set at the high or low concentrations or both. If truncated, the new data set will be used as the basis for the bias calculation. To be meaningful, the number of observations needs to be large enough to allow approximately 20 observations in each partition.

The differences between the means of each of the observations and their means are presented and the maximum differences are flagged. The operator can toggle between the differences of the means or either of the results of the test or comparative methods. This facilitates the identification of potential outliers. The differences are also graphically displayed (Fig. 4) in difference graphs. These are traditional Bland-Altman graphs, but the program also allows the differences to be displayed versus the results of the comparative method. This is usually recommended if the comparative method is a reference method. The 2 diagrams show the absolute and relative differences between results and the trend of the differences. The confidence limits of the differences are calculated but should be considered with caution. The estimated confidence level is only truly valid if the distribution of the differences is normal or close to normal. As mentioned above, this is also a prerequisite for applying the Student *t* _{dep} test.

A deviation from normality often leads to long tails, and it thus becomes necessary to present some indication of normality. The skewness (peakedness) of the distribution of the differences is displayed because it is one of the characteristics of a normal distribution. If the skewness is within −1 < skewness < 1, the skewness is generally regarded as being minor. If not, the distribution of the differences can be truncated and thus improve the validity of the calculations. The total number of observations left after a truncation should be considered.

Thus, there are several means to adjust the data set. Obvious outliers, identified from the graphs or the tables of differences, can simply be deleted from the input table. The data set itself can be truncated, which is particularly convenient if there are samples with very high or very low concentrations. Finally, the distribution of the differences can be truncated. The data set that is eventually included in the evaluation is the smallest that is obtained after truncation of both the data set and the differences.

The clinical performance of a procedure, often used in risk assessment, can be described as the number of observations that fall outside a certain deviation from the equal line or regression line, allowable total error (ATE). The remaining are outside the limit of erroneous results (LER). In the program, the ATE can be set for the low-, mid-, or high-concentration limits and optionally displayed in the scattergram. The program will calculate the number of results in the ATE and LER sectors of the comparison. This may be different depending on if the ATE and LER are estimated in relation to any of the regressions or the equal line.

## CONCLUSIONS

A standardized procedure for laboratory verification of precision and trueness is described in terms of a nonproprietary and downloadable software package.