. Guidelines for Assessing Analytical Quality Requirements

In ref. (30) (Chapter 2) the main principles of analytical goal-setting and formulation of analytical quality specifications (AQSpecs) were outlined. From this document it is possible to learn how to assess quality specifications according to 'the state of the art approach' and 'the biological approach', as well as 'the clinical usefulness approach'. Assessment of specifications based on clinical strategies/situations, however, need more preparation, starting with a detailed analysis of the problem. There are no simple formulas, but there are several applicable models for the purpose, which will be described in this chapter.

AQSpecs. The most relevant approach will be to apply a general strategy of 'not increasing the measured biological within-subject variation significantly' or of 'sharing common reference intervals', where analytical variation is generally included, cp. ref.

(30).
In the second case (b) of a defined clinical situation, the following steps should be considered: b. 1 Specify the clinical situation and define the outcome of the clinical decision making process in quantitative terms, e.g. number or fraction of misclassifications/misinterpretations, economical consequences etc. This could be the outcome of the total strategy/situation or of a well defined part of the process.
b. 2 Define the laboratory investigations, (generic quantities) (9, included in the clinical strategy. Are they determinative of the clinical outcome? If not or if the significance is doubtful, the assessment process may be difficult to perform or the AQSpecs may be uncertain. Therefore, the strategy should be reconsidered, aiming at a more clear definition of the impact of the results of laboratory investigations. In the third case (c) of a scientific investigation, the problem must be described in detail and the outcome must be clearly defined. It may be easier to separate the problem into a number of subproblems, to be investigated one by one. As the scientific problems may be very different, a general formula cannot be given. The steps (b.1 -b.2 above) for a defined clinical situation may, however, serve as a guideline for a relevant assessment.

Graphical, and Computer Analysis
The methods are often designated as 'statistical ', 'graphical', or as 'computer' methods. Many of the methods are based on general statistics, and for these the three approaches will lead to similar specifications, when the same assumptions are made. The word monitor is here used in the clinical sense ie.: "to keep close and constant watch of a condition or function".
A 'statistical method' based on the manual use of tabulated statistical distributions (usually gaussian or log-gaussian) does not allow a combination of different types of distributions. The 'graphical method' may be used to illustrate any gaussian or nongaussian distribution, but has got its limitations in combining gaussian analytical variation with non-gaussian biological distributions. The 'computer methods' have no limitations in mixing various statistics, graphics, and computational methods.
The choice between the three types of methods presented below, all involving strong elements of statistics, may be a question of avaiiable equipment or of individual taste and educational background, but it is also a matter of the complexity of the clinical situation studied.

Statistical (table-look-up) method
A Gaussian distribution describing a measured biological reference distribution has the following parameters: mean value = M, and standard deviation = sT (coefficient of variation = CVT). For explanation of abbreviations see rej (7) = Chapter 11 Any decision limit, DL (cut off point), can be expressed in terms of the parameter z = (DL -MT)/sT, and the fractions of the distribution above and below the DL can be read off from a statistical table for given z values.
The effect of analytical bias, B, , is simply calculated from Investigation of the effect of analytical imprecision (sA) is a two step process. First the biological standard deviation, sB = (sT2 -sA2)" , and z (ideal) = (DL -MT)/sB are calculated. Then, a different value of imprecision, s, , is assumed and the total standard deviation, s,, is calculated for this value of imprecision: The combined effect of various values of bias and imprecision can be read off from statistical tables using z (combined) = (DL -MT + BA)/sT. Statistical tables may be found in most books on statistics; see e.g. (3, 45).
A gaussian reference distribution can be delineated as a bell-shaped curve in a linear plot or, as a straight line in a probit-plot ( Fig. 4.2.1.). The bell-shaped presentation may be easier to grasp, but more difficult to evaluate, whereas the probit-plot is, after some practice, relatively easy to evaluate [for the theory c$ e.g. Bliis (2) or Gowans et al. (IS)].
A positive bias will move the distribution upwards resulting in a lower fraction below DL and a higher above DL ( Fig. 4.2.2). In fact, a bias will have the same effect as moving the DLbut with the opposite sign.
Evaluation of the effect of imprecision needs a few calculations like those for the statistical table-look-up method. The ideal biological distribution will show up as a more narrow bell-shaped curve and in the probit-plot the slope of the line will become steeper

Two reference distributions (Bimodal classification).
This procedure is used for single point measuring when two biological reference distributions are assumed, representing a diseased (or pre-diseased) and a healthy reference sample group. The prevalence for disease is an important parameter which may be more or less well-known , but can be varied within reasonable limits in the assessment. In the following example for demonstration ( The optimal decision limit is determined as the value minimizing the relative loss.
Diagnostic sensitivity and specificity, predictive values of positive and negative tests are calculated from conventional formulas.

Monte Carlo simulation techniques
Another computer method of great interest in this connection is the Monte Carlo simulation technique, based on random number generators and appropriate frequency distributions, and which can be used to generate synthetic data.
The method has the advantage that the outcome of classification can be studied on a "case-by-case'' basis, considering e.g. repeated measurements and reclassification of borderline cases (39). Furthermore, the influence of the size of the reference sample groups on the estimated decision limit and the outcome of the classification process can be studied. This

Assessment Procedure Prerequisites
Specification of: 1. The clinical strategy and the perceived consequences of the results, expressed in quantitative terms as a measurable outcome.

The distribution(s) of reference values, and decision limits (DL), estimates of
biological within-and between-subject variation, preanalytical factors, and the characteristics of the analytical measurement and quality control procedures.

2.
Describe the ideal error-free situation and calculate the clinical outcome.
Assume various analytical conditions: systematic error (bias) and random error (imprecision); one at the time and in combinations.
Calculate the outcome for the various analytical conditions. 3.

2.
From the demonstration example of a bimodal classification (Fig. 4.2.6) it can be seen that with B, and sA equal to zero the fraction of misclassified "diseased" is about 0.01 and the fraction of misclassified 'non-diseased' about 0.02 of the total number of classified; thus for a prevalence of 0.50 the total fraction of misclassified individuals is equal to 0.04. From Fig. 4.2.7. and Fig. 4.2.8. it is possible to graphically estimate the effect of bias and imprecision, respectively. Furthermore, it is possible to construct graphs that combine the effects of bias and imprecision. It will be the tolerable fraction of misclassifications that determines the analytical quality specifications.
Two reference distributions ('Bimodal clussification ' ) The following comments or conclusions can be made from the references:

Functions of misclassifications have been presented as combinations of imprecision
and bias (23,27,39) and imprecision and decision limits where also nomograms describing the type are given (48, 58).
In the paper of Jacobson et al. (39) a strategy of repeated measurements, has been investigated using Monte Carlo computer simulation technique. It was found that the influence of pre-analytical variation, duplicate measurements, reclassification of borderline cases and sizes of reference sample groups had some importance, but that the cost weighting ratio of false negatives: false positives was critical for the results.
Ross (49) used a theoretical model based on strict assumptions about the reference distributions, and the outcome was presented as efficiency.
In the work of Wide and Dahlberg (56) the analytical precision was optimized using a more sensitive function test for evaluation.

Two point monitoring
A unimodal model of repeated measuring has been described by Harris, from a statistical point of view, including the biological within-subject variation (24). An overlapping paper by Hyltoft Petersen et al. (33) describes the conversion of a two-point monitoring into a bimodal classification problem by calculating the ratios between measurement results from the same individual.
A series of investigations on 'the clinical usefulness approach' (10,11,15,43,50,51) have been described and discussed previously (30) (Chapter 2). These papers deal with how physicians and practitioners on the average react on a change in test result. In another series of papers a model is studied for evaluation of quality specifications in situations, where there is an agreement that a certain change of the analytical result ought to lead to clinical actions (15,28,34,35,44).
The predetermined change, A, is often empirical in nature, and the evaluation of quality specifications are based on the assumption that under stable (steady-state) conditions the probability of measuring a change 2 A should be less than a certain probability, P.

The general formula is
where the zp factor is set to a value corresponding to a specified probability (P), sA and sBW are the analytical and biological within-subject variation, respectively, and B,, is a possible difference in bias, either within the same instrument at the two measurement If bias (BwL or BbL) is assumed to be zero another rearrangement of the formula can be made, which gives: sA s [ (A2/2zp2) -sBw2]'. This expression has been used to study if multiple sampling can give a more accurate estimate of A, which can help to reduce the requirements on sA. This approach is only possible for components with comparatively high sBw-values (e.g. S--Creatinine and S--Cholesterol) (6).

Several point inonitonng
One example of the drug-monitoring is described in refs (12,13). Three other papers (21,22,31) deal with complicated turn-over models investigated by computer simulation techniques, which would need more space than available to describe in detail.
One paper (44) deals with the same situation of keeping concentrations of a selected quantity below (or above) a certain value in the treatment of a patient. Even if the problem is different from the unimodal classification, the theoretical handling is similar.
It is, however, easier here to introduce the extra information or assumption, by looking at patients with decision limits above (or below) the value, assuming that they should be interpreted analogously.

Other situations
These are very different in nature covering special aspects of quality specifications.
-Two papers (26,46) deal with computeraided diagnosis of jaundice, where the clinical chemical quantities are not determinative. This leads to the (expected) conclusion that analytical quality here is less important.
Two papers (14, 42) deal with preanalytical variation related to sampling technique.
In one paper computer supported decision analysis is used (57).
One theoretical paper (16) deals with quality specifications for interference.
Finally a paper (9) deals with the actual quality of reference intervals related to the current analytical quality. ----