MEASUREMENT UNCERTAINTY
Equation. The relationship between the constant and proportional bias in an observed result when comparing it to an expected result, for example from a reference value.
not a relative percentage. In the same example above, if the measurand concentration is again increased to 200 units (this time with a constant bias of 5 units) the difference would still be 5 units – 200 + 5. In a regression this would manifest as a deviation of the y-intercept from 0 – in our case crossing at 5 on the y-axis. Of course, it is entirely possible that both constant and proportional error exists. The relationship between them both, and the impact on the observed value compared to the expected value can be described by the equation shown above.
The difficulty with accurately assessing bias is shown by different possible methods for its determination. Using average bias values from either EQA, IQC or a regression equation describing the performance of monthly EQA, different Six Sigma results were found for 16/33 chemistry and 12/26 immunoassay measurands.1
Other methods such
as CRM studies are favoured for bias estimation, but are limited by availability, cost and commutability of the CRM material.
The uncertainty of comparisons to a reference material If a CRM material is measured a number of times in a local laboratory, under repeatability conditions, there will be variability around the mean of those values. For example, if the material is measured 10 times in one day, the mean value may be 25.4. The next day, the same material run 10 times in effectively the same way may provide a result (mean value of the 10 measurements) of 26.8. If this was repeated many times, the distribution of the mean values would
be normally distributed according to the central limit theorem. As such, the mean value of a series of experiments will have an uncertainty. That uncertainty is not described by the standard deviation, like we are used to. It is described by the standard error (formerly called the standard error of the mean), calculated by dividing the standard deviation of the mean results by the square root of the number of runs performed. The combination of the uncertainty of the local laboratory results and the uncertainty of the assigned value of the CRM means it is difficult, if not impossible, to be sure of exactly how much bias, if any, is present (Fig 1). If a correction is applied based on these findings, we cannot be sure all bias has been removed, and this itself is uncertainty of the bias correction.
EQA and IQC performance Routinely, laboratory bias is monitored through performance in EQA schemes. The influence of commutability in EQA samples is significant. Verified commutable materials showed smaller biases compared to non-verified materials in two EQA schemes.2
Only when this
commutability is demonstrated can the metrological traceability of the method be assured. In recent years EQA providers have implemented the uncertainty of the consensus assigned value that laboratories are compared against for performance. Alternatively, IQC peer review can detect bias among groups of laboratories using the same analytical conditions. This consensus value will also have an uncertainty much like the CRM activity above.
The statistical significance of bias There are still differing opinions about what significant bias means. There are statistical and clinical ways to determine this. Statistically, an absolute bias above two times the bias uncertainty indicates statistical significance. There are recognised performance specifications derived from biological variation that can define acceptable bias. It should be recognised that these limits were originally intended to verify transferability of reference intervals across local laboratory networks and not necessarily for the determination of performance specifications. Nevertheless, they are still often used for that purpose.
The clinical significance of bias
Routinely, laboratory bias is monitored through performance in EQA schemes. The influence of commutability in EQA samples is significant. Verified commutable materials showed smaller biases compared to non-verified materials in two EQA schemes. Only when this commutability is demonstrated can the metrological traceability of the method be assured
16
Given the geometric shape of the normal distribution, an increase in bias results in an exponential shift of the population from within the reference intervals to beyond them (Fig 2) as well as the overestimation of results in patients still within the range. When using the central 95% of a sample from the local population, and when bias=0,5% of the population is situated outside the reference intervals. Overall, 2.5% of ‘normal’ individuals are below and 2.5% above the reference range. As soon as bias increases to greater than 0, the proportion of the population located outside the reference intervals exceeds 5% and will be unbalanced depending on the direction of the bias. If a positive bias is encountered, the percentage of patients above the reference range will increase exponentially (Table 1) and the number below will be less than the 2.5% originally intended. The reverse is true for a negative bias. The net effect is risk of patient harm if clinical interventions are determined by the reference intervals or clinical decision limits as is often the case. Additionally, the validated diagnostic accuracy that we have verified is invalidated by changing the sensitivity and specificity of the test metrics that our clinical colleagues rely on for interpretation, as do we.
Bias correction Measurement uncertainty as a metrological concept subscribes to the same metrological concepts as those outlined in the GUM that
JUNE 2024
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