Hitchhiker's Guide to Measurement Uncertainty (MU) in Clinical Laboratories |

## The Hitch-hiker’s Guide to Measurement Uncertainty (MU) in Clinical Laboratories## April 2012## Graham White |

QC | 07/27/11 - 09/14/11 | Mean (mmol/L) | SD (μ_{c}) | 2 SD (U) (U = 2 x μ_{c}) |

level 1 | n=86 | 4.9 | 0.12 | 0.24 = 0.2 |

level 2 | n=86 | 28.7 | 0.73 | 1.46= 1.5 |

The imprecision under intermediate reproducibility conditions is used for calculating MU. Since patient results are reported to one decimal place, the expanded MU (U) is similarly treated i.e. Patients’ results in the range considered monitored by:

QC level 1: x1 ± 0.2 mmol/L (95.5 % confidence); QC Level 2: x2 ± 1.5 mmol/L (95.5 % confidence).

e.g. Patient 1 result: 6.3 ± 0.2 mmol/L (~95 % confidence). This means that the laboratory has ~95 % confidence that the true value lies in the range 6.1-6.5 mmol/L.

Patient 2 result: 34.6 ± 1.5 mmol/L (~95 % confidence). This means that the laboratory has ~95 % confidence that the true value lies in the range 33.1-36.1 mmol/L.

The best estimate of the true value is always the reported result, but this way of expressing MU indicates that other results could have been obtained. Note: error is not mentioned. MU is concerned with the probability of where a true value lies. Note: the term ‘true value’ is in relation to the reference used for calibration, and may be an arbitrarily set value e.g. WHO International Units.

### What if Bias is considered significant?

Suppose rhubarb assay results are clinically interpreted relative to decision values defined by an international expert body, and incorrect interpretations may have deleterious medical implications. Measurement bias is therefore important. Fortunately the assay manufacturer assigns calibrator values using a certified secondary (matrix-matched) reference material (CRM) that is metrologically traceable to the SI unit (mole), and claims the calibrator is commutable with the CRM. The laboratory purchases a vial of CRM and measures it 10 times under repeatability conditions.

Certified value | 1 SD (μ_{c}) | Lab repeatability study (n=10) | 1 SD (μ_{c}) | Bias | |

CRM | 3.87 ± 0.028 mmol/L (95.5 % CI) | 0.014 mmol/L | Mean = 3.97 ± 0.12 mmol/L (95.5 % CI) | 0.06 mmol/L | 0.10 mmol/L |

The positive bias of 0.1 mmol/L is judged significant and applicable across the measuring range, so the assay is re-calibrated down by that value. We need to calculate the uncertainty of the value of 0.1 mmol/L. Such calculations use 1 SD (μ_{c}), not 2 SD (*U*) so the standard uncertainty of the CRM is 0.014 mmol/L. The uncertainty of the mean value obtained by the laboratory is the standard error of the mean of the ten measurements i.e. 0.06/√10 = 0.019 mmol/L. We now combine the uncertainties of the CRM and the laboratory mean values to give the combined standard uncertainty of the bias value of 0.1 mmol/L. Because SDs cannot be added together they need to be converted to variances (SD^{2}), which can be added. The combined variance is then converted back to a combined SD by taking the square root e.g. the combined standard uncertainty of the bias value ubias = √(0.0142 + 0.0192) = 0.0236 mmol/L.

The uncertainty of the bias value should then be compared with the long term QC imprecision e.g. 0.0236 is ~11 % of 0.22 mmol/L, and is considered borderline large enough to be included in the calculation of the total MU of the results produced by the rhubarb procedure. Bias uncertainty and QC imprecision is combined in the same way as above.

For values around QC Level 1: μ_{c} = √(0.02362 + 0.122) = 0.1223 mmol/L

Level 2: μ_{c} = √(0.02362 + 0.732) = 0.730 mmol/L

The expanded standard uncertainty (*U*) for QC Level 1 is 0.122 x 2 = 0.244 mmol/L, (rounded to 0.2 mmol/L); and for QC 2: 0.73 x 2 = 1.46 mmol/L (rounded to 1.5 mmol/L).

Patients’ results in the range considered monitored by QC level 1: x ± 0.2 mmol/L (95.5 % confidence); QC Level 2: x ± 1.5 mmol/L (95.5 % confidence). Note: MU values are rounded to the same number of decimal places as used for reporting results.

In this example inclusion of bias uncertainty made no meaningful change to the expanded uncertainty as determined using just the long term QC imprecision data. For this reason laboratories often ignore the uncertainty of bias values if they are less than an arbitrary cut-off of 20-30 % of the intermediate imprecision.

### How is MU calculated for a measurement calculated from several other results?

e.g. Anion Gap = (Na+ + K+) – (Cl- + HCO3-)

Same as above. Suppose the uc (1 SD) for Na+ = 1.1 mmol/L, K+ = 0.1 mmol/L, Cl- = 1.2 mmol/L and HCO3- = 0.8 mmol/L

μAG = √(1.12 + 0.12 + 1.22 + 0.82) = 1.82 mmol/L; *U* = 3.64 mmol/L. Appropriate rounding gives an expanded uncertainty of ± 4 mmol/L.

Note that although the AG calculation includes addition and subtraction, the standard uncertainties are combined in the same way. If a calculated parameter includes divisions and/or multiplications (e.g. creatinine clearance), then the SDs must first be converted to CV before calculation i.e. √CV12 + CV22 + CV32 +… etc).

### How should MU estimates be assessed?

Before embarking on calculating MU, it is essential for a laboratory to set clinically acceptable MU targets for each analyte e.g. serum sodium, urine sodium etc. There is little point in estimating MU if there are no targets stating what is required for clinically acceptable performance. This important aspect will not be discussed here as approaches to target setting are well described elsewhere. e.g. use of biological variation data, international expert group recommendations, professional opinion.

### Summary

The approach described above is referred to as ‘top down’. Known significant bias should be eliminated or minimised, and residual bias assessed in terms of the uncertainty of the bias value used for re-calibration or result correction. Bias uncertainty is often trivial relative to imprecision and is ignored, so that intermediate QC imprecision data captures the overall uncertainty of measurement results. MU data should be periodically updated.

The ‘bottom up’ approach estimates the uncertainties associated with individual components of a measuring system, and combines them in a model to reflect their effect in the complete measuring system. This approach is best suited to the needs of IVD medical device manufacturers validating new measurement procedures or seeking technical steps where MU might be reduced, and also for labs developing in-house measurement procedures. For the bottom-up approach readers are referred to the recent CLSI C-51 guideline [3].

### Should MU be routinely reported to clinicians?

No, but should be available if requested e.g. clinical trials, clinical research.

**MU useful to the laboratory because it:**

- provides quantitative evidence that measurement results meet clinical requirements for reliability
- is essential for meaningful comparison of results with reference values, with previous results using the same measurement procedure*
- can provide insights as to which technical steps might be open to improvement, thereby reducing overall MU
- is an essential component for achieving standardised and harmonized measurement results through metrological traceability.

*MU can be used to assess whether a patient’s result is measurably different with ~95 % confidence from a reference value, or from a previous result, or combined with intra-individual biological variation, in exactly the same way as described by Fraser (4).

### Summary of MU and TE

- TE provides an approximate worst case value for the error of a measuring system.
- TE does not recognise that each individual patient result could have other possible outcomes with less error than Bias + 1.65 SD.
- TE is useful for setting upper limits of allowable error.
- MU is not concerned with estimating the total error of a measuring system
- MU is concerned with estimating an interval of values within which the ‘true’ value of a measured analyte is believed to lie, with a stated level of confidence.
- Known bias is eliminated or minimised
- MU considers a single measurement result to be the best estimate of a true value, and centres on it the dispersion of other values that could have been obtained if the measurement had been repeated (usually with ~95 % confidence).
- MU is the appropriate approach for meaningfully comparing measurement results with reference values and previous results of the same kind.

### References

- White GH. Basics of estimating measurement uncertainty. Clin Biochem Rev 2008;29:S53-S60.
- Requirements for the estimation of measurement uncertainty. National Pathology Accreditation Advisory Council, Australian Government Department of Health and Ageing, 2007. www.health.gov.au Search for NPAAC publications (accessed 2/04/2012).
- C51-A. Expression of Measurement Uncertainty in Laboratory Medicine. CLSI, Wayne, PA.
- Fraser CG. Biological Variation: From principles to practice. 2001; AACC Press, Washington DC.

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