All assessments up to now have used “global” measures of assay performance such as IQC/imprecision of the assay as a whole to capture, and quantify, uncertainty in the overall system. This is useful for two reasons:
- It is relatively quick and easy to perform
- All data is readily available from data already generated in the laboratory
However, there are assays that these simple methods cannot be used for, either because the data is not readily available or they do not adequately represent the contribution that other contributing factors make to the final uncertainty. The G.U.M. approach is recognised as the reference method for robust uncertainty determination in many scientific disciplines, and can be used when required in pathology testing. In fact, it is explicitly mentioned in the ISO 151892012 guidelines. The process is similar to all the others in that we need to collect data and convert that data to a standard uncertainty. However, using the G.U.M. principles every uncertainty contributor is considered.
The steps of the process are:
- Define the measurand
- Develop a model of the measurement
- Specify the process and the equation if applicable
- Identify and characterise each source of uncertainty and determine source of error
- Identify the most appropriate method for assessment for each uncertainty contributor (Type A or B)
- Perform the measurements dictated by the above processes
- Calculation of the standard uncertainties
- Convert uncertainty components to its standard deviation equivalent using sensitivity coefficients
- Identify correlation between uncertainty contributors and their standard uncertainties
- Combine all uncertainties
- Apply the coverage factor and calculate the expanded uncertainty
- Assess the uncertainty budget for appropriateness
- Review the uncertainty budget
Level of measurements
Central to the determination of the MU is the correct definition of the level of measurement as this will impact on the type of assessment made, and on the resolution error associated with the assay and distribution function that best explains it. This involves identifying which of the categories below best applies to the variable being measured
- Categorical Variables
- Binary variable
- Nominal variable
- Ordinal variable
- Continuous variable
- Interval variable
- Ratio variables
- Discrete variable
Sensitivity Coefficients (SC)
Sensitivity coefficients are fundamental for reporting MU for two different reasons:
- The addition of a SC provides a conversion factor for individual input components of the equation allowing them to have the same units as the final measurand being assessed. The uncertainties of each input quantity cannot be combined unless the units are equivalent.
- The SC assigns an absolute value to the influence that any change in the given measured input parameter has on the final measurand quantity. Simply put it is the amount that the measurand varies when a given change occurs in one of the input parameters.
It is important to note that, for assessments by the G.U.M. method, if the input variables (uncertainties) are measured in the same units it is not necessary to compute sensitivity coefficients (they are effectively = 1).
Incorrect use of the SC can result in inaccurate MU values. Differing methods SC may be assessed at any time in the process of MU assessment but must be finalised before uncertainties are combined. The model (i.e. the nature of the relationship between input quantities and measurand result) must be known before and the assessment must take place at values close to those values being used in the test.
Correlation of individual uncertainty contributors can have a significant impact on the way the combined uncertainty needs to be calculated. By identifying the presence and extent of correlation between uncertainty contributors different calculations are required to be performed.
An awareness of the different types that may present themselves when analysing our data, and particularly the impact that the correct choice of probability distribution will have on final results is very important.
While using the G.U.M. procedure, the probability distribution chosen for all input uncertainties must be documented within the uncertainty budget to allow complete transparency of the process of uncertainty determination.
Combination of Type A and B uncertainty contributors
By the GUM approach the combination of uncertainty contributors is dependant initially on the identification and characterisation of the degree of correlation if present.
Expanded Uncertainty/Coverage Factor
Combination of standard uncertainties, as the name suggests, will provide us with a Combined Standard Uncertainty. As it is, this does not define the limits of the uncertainty we are concerned with. In order to provide this, we are required to include a coverage factor (defined as k) which when multiplied by the combined standard uncertainty, will produce the Expanded Uncertainty. Customarily (but not exclusively k is given the value of 2)
The purpose of the coverage factor is to produce an interval around the measured result that will have a specified level of confidence that the “true result” will lie. The limits of the interval (+ and – the measured result) inform us of two things and is a function of:
- the values generated in the derivation of the standard uncertainty and therefore the magnitude of the standard uncertainty
- The required degree of confidence that the interval must describe
The second factor is defined by the coverage factor. The coverage factor is defined by the confidence you wish to have around the result you are reporting, be that the common 95% or any other level. The table below summarises the coverage factor levels that can be applied and their effective confidence
|Coverage Factor (k)||Confidence Level (%)|
The coverage factors available for the expanded uncertainty calculation and their actual levels of confidence derived from them
Particularly, it should be noted that the commonly applied coverage factor of 2 does not imply a confidence of exactly 95%. From this care must be taken when quoting the correct confidence level for the coverage factor used
The expanded uncertainty is the end point of all the calculations performed and is a simple multiplication of the combined standard uncertainty and the coverage factor.
Expanded Uncertainty = Coverage Factor x Combined Uncertainty