Uncertainty in measurement and the renal tubular reabsorption of phosphate.

OBJECTIVES: The ratio of tubular maximum reabsorption of phosphate to glomerular filtration rate (TmP/GFR) is used to evaluate renal phosphate transport. TmP/GFR is most probably calculated using the formula described by Kenny and Glen or obtained from the nomogram described by Walton and Bijvoet. Even though the calculation itself is well described, no attention has been given to its measurement uncertainty (MU). The aim of this study is to provide a procedure for evaluating the MU of the Kenny and Glen formula; a procedure which is based on the Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM). METHODS: TmP/GFR is a quantity value calculated from the input of measured values for serum (plasma) phosphate and creatinine, plus measured values of urine phosphate and creatinine. Given the measurement uncertainty associated with these input quantities, the GUM describes the mathematical procedures required to determine the uncertainty of the calculated TmP/GFR. From a medical laboratory perspective, these input uncertainties are the standard deviations of the respective internal quality control estimates for serum and urine phosphate, plus serum and urine creatinine. RESULTS: Based on representative measurements for the input quantities and their associated standard uncertainties, the expanded relative uncertainty for a calculated TmP/GFR is approximately 3.0-4.5 %. CONCLUSIONS: With the continued relevance of the TmP/GFR procedure and the use of creatinine clearance as an estimate of GFR, the addition of an uncertainty estimate is important as an adjunct to this diagnostic procedure.

ISO/TS 20914:2019 - a critical commentary.

The long-anticipated ISO/TS 20914, Medical laboratories - Practical guidance for the estimation of measurement uncertainty, became publicly available in July 2019. This ISO document is intended as a guide for the practical application of estimating uncertainty in measurement (measurement uncertainty) in a medical laboratory. In some respects, the guide does indeed meet many of its stated objectives with numerous very detailed examples. Even though it is claimed that this ISO guide is based on the Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM), JCGM 100:2008, it is with some concern that we believe several important statements and statistical procedures are incorrect, with others potentially misleading. The aim of this report is to highlight the major concerns which we have identified. In particular, we believe the following items require further comment: (1) The use of coefficient of variation and its potential for misuse requires clarification, (2) pooled variance and measurement uncertainty across changes in measuring conditions has been oversimplified and is potentially misleading, (3) uncertainty in the results of estimated glomerular filtration rate (eGFR) do not include all known uncertainties, (4) the international normalized ratio (INR) calculation is incorrect, (5) the treatment of bias uncertainty is considered problematic, (6) the rules for evaluating combined uncertainty in functional relationships are incomplete, and (7) specific concerns with some individual statements.

Bias in analytical chemistry: A review of selected procedures for incorporating uncorrected bias into the expanded uncertainty of analytical measurements and a graphical method for evaluating the concordance of reference and test procedures.

The Evaluation of measurement data - Guide to the Expression of Uncertainty in Measurement (GUM) provides the framework for evaluating measurement uncertainty. The preferred GUM approach for addressing bias assumes that all systematic errors are identified and corrected at an early stage in the measurement process. We review some procedures for treating uncorrected bias and its inclusion into an overall uncertainty statement. When bias and its uncertainty are recognised as metrological states independent of scatter in the test results, the uncertainty of the reference and uncertainty of the bias can be equated. The net standard uncertainty of a test result is the root-sum-square of the standard uncertainty of the bias and the standard uncertainty of measurements on the test. Since an incomplete and therefore potentially erroneous formula is often used for estimating bias standard uncertainty, we propose an alternative calculation. We next propose a graphical method using a simple algorithm that quantifies the discrepancy between the results of a test measurement and the corresponding reference value, in terms of the percentage overlap of two probability density functions. We propose that bias should be corrected wherever possible and we illustrate this approach using the graphical method. Even though this review is focused principally on analytical chemistry and medical laboratory applications, much of the discussion is applicable to all areas of metrology.

Uncertainty in measurement: A review of the procedures for determining uncertainty in measurement and its use in deriving the biological variation of the estimated glomerular filtration rate.

Procedures for assessing the uncertainty in measurement and estimates of biological variation are currently available for many measurands capable of direct analytical measurement. However, not all measurands or quantity values determined in a medical laboratory are provided by direct analytical measurement. Estimated glomerular filtration rate (eGFR) is such a quantity value. In this situation, the result is calculated from other measurements through a functional relationship in which the output value (the calculated quantity value) is derived from one or more input quantities by applying a defined mathematical equation. The aims of this review are: to summarise the principal methods for assessing uncertainty in measurement in complicated non-linear expressions; and to describe an approach for estimating the uncertainty in measurement and biological variation of the Chronic Kidney Disease Epidemiology Collaboration equations for eGFR. In practice, either the direct application of the propagation of uncertainty in measurement equation or a Monte Carlo simulation procedure using a readily available spreadsheet may be used to evaluate uncertainty in measurement or the propagation of biological variation. If the only recognised "uncertainty" is the biological variation in the measured serum creatinine, the equation for the propagation of uncertainties in measurement for the eGFR simplifies to an expression in which the coefficient of variation of the eGFR (or the biological variation of the eGFR) is directly proportional to the coefficient of variation of the measured serum creatinine (or the biological variation of the serum creatinine).

Uncertainty in measurement and total error: different roads to the same quality destination?

The debate comparing the benefits of measurement uncertainty (uncertainty in measurement, MU) with total error (TE) for the assessment of laboratory performance continues. The summary recently provided in this journal by members of the Task and Finish Group on Total Error (TFG-TE) of the EFLM put the arguments into clear perspective. Even though there is generally strong support for TE in many laboratories, some of the arguments proposed for its on-going support require further comment. In a recent opinion which focused directly on the TFG-TE summary, several potentially confusing statements regarding ISO15189 and the Evaluation of measurement data - Guide to the expression of uncertainty in measurement (GUM) were again promulgated to promote TE methods for assessing uncertainty in laboratory measurement. In this opinion, we present an alternative view of the key issues and outline our views with regard to the relationship between ISO15189, uncertainty in measurement and the GUM.

Uncertainty in Measurement: Procedures for Determining Uncertainty With Application to Clinical Laboratory Calculations.

In Part II of this review we consider the very common case of multiple inputs to a measurement process. We derive, using only elementary steps and the basic mathematics covered in Part I, the formula for the propagation of uncertainties from the inputs to the output. The Gaussian density distribution is briefly explained, since an understanding of this distribution is needed for the determination of so-called expanded uncertainties at the end of a measurement process. The propagation formula in general involves correlations among the inputs, although in many cases these correlations can be considered negligible. Correlations, however, need to be taken into account in related matters such as line-fitting and have particular relevance to method comparisons. These topics are addressed briefly. We next discuss the important question of bias and its incorporation into the expression of uncertainty. We present, finally, six real-world cases in clinical chemistry where uncertainty in the estimated value of the measurand is calculated using the propagation formula.

Uncertainty in Measurement: Procedures for Determining Uncertainty With Application to Clinical Laboratory Calculations.

The "Guide to the Expression of Uncertainty in Measurement" (GUM) is the foundational document of metrology. Its recommendations apply to all areas of metrology including metrology associated with the biomedical sciences. When the output of a measurement process depends on the measurement of several inputs through a measurement equation or functional relationship, the propagation of uncertainties in the inputs to the uncertainty in the output demands a level of understanding of the differential calculus. This review is intended as an elementary guide to the differential calculus and its application to uncertainty in measurement. The review is in two parts. In Part I, Section 3, we consider the case of a single input and introduce the concepts of error and uncertainty. Next we discuss, in the following sections in Part I, such notions as derivatives and differentials, and the sensitivity of an output to errors in the input. The derivatives of functions are obtained using very elementary mathematics. The overall purpose of this review, here in Part I and subsequently in Part II, is to present the differential calculus for those in the medical sciences who wish to gain a quick but accurate understanding of the propagation of uncertainties.

Uncertainty in measurement and total error - are they so incompatible?

There appears to be a growing debate with regard to the use of "Westgard style" total error and "GUM style" uncertainty in measurement. Some may argue that the two approaches are irreconcilable. The recent appearance of an article "Quality goals at the crossroads: growing, going, or gone" on the well-regarded Westgard Internet site requires some comment. In particular, a number of assertions which relate to ISO 15189 and uncertainty in measurement appear misleading. An alternate view of the key issues raised by Westergard may serve to guide and enlighten others who may accept such statements at face value.

The application of glucose point of care testing in three metropolitan hospitals.

The application of glucose point of care testing (PoCT) in hospitals has been a contentious subject for many years. No information is available regarding the extent to which glucose PoCT is used within the Australian hospital system and whether such testing is fit for its intended purpose. The aim of this study was to investigate the extent to which glucose PoCT is used within three teaching hospitals and whether testing procedures operate within a framework of quality management. Eighty operators of glucose PoCT participated in a descriptive electronic survey. Specific training in glucose PoCT was limited, with 26% of respondents reporting no specific training in glucose PoCT and 52% of respondents reporting no specific on-going competency assessment for glucose PoCT. The application of quality control (QC) for hand-held meters was generally good, with the majority of respondents indicating that QC was performed on a regular basis. However, 17% of respondents reported that QC was done irregularly or not at all. Electronic reporting of results was limited with 77% of respondents reporting they enter results manually into paper records. The survey obtained data not previously available. It established that glucose PoCT would benefit from a closer adherence to a quality management framework.

Uncertainty in measurement: a review of monte carlo simulation using microsoft excel for the calculation of uncertainties through functional relationships, including uncertainties in empirically derived constants.

The Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides the basic framework for evaluating uncertainty in measurement. The GUM however does not always provide clearly identifiable procedures suitable for medical laboratory applications, particularly when internal quality control (IQC) is used to derive most of the uncertainty estimates. The GUM modelling approach requires advanced mathematical skills for many of its procedures, but Monte Carlo simulation (MCS) can be used as an alternative for many medical laboratory applications. In particular, calculations for determining how uncertainties in the input quantities to a functional relationship propagate through to the output can be accomplished using a readily available spreadsheet such as Microsoft Excel. The MCS procedure uses algorithmically generated pseudo-random numbers which are then forced to follow a prescribed probability distribution. When IQC data provide the uncertainty estimates the normal (Gaussian) distribution is generally considered appropriate, but MCS is by no means restricted to this particular case. With input variations simulated by random numbers, the functional relationship then provides the corresponding variations in the output in a manner which also provides its probability distribution. The MCS procedure thus provides output uncertainty estimates without the need for the differential equations associated with GUM modelling. The aim of this article is to demonstrate the ease with which Microsoft Excel (or a similar spreadsheet) can be used to provide an uncertainty estimate for measurands derived through a functional relationship. In addition, we also consider the relatively common situation where an empirically derived formula includes one or more 'constants', each of which has an empirically derived numerical value. Such empirically derived 'constants' must also have associated uncertainties which propagate through the functional relationship and contribute to the combined standard uncertainty of the measurand.

Uncertainty of Measurement: A Review of the Rules for Calculating Uncertainty Components through Functional Relationships.

The Evaluation of Measurement Data - Guide to the Expression of Uncertainty in Measurement (usually referred to as the GUM) provides general rules for evaluating and expressing uncertainty in measurement. When a measurand, y, is calculated from other measurements through a functional relationship, uncertainties in the input variables will propagate through the calculation to an uncertainty in the output y. The manner in which such uncertainties are propagated through a functional relationship provides much of the mathematical challenge to fully understanding the GUM.The aim of this review is to provide a general overview of the GUM and to show how the calculation of uncertainty in the measurand may be achieved through a functional relationship. That is, starting with the general equation for combining uncertainty components as outlined in the GUM, we show how this general equation can be applied to various functional relationships in order to derive a combined standard uncertainty for the output value of the particular function (the measurand). The GUM equation may be applied to any mathematical form or functional relationship (the starting point for laboratory calculations) and describes the propagation of uncertainty from the input variable(s) to the output value of the function (the end point or outcome of the laboratory calculation). A rule-based approach is suggested with a number of the more common rules tabulated for the routine calculation of measurement uncertainty.