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.