Trueness and Uncertainty
From accuracy to working standard, ISO plans to redefine all the terminology used in the laboratory. Dr. Xavier Fuentes-Arderiu, who provided us with the Biological Data Bank, now presents an essay on the proposed changes. See also Dr. Westgard's comments on the usefulness of these proposals.
Servei de Bioquímica Clínica
Ciutat Sanitària i Universitària de Bellvitge
L'Hospitalet de Llobregat, Barcelona
Universitat de Barcelona
We've received a number of questions about the new terminology - trueness and uncertainty - that is being recommended to the International Organizations of Standards (ISO). We're pleased to present a guest essay on this new terminology by Dr. Xavier Fuentes-Aderiu. He also provides a detailed glossary of ISO terms related to analytical quality.
Philosophers say a property is that which when possessed by an object contributes to being as it is. Properties may be essentially divided in qualitative and quantitative ones; a quantitative property is called quantity in general sense by metrologists (1), but kind-of-quantity in clinical laboratory sciences (2).
When a kind-of-quantity belongs to a particular object we have a particular quantity; and when a particular quantity is subject to measurement then this is called measurand (1).
In order to describe a particular quantity unambiguously three elements must be mentioned (2):
- the system, that is to say the set of entities together, with a set of relationships between those entities, under study (e.g. patient, serum, urine); in the majority of cases the system coincides with the sample;
- the component, that is to say the entity (molecular entity, cytological entity, biological process, etc.) of interest belonging to the system under study (e.g. cholesterol, erythrocytes, Pseudomonas sp., corticotropin secretion); in analytical chemistry it is usually termed 'analyte';
- the kind-of-quantity, that is to say the quantitative property under study (e.g. substance concentration, catalytic concentration, number of entities).
These three elements, eventually accompanied by some specifications, may be presented in a systematic way according to the syntax recommended by different international scientific organizations (3-6): System(specifications)-Component(specifications); kind-of-quantity(specifications).
Examples of this are:
- Plasma-Thyrotropin; arbitrary substance concentration(IRP 80/558)
- Patient(Urine)-Creatininium excretion; substance rate(24 hours)
These quantities can also be written using the accepted symbols for systems (2) and abbreviations for kind-of-quantities (7):
- P-Thyrotropin; arb.subst.c. (IRP 80/558)
- Pt(U)-Creatininium excretion; subst.rate(24 hours)
Thousands of examples can be found in the website of the Commission/Committee on Nomenclature, Properties and Units of the International Union of Pure and Applied Chemistry (IUPAC) and the International Federation of Clinical Chemistry and Laboratory Medicine (IFCC).
Any particular quantity has a value. Values of quantities are real numbers multiplied by a unit of measurement (although when the unit of measurement is 1, it is usually omitted).
The process used to investigate the value of a particular quantity is termed measurement procedure (1). Quantities need measurement procedures with different degrees of complexity. Thus the measurement procedure needed to measure the particular quantity "number of fingers in the hand of a given person" is very simply: counting by direct visual inspection is enough; contrarily, the measurement procedure needed to measure the particular quantity "substance concentration of glucose in plasma of a given person in a given time" is a chemical process with a relatively high degree of complexity.
Apart from the complexity of the measurement procedure, there is a very important fact that differentiates the two examples given in the paragraph above. In the first example, the measurement procedure enables to know the true value of the particular quantity without any kind of doubt: the measurement procedure when applied to the mentioned particular quantity has nor random neither systematic errors. However, in the second example, the true value of the particular quantity is, at the present state of science and technology, unknowable whatever the measurement procedure is. Unfortunately, quantities which measurement is useful in clinical laboratory sciences are like that presented in the second example.
The true value is a value consistent with the definition of a given particular quantity and that would be obtained by a perfect measurement (1). Keeping apart some exceptions like that in the first example, as a perfect measurement -without random or systematic errors- does not exist, the true value is an ideal object that never can be entirely known. This fact is epistemologically relevant but a practical solution to circumvent this obstacle is needed for the real life in clinical laboratory sciences. The solution is the use of values attributed by convention to particular quantities related to measurement standards instead of the true value, when necessary; a value of this kind of is termed conventional true value (1).
There are some ways to attribute a conventional true value -that will be used as a true value- to a particular quantity, specially related to reference materials. The best way is the use of definitive or reference measurement procedures, when available (8).
When measuring several times a measurand with a particular measurement procedure, the mean of the results obtained may be more or less close to the true (or conventional true) value. The trueness is a metrological characteristic of a measurement procedures that give qualitative information about its capacity of produce true (or conventional true) values. A practical definition, based on others more theoretical (8, 9), may be: closeness of agreement between the mean of the results of measurements of a measurand obtained under specific between-day precision conditions and the true or conventional true value of the measurand. It should be remarked that this concept is practically equivalent to the now old fashioned concept of "accuracy" as defined by the IFCC twenty years ago (9)
The quantitative counterpart of this concept is systematic error. This is what is estimated in practice when evaluating and validating measurement procedures. A practical definition for the estimated systematic error of measurement, also based on theoretical definitions (1, 10, 11), may be: mean of twenty or more results of measurements of a measurand obtained under specific between-day precision conditions minus the true or conventional true value of the measurand. In this case, the old fashioned IFCC concept is "inaccuracy" (9).
Systematic errors in some instances can be identified and corrected but depending on its nature may be difficult or impossible to identify or quantify. That means that in many cases one can doubt about the reliability of a particular result of measurement. Unfortunately not only systematic error can introduce a doubt about a result of measurement: random errors also may move away a result of measurement from the true value. Random and systematic errors act together on a measurement result producing an error of measurement (also known as 'total error', though not metrologically recognized) and generating doubt -uncertainty- about the true value of the measurand.
The international metrology organizations, keeping in mind these facts, have developed the concept uncertainty of measurement, defined as a parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand (1, 12); the parameter may be a multiple of a standard deviation or the half-width of an interval having a stated level of confidence, for example.
Uncertainty is described as one of the following three parameters (12):
- Standard uncertainty, u, is the standard deviation that denotes the uncertainty of the result of a single measurement.
- Combined standard uncertainty, uc, is the standard deviation that denotes the uncertainty of the result obtained from other results of measurement. It is obtained by combining the standard uncertainties of all individual measurements according to the law of propagation of uncertainty.
- Expanded uncertainty, U, is the statistic defining the interval within which the value of the measurand is believed lie with a particular level of confidence. It is obtained by multiplying the combined standard uncertainty by a coverage factor, k, the choice of which is based on the level of confidence (1-a) desired. If k = 2, then 1-a » 0,95; if k = 2,6, then 1-a » 0,99. This concept is similar to the concept "total analytical error" classically used in chemometrics.
In general, the most relevant components of the uncertainty of measurement of the patient's results obtained in clinical laboratories may be grouped as follows:
- uncertainty components due to the premetrological phase (e.g. phlebotomists' skills, storage conditions, centrifuging conditions);
- uncertainty components due to calibrators;
- uncertainty components due to the measurement procedure -including calibration fluctuations- estimated from systematic error and between-day imprecision, taking into account the possible heteroscedasticity of data, that is to say the variation of the between-day metrological standard deviation according the value of the mesurand.
Each component of uncertainty of measurement can be expressed as a standard deviation that may be estimated from the probability distribution of values with repeated measurements, termed type A standard uncertainty, or estimated by using assumed probability distribution based on experience or other available information, termed type B standard uncertainty.
For many measurement procedures used in clinical laboratory sciences, the standard deviation of the results obtained by replicate measurements of a measurand varies with the value of the measurand; this phenomenon is called heteroscedasticity, and the opposite is called homoscedasticity. Which of these phenomena occurs should be always taken into account when estimating the uncertainty of measurement.
There is general agreement among international bodies (2, 13) regarding the use of the uncertainty of measurement in clinical laboratory sciences. The common opinion is that clinical laboratories must supply information about the uncertainty of their results of measurement, when applicable; this information may be attached to each patient's result, may be contained in the user's laboratory handbook or may be available on request. When decided the uncertainty of measurement should be attached to the patients' results, the formal presentation may be as shown in this example:
Where 1.15 mkat/L is the result given by the analyzer and 0.23 mkat/L is the expanded uncertainty multiplied by 2 as coverage factor.
Although all above, in clinical laboratory sciences probably it will be difficult to bring into general use the uncertainty of measurement. In the meantime some questions are waiting for an answer:
- When a clinical laboratory has produced in-house reference values according the IFCC recommendation, to estimate the combined standard uncertainty the systematic error should be referred to the conventional true value of the calibrators used during the production of reference values?
- Under a practical (clinical) point of view, if a measurement procedure meets the metrological requirements, why to know the uncertainty of results?
- When comparing a patient's result with the biological reference limits, the physician should be aware of the uncertainty of measurement of that result or it may be a disturbing, perhaps confusing, information?
- When monitoring a patient, what is better: (i) to attach the uncertainty to each result, (ii) to attach to each result the uncertainty combined with the within-subject biological variability (14), or (iii) to indicate if the current patient's result is significantly different with regard to the previous one (15)?
Dr. Fuentes-Arderiu graduated in pharmacy at the University of Barcelona in 1973, and received a Ph.D. in 1978 at the same university. In 1975 he joined the Catalan Institute for Health, working in non-hospital clinical laboratories as general clinical pathologist during five years, then he moved to an university hospital, within the same Institute, where he is the quality manager of the clinical biochemistry service. In 1992 he became assistant professor of clinical biochemistry in the University of Barcelona.
Besides his usual task at hospital and university, he has served during ten years as associate, titular member and chairman of the Commission/Committee on Nomenclature, Properties and Units of IUPAC/IFCC. He is also the chairman of the IFCC Working Group on Spanish terminology and Nomenclature in Clinical Chemistry, and titular member of the IUPAC Interdivisional Committee on Nomenclature and Symbols.
He is actively involved in the Technical Committee 212 of the International Organization for Standardization (ISO), the Technical Committee 140 of the European Committee for Standardization (CEN), and the Technical Committee 129 of the Spanish Association for Standardization and Certification (AENOR), all three committees devoted to the standardization of clinical laboratories and in vitro diagnostic products. He is vice-president of the Catalan Association for Clinical Laboratory Sciences and member of the Technical Council and chairman of the Commission on Metrology of the Spanish Society of Clinical Biochemistry and Molecular Pathology.
He has produced more than two hundred publications, including research articles, scientific letters, chapters in books and books, on a diversity topics related to clinical laboratory sciences, such as qualitology, metrology, chemometrics, scientific terminology and biometrics applied to clinical laboratory data communication and interpretation.
- International Bureau of Weights and Measures, International Electrotechnical Commission, International Organization for Standardization, International Organization of Legal Metrology, International Federation of Clinical Chemistry, International Union of Pure and Applied Chemistry and International Union of Pure and Applied Physics. International Vocabulary of Basic and General Terms in Metrology. ISO: Geneva, 1993.
- International Union of Pure and Applied Chemistry, International Federation of Clinical Chemistry. Compendium of Terminology and Nomenclature of Properties in Clinical Laboratory Sciences (Recommendations 1995). (Prepared for publication by J.C. Rigg, S.S. Brown, R. Dybkaer, H. Olesen). Oxford: Blackwell Science, 1995.
- International Society on Thrombosis and Haemostasis, International Union of Pure and Applied Chemistry, International Federation of Clinical Chemistry. Nomenclature of Quantities and Units in Thrombosis and Haemostasis (Recommendation 1993). Thromb Haemost 1994; 71: 375-394.
- International Union of Pure and Applied Chemistry, International Federation of Clinical Chemistry. Properties and Units in the Clinical Laboratory Sciences. I. Syntax and Semantic Rules. Pure Appl Chem 1995; 67:1563-1574.
- European Committee for Standardization. Healthcare informatics - Structure for nomenclature, classification, and coding of properties in clinical laboratory sciences. ENV 1614. Brussels, 1995.
- International Society on Andrology, International Union of Pure and Applied Chemistry, International Federation of Clinical Chemistry and Laboratory Medicine. Properties and Units in the Clinical Laboratory Sciences. XIII. Properties and Units in Reproduction and Fertility. Clin Chem Lab Med 1998: 36: 57-65.
- International Union of Pure and Applied Chemistry, International Federation of Clinical Chemistry. Properties and Units in the Clinical Laboratory Sciences. II. Kinds-of-property. Pure Appl Chem 1997; 69:1015-1042.
- National Committee for Clinical Laboratory Standards. Soucerbook of Reference Methods, Material, and Related Information for the Clinical Laboratory; Proposed Guideline. (NRSCL12-P). NCCLS: Villanova, 1994.
- International Federation of Clinical Chemistry. Approved Recommendation (1978) on Quality Control in Clinical Chemistry. Part 1 General Principles and Terminology. J Clin Chem Clin Biochem 1980: 18: 69-77.
- International Organization for Standardization. Statistics - Vocabulary and Symbols. Part 1: Probability and general statistical terms. ISO 3534-1. Genève: ISO, 1993.
- Dybkaer R. Terminological problems around "accuracy" and "uncertainty". Scand J Clin Lab Invest 1998; 58: 35-46.
- International Organization for Standardization, International Electrotechenical Commission, Interantional Organization of Legal Metrology, International Bureau of Weights and Measures. Guide to the expression of uncertainty in measurement. Genève: ISO, 1993.
- ENV 12435 European Committee for Standardization. Medical informatics - Expression of the results of measurement in health sciences. ENV 12435. Brussels: CEN, 1997.
- Fuentes-Arderiu X, González de la Presa B. Biometrological uncertainty. Eur J Clin Chem Clin Biochem 1996; 34: 273.
- Harris EK, Yasaka T. On the calculation of "reference change" for comparing two consecutive measurements. Clin Chem 1983; 29: 25-30.