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The concept of uncertainty in an isotopic analysis is not uniform in the scientific community worldwide and can compromise the risk of false compliance assessment applied to carbon isotopic analyses in natural gas exploratory evaluation. In this work, we demonstrated a way to calculate one of the main sources of this uncertainty, which is underestimated in most studies focusing on gas analysis: the δ13C calculation itself is primarily based on the raw analytical data. The carbon isotopic composition of methane, ethane, propane, and CO2 was measured. After a detailed mathematical treatment, the corresponding expanded uncertainties for each analyte were calculated. Next, for the systematic isotopic characterization of the two gas standards, we calculated the standard uncertainty, intermediary precision, combined standard uncertainty, and finally, the expanded uncertainty for methane, ethane, propane, and CO2. We have found an expanded uncertainty value of 1.8‰ for all compounds, except for propane, where a value of 1.6‰ was obtained. The expanded uncertainty values calculated with the approach shown in this study reveal that the error arising from the application of delta calculation algorithms cannot be neglected, and the obtained values are higher than 0.5‰, usually considered as the accepted uncertainty associated with the GC-IRMS analyses. Finally, based on the use of uncertainty information to evaluate the risk of false compliance, the lower and upper acceptance limits for the carbon isotopic analysis of methane in natural gas are calculated, considering the exploratory limits between -55‰ and -50‰: (i) for the underestimated current uncertainty of 0.5‰, the lower and upper acceptance limits, respectively, are -54.6‰ and -50.4‰; and (ii) for the proposed realistic uncertainty of 1.8‰, the lower and upper acceptance limits would be more restrictive; i.e., -53.5‰ and -51.5‰, respectively.

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Abstract The quality, efficacy, and safety of medicines are usually verified by analytical results. Measurement uncertainty is a critical aspect for the reliability of these analytical results. The pharmacopeial compendia usually adopt a simple acceptance rule that does not consider information from measurement uncertainty. In this work, we compared decision-making using simple acceptance and decision rules with the use of guard-band for multiparameter evaluation of ofloxacin ophthalmic solution and acyclovir topical cream. Ciprofloxacin ophthalmic solution and acyclovir topical cream samples were subject to pharmacopeial tests and assays. Multivariate guard-band widths were calculated by multiplying the standard uncertainty (u) by an appropriate multivariate coverage factor (k'). The multivariate coverage factor (k') was obtained by the Monte Carlo method. According to the simple acceptance rule, all the results obtained for ciprofloxacin ophthalmic solution and acyclovir topical cream are within the specification limits. However, the risk of false conformity decisions increases for ciprofloxacin tests. Decisions made using the simple acceptance rule and decision rules with the use of guard-band may differ. The simple acceptance rule may increase the risk of false conformity decisions when the measured value is close to the regulatory specification limits and/or when the measurement uncertainty value is inappropriately high. Nevertheless, the guard-band decision rule will always reduce the risk of false conformity decisions. Therefore, using information on measurement uncertainty in conformity assessment is highly recommended to ensure the proper efficacy, safety, and quality of medicines.

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Abstract Medicines must be subject to physical, chemical, and biological analysis to guarantee their quality, safety, and effectiveness. Despite the efforts to ensure the reliability of analytical results, some uncertainty will always be associated with the measured value, which can lead to false decisions regarding conformity/non-conformity assessment. This work aims to calculate the specific risk of false decisions regarding conformity/non-conformity of acetaminophen oral solution dosage form. The acetaminophen samples from five different manufacturers (A, B, C, D, and E) were subject to an active pharmaceutical ingredient assay, density test, and dose per drop test according to the official compendia. Based on measured values and their respective uncertainties, the risk values were calculated using the Monte Carlo method implemented in an MS Excel spreadsheet. The results for two acetaminophen oral solution samples (C and D) provided an increased total risk value of false acceptance (33.1% and 9.6% for C and D, respectively). On the other hand, the results for the other three acetaminophen samples (A, B, and E) provided a negligible risk of false acceptance (0.004%, 0.025%, and 0.045% for A, B, and E, respectively). This indicates that measurement uncertainty is very relevant when a conformity assessment is carried out, and information on the risks of false decisions is essential to ensure proper decisions.

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Radiopharmaceuticals have been used to diagnose several diseases, particularly because the procedure is non-invasive. However, it is important that the correct amount of radiopharmaceutical is used to avoid inaccurate diagnostic results and suboptimal therapeutic outcomes. The amount of the radiopharmaceutical is measured when produced (by the supplier) and a second time (by the receiver), before it's use. When measured at the receiver, the result is corrected for its normal radioactivity decay. Even then, it is possible that both measurements should be considered nominal different or even statistically different when compared through various statistical tools. This research combines two innovative techniques in the field of clinical metrology. The first technique is data reconciliation, which not only enhances measurement accuracy but also reduces measurement uncertainty. The second technique involves using uncertainty information to establish specification limits for compliance assessments. In this way, our proposal aimed to minimize the risk of making incorrect decisions regarding the conformity of the concentration of radiopharmaceutical activity, that is, rejecting an item or batch that is within specification or accepting an item or batch that is outside of specification. A spreadsheet, based on these metrology fundamentals, is available to help the user with the calculations, presenting numerical and graphical results for some common radioisotopes. Reliable specification limits can be calculated and used to determine if the radiopharmaceutical is in accordance with its proposed application.

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Currently, the use of algorithms and computer vision systems for metrological purposes has increased in different areas of knowledge to reduce human error and process deviations, consequently increasing reliability and reducing measurement uncertainties. This study presents a model for estimating the uncertainty of Feret's diameter (DF ) measurements of scanning electron microscopy (SEM) images from regular and irregular gunshot residue (GSR) particles at different magnifications. The data were extracted using the automatic measurement algorithm developed by the Brazilian Institute of Metrology, Quality and Technology (Inmetro). The proposed uncertainty model was based on the recommendations of the guide to the expression of uncertainty in measurement (GUM). The gold standard technique to identify and detect GSR particles is the SEM coupled to energy dispersive X-ray spectroscopy (SEM/EDS), which was used in the study. The low uncertainty values obtained in this study are justified by the refinement of the measurements performed at each stage of digital image procedures. The proposed uncertainty model contributes in an innovative way to the metrological evaluation of regular and irregular GSR particles at different images magnifications. The correct morphometry definition of these particles allows to study their distinction from other possible sources of GSR and, above all, their correlation with the type of ammunition used when firing the firearm. These measurement uncertainty calculations can be applied to any object images acquired by SEM, which provides more confidence in the results of measurements of the object of interest.

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Dissolution is used to determine the rate and extent of drug release from the dosage form into a dissolution medium, which allow to assess the batch-to-batch variability. Considering that the dissolution test is used to predict the vivo performance of the drug as well, it is important to guarantee the quality and reliability of dissolution test results. The aim of this work was to evaluate the measurement uncertainty arising from sampling and analytical steps of dissolution test of prednisone tablets. Dissolution test was performed using 900 mL of purified water as dissolution medium and a dissolution apparatus equipped with paddles rotating at 50 rpm for 30 min. Quantification was performed by UV spectrophotometer. Uncertainty arising from sampling was estimated using the duplicate method (empirical approach), using 17-sampling target, two samples for each sampling target, and three replicas for each sample, totalizing 102 analyses. Uncertainty arising from analytical steps considered the uncertainty from dissolution step (estimated using Monte Carlo method and regression equation obtained using DoE) and uncertainty from quantification step. Overall uncertainty value was found to be 2.2%, which is below the target uncertainty value (ut =2.5%). The contributions of uncertainty sources in this study were as follows: 24% from sampling uncertainty, 29% from the dissolution step uncertainty, and 47% from the quantification step uncertainty. The results of dissolution test should be compared to the specification limits (Q). According to the pharmacopeia requirements, the batch of the medicine should be declared compliant if the dissolved amount of prednisone for six tablets are above the specification limits + 5% (Q+5%=85%). Since the measured values for all six tablets (96.5%, 94.0%, 96,4%, 95.3%, 96.0%, and 96.9%) were above the multivariate acceptance limit (90.2%, calculate as the standard uncertainty multiplied by multivariate coverage factor), the batch of the prednisone tablets was declared complaint, with a reduced total risk of false decision (total risk value below 5%).

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Measurement uncertainty is one of the widespread concepts applied in scientific works, particularly to estimate the accuracy of measurement results and to evaluate the conformity of products and processes. In this work, we propose a methodology to analyze the performance of measurement systems existing in the design phases, based on a probabilistic approach, by applying the Monte Carlo method (MCM). With this approach, it is feasible to identify the dominant contributing factors of imprecision in the evaluated system. In the design phase, this information can be used to identify where the most effective attention is required to improve the performance of equipment. This methodology was applied over a simulated electrocardiogram (ECG), for which a measurement uncertainty of the order of 3.54% of the measured value was estimated, with a confidence level of 95%. For this simulation, the ECG computational model was categorized into two modules: the preamplifier and the final stage. The outcomes of the analysis show that the preamplifier module had a greater influence on the measurement results over the final stage module, which indicates that interventions in the first module would promote more significant performance improvements in the system. Finally, it was identified that the main source of ECG measurement uncertainty is related to the measurand, focused towards the objective of better characterization of the metrological behavior of the measurements in the ECG.

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Historically, owing to the increase in processing capacity over the years, validation and adjustment of measurements have become imperative. In particular, concerning discussions related to data and results in analytical chemistry, there is always a need to improve their reliability. The data reconciliation technique has the objective of using measurement redundancies to obtain the best estimate of the true value and, consequently to minimize its uncertainty. Unfortunately, this powerful tool is less known and used by analytical chemists compared to other areas. This approach can be satisfactorily performed in decision-making procedures that focus on chemical analysis, chemometrics, biochemistry analysis, forensics, and environmental sciences, such as in a characterization study, regarding conformance or nonconformance with the specification, doubts related to the malfunctioning of meters and about the compatibility of test methods. This work discusses and sheds light on the importance of data reconciliation, including data reconciliation statistics and application of the technique, traditional data reconciliation in analytical chemistry, principal component analysis based on data reconciliation in analytical chemistry, and fuzzy data reconciliation in analytical chemistry.

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Analytical results are often used in scientific research, industrial and clinical applications to support decision making. Despite all efforts to ensure the reliability of analytical results (including method validation, internal quality control, use of certified reference materials, proficiency tests, and ISO 17025 accreditation), there will always be an uncertainty associated with the measured value. The measurement uncertainty expresses the quality of the analytical result and allows the comparability between analytical results or between the measured value and the specification limit(s). This work discusses the importance of measurement uncertainty, including the steps involved in the measurement uncertainty evaluation, the bottom-up and top-down approaches used in measurement uncertainty calculation, the measurement uncertainty evaluation in drug and medicine analyses, and the application of measurement uncertainty in conformity assessment for quality control, stability studies, and pharmaceutical equivalence.

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The quality assessment of medicines involves multiple compliance parameters, such as identity, dosage, purity, potency, content uniformity, disintegration time, dissolution rate, among others. The measurement uncertainty associated with a measured value can affect the conformity assessment and, consequently, it impacts decision-making. Even if the particular risks are acceptable, the total risk may be significantly high. Thus, the aim of this work was to develop a procedure for the definition of acceptance (or rejection) limits applied to multiple compliance assessments, that ensure acceptable particular and total risks. The multiple compliance assessments were performed and applied in the pharmaceutical equivalence studies for cisplatin injectable solution, carboplatin injectable solution, ranitidine tablets, and acetaminophen oral solution from several manufacturers. Pharmaceutical equivalence studies were performed adopting pharmacopeial analytical procedures. All chromatographic system suitability results complied with the requirements regarding the resolution between peaks, the capacity factor, the tailing factor, the theoretical plates, and the relative standard deviation for replicate injections. Univariate and multivariate guard-bands (g and g', respectively) were calculated by multiplying the standard uncertainty (u) by an appropriate univariate and multivariate coverage factor (k and k', respectively).The values of multivariate guard band (g') were higher than the values of univariate guard bands (g), which leads to more restrictive acceptance intervals. Measured values between the conventional and the multivariate acceptance limits will ensure particular risk values below the maximum acceptable value, however, the total risk may be significantly high. On the other hand, measured values within the multivariate acceptance limits ensure that particular risk values and total risk value are below the maximum acceptable value The application of multivariate guard bands is a simple way to ensure reduced particular and total risks of false conformity decisions, which is of great interest to regulatory agencies and the manufactures of the medicines.

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Pharmaceutical products must meet quality requirements to ensure the efficacy and safety of pharmacological treatment. Non-compliance of medicines can cause economic losses and compromise the patient's health. In this work, the risks of false compliance/non-compliance decisions for parenteral antibiotics (cephalothin, ciprofloxacin and metronidazole) were evaluated on the basis of analytical results, measurement uncertainties and specification limits. Physicochemical and biological quality assays were performed according to pharmacopeial procedures. Measurement uncertainties were determined using the bottom-up approach or the probability of false-positive/false-negative results. The risks of false compliance/non-compliance decisions were estimated using the frequentist approach and Monte Carlo simulations. Guard-bands were determined through a validated spreadsheet for calculating univariate and multivariate acceptance limits. All risk values (particular risks and total risk, consumer's or producer's risk) were below the maximum permissible risk value. The univariate and multivariate guard-bands defined more restrictive specification values, reducing the risks of false compliance/non-compliance decisions. One antibiotic presented unsatisfactory results regarding the drug content and was classified as out of specification product. The application of risk management tools in the pharmaceutical area contributes to improving the quality and safety of products and supports decision-making.

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A contaminação microbiana pode comprometer a eficácia e a segurança dos produtos farmacêuticos. Os testes de contagem microbiana são utilizados para avaliar a qualidade microbiológica de produtos farmacêuticos não estéreis, exigidos pela maioria dos compêndios farmacopeicos. Apesar disso, raramente é considerada a avaliação da incerteza de medição para testes de contagem microbiana, o que pode levar a falsas decisões quanto à conformidade/nãoconformidade. Neste trabalho avaliamos os efeitos de matriz nos testes de contagem microbiana e sua avaliação de incerteza top-down, e avaliamos a incerteza da medição utilizando a abordagem bottom-up, além de que estimamos os riscos do consumidor ou do produtor devido à incerteza da medição. As incertezas combinada e expandida são calculadas empregando-se a abordagem topdown consideraram a exatidão (recuperação) e a precisão como os principais componentes de incerteza. O componente de incerteza da exatidão foi o mais relevante em 59% das amostras estudadas, enquanto a precisão foi a principal fonte de incerteza em apenas 41% das amostras, sendo observado que quanto maior a interferência da matriz, maior o fator de incerteza e, consequentemente, maior a assimetria para o intervalo em torno da medida. A partir da abordagem bottom-up, foram identificadas e quantificadas três principais fontes de incerteza: fator de diluição, volume plaqueado e contagem das placas. A contribuição dessas fontes de incerteza depende do valor medido da carga microbiana em produtos farmacêuticos, a contribuição do fator de diluição e das incertezas do volume plaqueado aumentam com o aumento do valor medido, enquanto a contribuição da contagem das placas diminui com o aumento do valor medido. Foi possível avaliar o risco de decisões falsas devido à incerteza de medição, por meio das estimativas dos riscos do consumidor ou do produtor. Os riscos foram avaliados utilizando-se o método Monte Carlo. Portanto, foi demonstrado a relevância da avaliação da incerteza de medição para garantir a confiabilidade dos resultados dos testes de contagem microbiana e a apoiar a tomada de decisões quando a avaliação da conformidade/não-conformidade dos produtos farmacêuticos não estéreis

Microbial contamination can compromise the efficacy and safety of pharmaceutical products. Microbial counting tests are used to assess the microbiological quality of non-sterile pharmaceutical products required by most pharmacopoeia compendiums. Despite this, measurement uncertainty assessment for microbial count tests is rarely considered, which can lead to false compliance/non-compliance decisions. In this work we evaluated the matrix effects on microbial counting tests and their top-down uncertainty assessment, and evaluated measurement uncertainty using the bottom-up approach, inaddition to estimating the consumer's or producer's risks due to measurement uncertainty. The combined and expanded uncertainties calculated using the top-down approach considered accuracy (recovery) and accuracy as the main components of uncertainty. The uncertainty component of accuracy was the most relevant in 59% of the samples studied, while accuracy was the main source of uncertainty in only 41% of the samples, being observed that the greater the interference of the matrix, the greater the uncertainty factor and, consequently, the greater the asymmetry for the interval around the measurement. From the bottom-up approach, three main sources of uncertainty were identified and quantified: dilution factor, platelet volume and plaque count. The contribution of these sources of uncertainty depends on the measured value of microbial load in pharmaceutical products, the contribution of the dilution factor and uncertainties of the plated volume increase with the increase in the measured value, while the contribution of plate counting decreases with the increase of the measured value. It was possible to assess the risk of false decisions due to measurement uncertainty by estimating consumer or producer risks. The risks were evaluated using the Monte Carlo method. Therefore, the relevance of measuring uncertainty assessment has been demonstrated to ensure the reliability of microbial count test results and to support decision-making when assessing non-sterile pharmaceutical conformity/non-compliance

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The need to estimate the orientation between frames of reference is crucial in spacecraft navigation. Robust algorithms for this type of problem have been built by following algebraic approaches, but data-driven solutions are becoming more appealing due to their stochastic nature. Hence, an approach based on convolutional neural networks in order to deal with measurement uncertainty in static attitude determination problems is proposed in this paper. PointNet models were trained with different datasets containing different numbers of observation vectors that were used to build attitude profile matrices, which were the inputs of the system. The uncertainty of measurements in the test scenarios was taken into consideration when choosing the best model. The proposed model, which used convolutional neural networks, proved to be less sensitive to higher noise than traditional algorithms, such as singular value decomposition (SVD), the q-method, the quaternion estimator (QUEST), and the second estimator of the optimal quaternion (ESOQ2).

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In this work, high frequency and low power ultrasound without external heating source and mechanical stirring in biodiesel production were studied. Transesterification of soybean oil with methanol and catalyzed by KOH was investigated using ultrasound equipment and ultrasonic transducer. The effect of ultrasonic output power (3 W-9 W), ultrasonic frequency (1 MHz and 3 MHz), and alcohol to oil molar ratio (6:1 and 8:1) have been investigated. The increase in ultrasonic power provided higher conversion rates. In addition, higher conversion rates were obtained by increasing the ultrasonic frequency from 1 MHz to 3 MHz (48.7% to 79.5%) for the same reaction time. Results also indicate that the speed of sound can be used to evaluate the produced biodiesel qualitatively. Further, the ultrasound system presented electric consumption (46.2W∙h) four times lower than achieved using the conventional method (211.7W∙h and 212.3W∙h). Thus, biodiesel production using low power ultrasound in the MHz frequency range is a promising technology that could contribute to biodiesel production processes.

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Microbial enumeration tests are widely used to assess the microbiological quality of non-sterile pharmaceutical products. Despite of all efforts to guarantee the reliability of microbial enumeration tests, there will always be an uncertainty associated with the measured values, which can lead to false conformity/non-conformity decisions. In this work, we evaluated the measurement uncertainty using a bottom-up approach and estimate the consumer's or producer's risk due to the measurement uncertainty. Three main sources of uncertainty were identified and quantified: dilution factor, plated volume, and microbial plate counts. The contribution of these sources of uncertainty depends on the measured value of microbial load in pharmaceutical products. The contribution of dilution factor and plated volume uncertainties increase with an increase of measured value, while the contribution of microbial plate count uncertainty decreases with an increase of measured value. The overall uncertainty values were expressed as uncertainty factors, which provide an asymmetric 95% level confidence level of microbial load in pharmaceutical products. In addition, the risk of false conformity/non-conformity decisions due to measurement uncertainty was assess using Monte Carlo method. When the measured value is close to the upper specification limit and/or the measurement uncertainty is large, the risk of false conformity/non-conformity decisions may be significantly high. Thus, we conclude that the use of uncertainty factor in the conformity/non-conformity assessment is important to guarantee the reliability of microbial enumeration test results and to support decision-making.

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The pharmaceutical equivalence between test (generic or similar) and reference medicine is evaluated through in vitro quality tests involving multiple compliance parameters. Despite efforts to ensure the reliability of the analytical results obtained in the pharmaceutical equivalence studies, measurement uncertainties lead to a risk of false decisions. Thus, the aim of this work was to evaluate the measurement uncertainties associated with the analytical results obtained in the pharmaceutical equivalence studies of different pharmaceutical forms and to estimate the risks of false decisions in the evaluation of pharmaceutical equivalence. The measurement uncertainties associated with the test results were evaluated using the bottom-up and top-down approaches. The consumer's or producer's combined particular risks and combined total risks were estimated using the Monte Carlo method implemented in MS-Excel spreadsheet (available as supplemental material). Considering the seven pharmaceutical equivalence studies performed in this work, three studies were not conclusive (risk of false pharmaceutical equivalence decisions higher than 5 %). Moreover, we concluded pharmaceutical equivalence and pharmaceutical non-equivalence in one and three studies, respectively. The particular and total combined risks are useful to make decisions regarding the evaluation of pharmaceutical equivalence between the test (generic or similar) and reference medicines. Regulatory bodies and pharmaceutical equivalence centers are very interested in the estimation of the risks of false decisions, particularly to evaluate the quality of medicines that are not submitted to bioequivalence studies.

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Phytochelatins (PCs) are peptides that play an important role in homeostasis and detoxification of heavy metal in plants. Furthermore, they have been proposed as earlier potential biomarkers of aquatic pollution by heavy metals. Nowadays, several researchers have reported on current methods for quantification of glutathione (GSH) and the PCs (phytochelatin 2, phytochelatin 3, phytochelatin 4) quantification in plants. However, no method has reported the uncertainty of the measurement, which helps to improve the accuracy and quality assurance in the PC quantification. In this work, a new methodology using ultra-high-performance liquid chromatography coupled to mass spectrometry (UPLC-MS) to measure with high precision and accuracy the PCs in aquatic plants, was validated. Selectivity, linearity, limit of detection, limit of quantification, precision, trueness and uncertainty estimation were examined as parts of the method validation. The described method shows excellent linearity in different ranges for all analytes with coefficients of determination higher than 0.99. The relative standard deviation for intra-day precision was <3% and for inter-day <10%. All LOD and LOQ analytes ranged from 0.02 to 0.08 µg ml-1, and from 0.03 to 0.09 µg ml-1, respectively. The recoveries varied from 61% to 89%. In order to obtain an interval of results with the highest confidence levels, the uncertainty associated with the measurements was evaluated. The calibration curve (>50%) and recovery (19-44%) were the most important contributors to the total uncertainty. The proposed method was applied to quantify GSH and PCs in the aquatic plants Lemna gibba L., Myriophyllum heterophyllum Michx., Arenaria paludicola and Hydrocotyle ranunculoides L. fil., showing statistical differences in the mass fraction of the analytes.

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The low-quality of automotive fuels may lead to the generation of pollutants harmful to both environmental and human health. The quality evaluation of automotive fuels requires a multiparameter conformity assessment, which may lead to an increased total risk of false conformity decisions even if all parameters comply with the acceptance limits. Thus, the aim of this work was to propose the establishment of multivariate acceptance limits in order to ensure a reduced total risk of false conformity decisions applied to automotive fuels analysis. Particular and total (consumers' and/or producers') risks were estimated using frequentist (specific) and Bayesian (global) approaches. Multivariate acceptance limits were estimated using Monte Carlo method, adopting an appropriate multivariate coverage factor (k') defined using MS Excel Solver function. The definition of multivariate acceptance limits ensures a total risk below the maximum admissible risk (typically 5%) and was successfully employed in the conformity assessment of automotive fuels (diesel and gasoline). The employment of the multivariate acceptance limits may be useful in the conformity assessment of several multiparameter products.

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This research was motivated by technical-economic challenges imposed by mass metrology, specifically, in matters concerning calibration methods of non-automatic type weighing instruments (i.e.: digital scales). In order to contextualize the problem detected, in the industry there are different processes of mass measurement that are controlled by digital scales, such as: mass of liquids, chemicals, food, body mass of a person. In these processes, the scale is used in the following four conditions for mass measurement: (i) ascending and descending load, returned to zero; (ii) ascending and descending load, without the need to return to zero; (iii) only with ascending load and (iv) only with descending load. In this context and, maintaining the principles for the calibration of a measurement instrument in which it must be carried out under the same operating conditions as the instrument, metrology laboratories must knowing the metrological reliability (i.e.: errors and uncertainties) for each situation. This is exactly the main motivation for the development of the research. Thus, the experimental data obtained in a research laboratory under controlled environmental conditions allowed obtaining a minimum expanded uncertainty associated with the mass measurement of 0.0012 kg (k=2; confidence level: 95%).

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INTRODUCTION: By quantifying the measurement uncertainty (MU), both the laboratory and the physician can have an objective estimate of the results' quality. There is significant flexibility on how to determine the MU in laboratory medicine and different approaches have been proposed by Nordtest, Eurolab and Cofrac to obtain the data and apply them in formulas. The purpose of this study is to compare three different top-down approaches for the estimation of the MU and to suggest which of these approaches could be the most suitable choice for routine use in clinical laboratories. MATERIALS AND METHODS: Imprecision and bias of the methods were considered as components of the MU. The bias was obtained from certified reference calibrators (CRC), proficiency tests (PT), and inter-laboratory internal quality control scheme (IQCS) programs. The bias uncertainty, the combined and the expanded uncertainty were estimated using the Nordtest, Eurolab and Cofrac approaches. RESULTS: Using different approaches, the expanded uncertainty estimates ranged from 18.9-40.4%, 18.2-22.8%, 9.3-20.9%, and 7.1-18.6% for cancer antigen (CA) 19-9, testosterone, alkaline phosphatase (ALP), and creatinine, respectively. Permissible values for MU and total error ranged from 16.0-46.1%, 13.1-21.6%, 10.7-26.2%, and 7.5-17.3%, respectively. CONCLUSION: The bias was highest using PT, followed by CRC and IQCS data, which were similar. The Cofrac approach showed the highest uncertainties, followed by Eurolab and Nordtest. However, the Eurolab approach requires additional measurements to obtain uncertainty data. In summary, the Nordtest approach using IQCS data was therefore found to be the most practical formula.

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