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.

[1]  David J Handelsman,et al.  Empirical estimation of free testosterone from testosterone and sex hormone-binding globulin immunoassays. , 2005, European journal of endocrinology.

[2]  Tim Usherwood,et al.  Chronic kidney disease and automatic reporting of estimated glomerular filtration rate: new developments and revised recommendations , 2012, The Medical journal of Australia.

[3]  R F Martin,et al.  General deming regression for estimating systematic bias and its confidence interval in method-comparison studies. , 2000, Clinical chemistry.

[4]  Mauro Panteghini,et al.  Article in press-uncorrected proof Editorial Application of traceability concepts to analytical quality control may reconcile total error with uncertainty of measurement , 2009 .

[5]  C. Florkowski,et al.  Methods of Estimating GFR - Different Equations Including CKD-EPI. , 2011, The Clinical biochemist. Reviews.

[6]  M. Wheeler,et al.  Plasma Free Testosterone—is An Index Sufficient? , 1985, Annals of clinical biochemistry.

[7]  David J Handelsman,et al.  Predictive accuracy and sources of variability in calculated free testosterone estimates , 2009, Annals of clinical biochemistry.

[8]  Tom Greene,et al.  Using Standardized Serum Creatinine Values in the Modification of Diet in Renal Disease Study Equation for Estimating Glomerular Filtration Rate , 2006, Annals of Internal Medicine.

[9]  R Wood,et al.  A simulation study of the Westgard multi-rule quality-control system for clinical laboratories. , 1990, Clinical chemistry.

[10]  C R Tillyer,et al.  Error estimation in the quantification of alkaline phosphatase isoenzymes by selective inhibition methods. , 1988, Clinical chemistry.

[11]  J S Krouwer,et al.  Estimating total analytical error and its sources. Techniques to improve method evaluation. , 1992, Archives of pathology & laboratory medicine.

[12]  C. Schmid,et al.  A new equation to estimate glomerular filtration rate. , 2009, Annals of internal medicine.

[13]  Mary Stoddart,et al.  Calculated free testosterone in men: comparison of four equations and with free androgen index , 2006, Annals of clinical biochemistry.

[14]  John Middleton,et al.  Effect of analytical error on the assessment of cardiac risk by the high-sensitivity C-reactive protein and lipid screening model. , 2002, Clinical chemistry.

[15]  J O Westgard,et al.  Criteria for judging precision and accuracy in method development and evaluation. , 1974, Clinical chemistry.

[16]  N. Madias,et al.  Serum anion gap: its uses and limitations in clinical medicine. , 2006, Clinical journal of the American Society of Nephrology : CJASN.

[17]  R C Hawkins,et al.  The significance of significant figures. , 1990, Clinical chemistry.

[18]  E W Holmes,et al.  Verification of reference ranges by using a Monte Carlo sampling technique. , 1994, Clinical chemistry.

[19]  Susan R. Wilson,et al.  Objective determination of appropriate reporting intervals , 2004, Annals of clinical biochemistry.

[20]  Jan S Krouwer,et al.  Critique of the Guide to the expression of uncertainty in measurement method of estimating and reporting uncertainty in diagnostic assays. , 2003, Clinical chemistry.

[21]  Apostolos Burnetas,et al.  Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS. , 2011, Talanta.

[22]  Ian Farrance,et al.  Uncertainty of Measurement: A Review of the Rules for Calculating Uncertainty Components through Functional Relationships. , 2012, The Clinical biochemist. Reviews.

[23]  T. Bäckström,et al.  Calculation of free and bound fractions of testosterone and estradiol-17 beta to human plasma proteins at body temperature. , 1982, Journal of steroid biochemistry.

[24]  T Pettersson,et al.  A method to estimate the uncertainty of measurements in a conglomerate of instruments/laboratories , 2005, Scandinavian journal of clinical and laboratory investigation.

[25]  Jan S Krouwer,et al.  Setting performance goals and evaluating total analytical error for diagnostic assays. , 2002, Clinical chemistry.

[26]  A. Vermeulen,et al.  A critical evaluation of simple methods for the estimation of free testosterone in serum. , 1999, The Journal of clinical endocrinology and metabolism.

[27]  A. Levey,et al.  A More Accurate Method To Estimate Glomerular Filtration Rate from Serum Creatinine: A New Prediction Equation , 1999, Annals of Internal Medicine.

[28]  S. Lolekha,et al.  Value of the anion gap in clinical diagnosis and laboratory evaluation. , 1983, Clinical chemistry.

[29]  Gina Chew,et al.  A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software , 2012, Analytical and Bioanalytical Chemistry.

[30]  V Kairisto,et al.  Regression-based reference limits: determination of sufficient sample size. , 1998, Clinical chemistry.

[31]  V. M. Chinchilli,et al.  Evaluating test methods by estimating total error. , 1994, Clinical chemistry.

[32]  E. Theodorsson,et al.  Routine internal- and external-quality control data in clinical laboratories for estimating measurement and diagnostic uncertainty using GUM principles , 2012, Scandinavian journal of clinical and laboratory investigation.

[33]  Sverre Sandberg,et al.  Confidence intervals and power calculations for within-person biological variation: effect of analytical imprecision, number of replicates, number of samples, and number of individuals. , 2012, Clinical chemistry.

[34]  John Middleton,et al.  Evaluation of assigned-value uncertainty for complex calibrator value assignment processes: a prealbumin example. , 2007, Clinical chemistry.

[35]  J C Boyd,et al.  Quality specifications for glucose meters: assessment by simulation modeling of errors in insulin dose. , 2001, Clinical chemistry.