EVALUATING THE UNCERTAINTY OF MEASUREMENT ON BLOOD'S GLUCOSE LEVEL

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1 BIOMEDICAL ENGINEERING- APPLICATIONS, BASIS & COMMUNICATIONS EVALUATING THE UNCERTAINTY OF MEASUREMENT ON BLOOD'S GLUCOSE LEVEL 91 HUNG-CHUN HUANG 1,2, CHIA-HUNG CHIEN 1,2, CHENG-YI WANG 1, FOK-CHING CHONG 1 1 Department of the engineering of the medicine of the hospital, National Taiwan University 2 Institute of Electrical Engineering, National Taiwan University Taipei, Taiwan ABSTRACT Judging from the continuous increase in population suffering from chronic illnesses in the past 30 years in Taiwan, we can predict that the number of diabetes victims will reach 1.5 million in 15 years. This increase is global. According to an estimate provided by WTO, one out of two diabetes sufferers is not identified as the illness victim. An estimate of 100 million people in the world are diabetes patients. Although there is currently no way to completely cure diabetes, this disease can be controlled, monitored, and improved through education, research and development of new medication and techniques. However, the quality control of glucose monitoring has posed a stubborn problem to all fields related to the medical realm in Taiwan. By contrast, there is already a welldeveloped management system of blood glucose measurement in the West. All the standard-setting organizations, such as NCCLS and ISO, have published relevant Standard Operation Procedure (SOP). In Taiwan, we haven't had any similar certification mechanism. It is urgent for Taiwan to establish such standards specifically for the yellow race. Now, CNLA has introduced ISO in clinical test. Although it offers a general guideline, it doesn't specify detailed operation steps. As a result, it cannot offer an accurate result in blood glucose measurement. This paper is focused on ways to evaluate the uncertainty of measurement on blood glucose level based on the standard environment lab for medical device testing in the biomedical engineering department of National Taiwan University Hospital, so as to establish a function of uncertainty of measurement on blood glucose level and make it a stepping stone for certification of the measurement. Biomed Eng Appl Basis Comm, 2005 (April); 17: UNCERTAINTY OF MEASUREMENT According to the international standards regulated by ISO, the measurement conducted in a medical lab should give an accurate and precise result for both doctors and patients, in order to ensure a reliable medical quality. In addition, the paradigms for medical examination labs as stipulated by ISO require Received: Feb 19, 2005; Accepted: Mar 5, 2005 Correspondence: Hung-Chun Huang Department of the engineering of the medicine of the hospital, National Taiwan University, Taipei, Taiwan bluegallery@ha.mc.ntu.edu.tw that the uncertainty of measurement be evaluated. Methods of evaluation are based on ISO GUM, in which traceable chains with a comparison process achieve a precision that meets the national standard. It is evident, therefore, that traceability and precision are directly related to uncertainty of measurement. Uncertainty of measurement is a parameter of measurement results, which is used to represent a reasonable dispersing level of measurement results. So the content of measurement uncertainty includes the dispersing level of measurement results, possible bias, and possible bound. According to ISO GUM 3.3.2, the following measurement procedures will contribute to uncertainty of measurement: 1. incomplete definition of the measured objects 2. inadequate realization of measured quantity 31

2 92 3. insufficient sampling of the measured objects 4. lack of optimal environment for the measurement 5. human errors in reading the measurement results from devices 6. decision of the device resolution and critical point 7. lack of an definite value for a standard measurement device and its reference material 8. oversimplification of constant value or values from other sources, resulting in adequate representation of reality through the value 9. bias caused by addition of approximates or hypotheses during measure process 10. variation in repetition of the identical measurement process The above problems need to be addressed in estimation. 2. STEPS Important factor analysis is conducted based on measurement procedures and experience, in order to define the measurement function, that is, to determine the functional relationship between measured quantity Y and measurement quantity and factors that contribute to measurement uncertainty. This measurement function is employed to build uncertainty function. Then the uncertainty function is used to evaluate standard uncertainty values, which can be broken down into types A and B: Type A is a way of statistical analysis on a series of observation values, in order to calculate standard uncertainty level. Its specific steps are as follows: 1. repeat the test for n times 2. obtaining the average X and standard deviation S 3. calculate the average standard deviation =S/ n According to central limit theorem, the optimum standard deviation is acquired from the average after sampling from the matrix of normal distribution. In practice, if an independent measurement times are over 30, they are regarded as normal distribution by central limit theorem. If measurement procedure is destructive or resistant to multiple repetitions, then its type A uncertainty level can be achieved by transforming sample standard deviations of the two cases with t- distribution factors. Type B is a method of estimation using past measurement data, present understanding of devices or materials, specifications, calibration, or other figures provided by traceable certificate reports. Its steps of estimation are as follows: 1. finding possible bias Vol. 17 No. 2 April making an hypothesis about probability distribution 3. calculating standard deviation according to hypothesized probability distribution The standard deviation summation is achieved by communication theorem, multiplying type A and type B respectively by the weighting value endowed on importance of the measurement results, adding the respective products, find the square root of the total products, and acquiring the combination uncertainty value. After the combination uncertainty value is obtained, in order to achieve a wider coverage, we multiply the value by the coverage factor K. Usually, we set the confidence coverage range to 95%, and expansion uncertainty U is acquired by multiplying the combination uncertainty value by K. The final outcome of measurement: (Y = y U). 3. EVALUATION OF BLOOD GLUCOSE UNCERTAINTY MEASUREMENT The measurement of blood glucose level is conducted using YSI 2300 STAT PLUS. This device adopts the primary standard solution of YSI 2747 (180 mg/dl) to achieve auto calibration. The blood glucose level readings of subjects are obtained based on the examination lines from the data. The measurement system is shown as followed. The uncertainty of blood glucose level is estimated according to the standards set up by ISO GUM. The measurement precision of the device is tested against standard glucose solution. First, we calibrate the examination line with the standard glucose solution NIST SRM965, and obtain measurement function by means of regression analysis. Factors that may affect the measurement system uncertainty include the linearity of the examination lines, resolution of devices, the natural bias among subjects caused by temperature and humidity, and the total uncertainty acquired through addition of uncertainty of the examination line. 3.1 Evaluating the Uncertainty of 32

3 BIOMEDICAL ENGINEERING- APPLICATIONS, BASIS & COMMUNICATIONS Measurement Function Use mg/dl standard glucose solution (NIST SRM965) to do 15 times measurement and means of regression analysis its data of the measurement is as follows the table 1 so we can say that the measurement equation Table model is good Uncertainty of Measurement of NIST SRM965 as follows the table3 Table 3. r 2 =SSR/SSTO= Yo=BX+A= X (B= A= ) Table 2. Sum of Squares corrected Total S = where S X = S Y = S c(100) = S c(200) = S c(300) = N00=3 M = number of measurement 3.2 Evaluating the Uncertainty of Instrument Resolution According to instrument menu, instrument resolution is 1mg/dL, because its value don t exceed to 0.5 mg/dl range, so here the probability that inside of the district appear for 100%.It make as rectangle distributed, free degree is 1.00 Es+10, intelligent coefficient is 1, then the degree of the indetermination of the resolution is: 0.5/ 3 = 0.29 (mg/dl) 3.3 Evaluating the Uncertainty of Environment Referring to the standards proposed by CNLA, temperature should be kept between 21 and 25?C, and humidity should be kept between 40%~60% in laboratories. Several cases with different operating conditions were simulated in our laboratory and the natural variations of the specimens were measured as follows: Sum of Squares due to Regression 33

4 94 Table 4. Temp. :21 C humidity:50%rh specimen: serum interval:2min Vol. 17 No. 2 April 2005 Table 5. Temp. :25 C humidity:60%rh specimen: serum interval:2min In statistics, standard deviations and variances are often used to measure the dispersion. Variance is applicable to static data which are irrelevant to time. When enough samples are collected, the mean and variance could be calculated. The data of the specimens, however, are not static. Following IEEE's recommendations, Allan variance was employed to assess the uncertainty of blood glucose measurement instead. Thus, Allan variances could be calculated using Allan variance formulas and the data in table4 and 5. Table 6. The sensitivity coefficient was 1 and the degree of freedom was 34. The means (0.84 mg/dl,1.82 mg/dl,2.50mg/dl) of those intervals were selected to represent the measurement uncertainty. 3.4 Assessing the Uncertainty caused by Rounding Since the data mentioned above were rounded to the hundredth, the uncertainty of rounding was 0.01and uncertainty of a half interval was Assuming the distribution of uncertainty was rectangle and d.o.f was 34

5 BIOMEDICAL ENGINEERING- APPLICATIONS, BASIS & COMMUNICATIONS E+10(unlimited), and sensitivity coefficient was 1, the uncertainty caused by rounding would be: 0.005/ 3= However, the uncertainties of measurement function, examination lines, resolution, lab conditions, and rounding were all rounded to the hundredth. After adding the rounding uncertainty, the overall uncertainty would be: *5= Overall Assessment of Measurement Uncertainty Those uncertainties mentioned above could be summarized as table7: Table 7. In order to assess the uncertainty, data in Table 1 were used as measurement inputs: Y 0100 =100.68= X Sx 0100 = Let confidence interval=95%.thus table 8 could be produced. Table 8. Table 9. Y 0300 =294= X S X 03= Let confidence interval=95%.thus table 10 could be produced. Table CONCLUSION This article used correction coefficient to verify the measured blood glucose levels. The results of the analysis were as follows, The uncertainty of blood glucose measurement in our lab. was determined as: Y 0200 =196.6= X S x0200 = Let confidence interval=95%.thus table 9 could be produced. 35

6 96 Vol. 17 No. 2 April 2005 blood glucose range of assessed cases: ~ mg/dl expansion uncertainty of assessed cases : 4.32~9.32 mg/dl coverage factor: 2.04~2.08 confidence interval : 95% REFERENCE 1. DR.G.K.N.S SUBASINGHE Expression of uncertainty in measurements made by calibrated equipment Technique OIML BULLETIN number4 October Douglas A.Skoog Donald M.West F.James Holler Fundamentals of analytical chemistry Saunders College Publishing JYC Annex A. 36