Fresenius' Journal of
Fresenius J Anal Chem (1990) 338:408-410
@ Springer-Verlag1990
Certification Statistical aspects of the use of reference materials John Mandel National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
Summary. Interlaboratory testing, even when coupled with careful calibrations in terms of SRM's, is a complex process. It often raises problems that only the subject-matter specialists can solve. The problems are definitely not solved by rejecting test results or laboratories.
Introduction In recent years, instrumental methods of analysis have become the norm, whose advantages are widely recognized. On the other hand, one of the characteristics of instrumental methods is that they are often unusable unless coupled with adequate calibration procedures of the measuring instrument. Thus paper presents one concrete example to illustrate the use of reference materials in an actual case.
Determination of glucose by the hexokinase method This method involves a certain a m o u n t of wet chemistry, followed by a reading on a spectrophotometer. It is important that the latter be properly calibrated. In an interlaboratory study, five samples of serum containing increasing a m o u n t s of glucose, from about 40 to 450 mg/100 ml of glucose, were sent to seven participating laboratories. Each laboratory ran all five samples in 1 day, but preceded and followed the measurements by a calibration of the instrument. F o r the calibration seven solutions of glucose certified to contain precisely given amounts of an SRM of glucose were used. In this manner, the absorbance value read on the instrument could be converted to concentration of glucose.
Absorbanee measurements of the serum samples Table 1 shows the absorbance values for all laboratories. This table was analyzed column-by-column as illustrated for the first column in Table 2. Note that the h-values are essentially standardized deviations from the average. A positive h indicates a value above the average; a negative h indicates a value below the average. There are 7 h-values for this one material. If the same analysis is carried out for all five materials, we obtain the h-values shown in Table 3. Now the h-values were obtained independently for each material (column), but it is instructive to graph them by rows, i.e., by laboratories as shown in Fig. 1. The laboratory biases are apparent, as are certain trends within laboratories.
Conversion to concentration of glucose As mentioned above, a calibration experiment was carried out simultaneously with the measurements of glucose as shown in Table 4. Seven solutions were used, with the indicated concentrations. The tabulated value is absorbance measurement.
Table 1. Glucose: absorbance Lab
1 2 3 4 5 6 7
Material A
B
C
D
E
0.117 0.166 0.167 0.211 0.178 0.165 0.173
0.208 0.270 0.265 0.312 0.272 0.258 0.287
0.369 0.439 0.423 0.478 0.429 0.412 0.415
0.571 0.639 0.620 0.680 0.624 0.592 0.594
1.246 1.316 1.292 1.362 1.270 1.245 1.243
Table 2. Worksheet for concentration A Lab
Average
D
h
1 2 3 4 5 6 7 Averge S
0.117 0.166 0.167 0.211 0.178 0.165 0.173 0.1682 0.0277
--0.0512 -- 0.0022 --0.0012 0.0430 0.0098 --0.0032 0.0048
-1.85 - 0.08 -0.04 1.55 0.35 --0.11 0.17
h = D/S
Table 3. h-Values - 1.847 - 0.078 --0.042 1.553 0.355 --0.114 0.174
-- 1.876 0.081 --0.077 1.407 0.144 -0.298 0.618
-- 1.669 0.472 --0.017 1.664 0.166 --0.354 --0.262
-- 1 . 2 8 5 0.611 0.082 1.741 0.193 --0.699 -0.643
--0.805 0.761 0.224 1.790 --0.268 --0.828 --0.873
409 Table 4. Calibration experiment 2
Lab
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Laboraf0ry Fig. 1. Graph of h-values by laboratories on absorbance values
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0
50
100
150
200
400
600
0.050 0.049 0.058 0.094 0.075 0.055 0.062 0.063
0,189 0,191 0,197 0,237 0,202 0,183 0,191 0,198
0.327 0.334 0.337 0.375 0.340 0.312 0.321 0.335
0.467 0.471 0.468 0.520 0.480 0.439 0.459 0,472
0.605 0,615 0.611 0.661 0.613 0.567 0.580 0.607
1.156 1.172 1.156 1.221 1.135 1.089 1.109 1.148
1.704 1.720 1.709 1.776 1.620 1.605 1.634 1.681
Table 5. Glucose in serum
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1 2 3 4 5 6 7 Average
Concentration
Lab
Using average calibration
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1.28
1 2 3 4 5 6 7 Average S
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0.32
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A
B
C
D
E
19.192 37.347 37.718 54.094 41.793 36.977 39.941 38.152 10.266
52.908 75.880 74.027 91.441 76,621 71.434 82.179 74.927 11.740
112.560 138.496 132.568 152.946 134.791 128.492 129.604 132.779 12.116
187,403 212.597 205.558 227.603 207.040 195.183 195.924 204.473 13.289
437.495 463,431 454.539 480.474 446.388 437.125 436.384 450.834 16.560
I
120 240 360 480 600 720
Table 6. Precision parameters
Concenfrafion
Fig. 2. Calibration line
3 2 1
Level
Average
SR (j)
1 2 3 4 5
38.152 74.927 132.779 204.473 450.834
10.266 11.740 12.116 13.289 16.560
-~ 0 > "-1 Table 7. Glucose data individually calibrated
-2 -3 1
2
3
4
5
6
7
Laboratory Fig. 3. Graph of h-values~by laboratories. Individual calibrations
We can use these results in two different ways: (1) F o r each c o n c e n t r a t i o n , we can use the a v e r a g e a b s o r b a n c e o v e r all 7 l a b o r a t o r i e s and p l o t it against concent r a t i o n , to o b t a i n a c a l i b r a t i o n curve, or (2) We can use the results o f each l a b o r a t o r y to o b t a i n an individual c a l i b r a t i o n curve for t h a t l a b o r a t o r y . One calibration curve
U s i n g the first option, we o b t a i n the c a l i b r a t i o n line s h o w n in Fig. 2, w h i c h shows excellent linearity. T h i s curve yields
Lab
A
B
C
D
E
1 2 3 4 5 6 7
23.673 40.509 39.361 40,740 36.522 43.298 42.915
56.681 77.838 75.023 76.695 72.853 79.269 86.405
115.080 138.499 132.520 135.907 133.534 138.835 135.236
188.351 210.286 204.208 207.781 208.902 208.456 203.522
433.191 453.287 448.750 451.227 458.583 461.028 451.109
the results, in units o f c o n c e n t r a t i o n , s h o w n in Table 5. A l s o s h o w n in this table are the averages, a n d s t a n d a r d d e v i a t i o n s b e t w e e n l a b o r a t o r i e s , at the b o t t o m o f the table. A s u m m a r y o f these results is s h o w n in Table 6, w h e r e SR(j) is the socalled reproducibility s t a n d a r d d e v i a t i o n b e t w e e n l a b o r a t o r ies, As can be seen SR(j) increases slightly w i t h the level o f the glucose c o n c e n t r a t i o n .
410 Table 8. Individual calibrations. Precision parameters
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Level
Average
SR(j)
1 2 3 4 5
38.145 74.966 132.801 204.501 451.025
6.772 9.123 8.156 7.540 8.996
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3
4 5 Laboratory
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Fig. 4. Graph of h-values by laboratories. Lab 1 rejected
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Fig. 5. Graph of SR(j)
Individual calibration curves
The second option is to use individual calibration curves for the laboratories. The results are shown in Table 7. If we calculate h-values for these data, we obtain the graph of Fig. 3. It is now evident that laboratory 1 is somewhat of a loner, obtaining appreciably lower results than all other laboratories. Nevertheless, the reproducibility standard deviations have decreased, as shown in Table 8. Remember that for a single calibration curve the numbers varied from 10 to 16.5. Now they hover around 8.
Table 9. Summary ofprecision parameters Average
SR (j)
40.558 78.014 135.755 207.192 453.997
2.483 4.676 2.558 2.713 4.786
Thus, we have demonstrated the advantage of using individual calibration curves in each laboratory. If the laboratory uses its o w n calibration curve, it obtains results that are closer to those of the other laboratories, doing likewise. However, the picture we now obtain raises serious questions. Why is laboratory 1 so different? If we play the game of significance testing, it will turn out that laboratory I is significantly different from all others. According to current practice, the statistician would then reject laboratory 1. If we do this, we obtain the h-graph shown in Fig. 4, and the reproducibility standard deviations in Table 9. We may congratulate ourselves for having "improved" the variability of the method to such an extent. These congratulations may very well be premature. Figure 5 shows the relationship between the standard deviation and the level of the sample. We still have problems! These problems should be further investigated by both the statistician, and, by examination of the underlying chemistry. Simply rejecting test results, or entire laboratories, is sweeping the difficulties under the rug. Rejection does n o t improve the chemical method.
Received June 22, 1990
