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Letters |
Laboratory of Clinical Biochemistry, Psychiatric University Hospital, DK-8240 Risskov, Denmark, E-mail linnet{at}post7.tele.dk
To the Editor:
In recent years, the difference or bias plot for evaluation of
method comparison data has become increasingly popular. Originally
suggested by Bland and Altman for comparison of measurements in
clinical medicine, the procedure also has been adopted in clinical
chemistry (1)(2)(3). The difference plot is very instructive
for the display of differences as functions of the measurement
average. In addition to the graphical display, however, it is
usual to present some form of summary statistics for a method
comparison study. In association with the difference plot, the paired
t-test is usually applied (1). The paired
t-test is ideal for evaluation of a constant difference
between two sets of values (4)(5). When it is used to
analyze other types of differences, however, problems may arise.
For example, consider the case shown below, in which y
measurements tend to exceed x measurements in the low range,
and vice versa in the high range (Fig. 1
). The actual data set of n = 50 (x, y)
measurement sets were generated as a random sample based on the
relationship y = 20 + 0.8x between the true
values (target values), with added measurement errors corresponding to
analytical SDs of 5 for both x and y (CV
of ~5% at the mean of 100). The x target values were
assumed uniformly distributed on the interval (25, 175). In this
situation, the overall averages of both sets of measurements are nearly
identical, and the paired t-test yields a nonsignificant
result because the average paired difference is close to zero: mean of
x values, 101.8; SD, 43.8; SE, 6.2; mean of y
values, 100.1, SD, 35.4; SE, 5.0; mean of paired (y -
x) differences, -1.7; SD, 10.9; SE, 1.5; paired
t-test, t = -1.7/1.5 = -1.1 (not
significant).
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Thus, this test is unsuitable for characterization of the measurement relationship in the present situation, which may arise frequently in the context of method comparison studies. Rather, subjecting the data to a type of regression analysis (e.g., the Deming approach) clearly discloses the relationship (6): slope (b), 0.81; SE, 0.026; test against 1.00, t = (0.81 - 1.00)/0.026 = -7.4 (P <0.001); intercept (a0), 18; SE, 3.1; test against zero, t = (18 - 0)/3.1 = 5.7 (P <0.001).
The results of the regression analysis confirm the existence of both a systematic constant difference (intercept different from zero) and a systematic proportional difference (slope different from 1). Therefore, the paired t-test should not be applied uncritically to method comparison data. Only when the graphical display suggests that a systematic constant difference, but not a systematic proportional difference, is involved should this test be applied. With this background, it appears surprising that a clinical chemistry journal has directly prohibited the use of regression analysis in method comparison studies, a point of view also expressed in another journal (7)(8). Opposition against this practice has previously been put forward (9).
References
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