44
| 4 | 2011
Klinisk Biokemi i Norden
(
Fortsat fra side 43)
A linear regression function can be found from the
observations. The function should ideally have a slope
of one and an intercept of zero, i.e. coincide with the
equal line. Different methods to estimate the regression
function are available; the ordinary linear regression
(
OLR) allowing a variance of the results of the test
procedure but not of the comparative procedure. The
Deming regression analysis (DRA) allows variation in
the results of both procedures but the variances need
to be defined, often assumed equal in both procedures.
If the variance in the test procedure is considerably
larger than in the comparative procedure the DRA
approaches the OLR. The Passing-Bablok has no res-
trictions on the distribution of the results but requires
more advanced calculations.
The regression function, if based on a sufficient
number of representative samples, may be used for
recalculation of results of the test procedure thereby
eliminating or reducing a bias. Often 40 observations
are recommended, measured in duplicates (EP9) [2].
Provided there is a linear relationship between
results obtained by two measurement procedures the
relation can be determined by measuring concentra-
tions repeatedly of two representative samples and
estimating the regression by a two-point formula.
A statistical power of the same magnitude as by the
method in EP9 is obtained by six repeats of each con-
centration by each procedure.
The difference between the procedures is usually
displayed in a difference plot [7] (figure 2), often in
both absolute and relative numbers. Assuming the
differences are Gaussian distributed the average of all
differences and the width of the distribution e.g. ±2
sd are displayed. If the dataset can be partitioned the
information may be more detailed. It is interesting to
note that the difference graph is the same as the regres-
sion, tilted 45 degrees. The confidence interval is the
Figure 2
.
Difference plot. The blue
horizontal lines represent the average
difference (solid) and ±1,96sd (dot-
ted). The dotted red lines show the
average difference in each of the
partitions which are delineated by the
vertical red lines. A regression line
(
green dotted) illustrates the trend of
differences.
Figure 3.
The “tilted mountain plot”
with the 2.5 and 97.5 percentiles indi-
cated by a vertical line, thus identify-
ing samplesbelonging to the tails of
the distribution.
