NORIP

Nordic Reference Interval Project

Some errors corrected in the text 20/8-2003

 

Homogeneity for CAL and X

Pål Rustad (prustad@furst.no), 31/7-2003

 

Method

Standard deviation

Each laboratory has measured 10 replicates from one vial of CAL and 3 replicates from one vial of X in one series on the same day as the controls are thawed from -80ºC. Production of the materials and matrix and component concentrations are about the same, so one can assume that within series variance will be about the same for both materials and can be calculated as follows:

Si2 = [Sci2× (Nci-1)+Sxi2× (Nxi-1)]/(Nci+Nxi-2) where Sci, Sxi, Nci, Nxi are standard deviation and number of measurements respectively for CAL and X i serie i.

Standard deviation for Fi = Mxi/Mci for series i (quotient of mean of X and mean of CAL for series i) can then be calculated as:

Sfi2 = Fi2× Si2 * [1/(Nci× Mci2) + 1/(Nxi× Mxi2)]

The variance of these factors if only the within series variation is taken into consideration is expected to be:

Sa2 = å Sfi2/N where N is number of series.

The contributions to the variance of all Fi that is not related to within series variation, can then be calculated as St2 = Sf2 – Sa2 where Sf is standard deviation of all Fi.

This is the sum of extra variance components for X and CAL. Because the materials are similar, it is reasonable to assume that the contribution from X is  St2/2.

 

F-test and confidence intervals

A one sided F-test (p=0.05) can be made testing if K = Sf2/Sa2 is significantly greater than 1. The degrees of freedom for Sf is N-1 and for Sa: Sa4/å Sfi4/(Nci+Nxi-2) where Nci+Nxi is the sum of control values in series i.

If the critical value for significance for K is G, the lower and upper 90% confidence limits for K is  K/G and K×G respectively. This can be expressed as 90% lower and upper confidence limits for St as Sa(K/G-1)1/2 and Sa(K×G-1)1/2 respectively.

Calculations

The calculations are made separately for Ortho (Vitros), Roche Cobas og Roche Hitachi and for these together.

Only series with Nxi + Nci >10 have been used.

Laboratories with least significant digit (lsd) in the measurements higher than normal have been deleted.

If the measurement value (R) have least significant digit lsd, it is added a random number (rectangular distribution) between -lds/2 and +lsd/2.

Outliers

Because the uncertainty of the of the figures for inhomogeneity increases with increasing analytical variation, it is important to delete series with high analytical variation. All series with within series variance greater than four times mean variance are deleted: 5.8% (66 series) – 2 to 6 series for each component, but 9 for sodium.

Outliers for F are deleted with alpha-test (p=0.02): 1.0% (11 series).

Total number of outliers deleted are 6.4% (73 series). 4 series are therefor outliers on both tests.

table

 

Uncertainty

All

Hitachi

Cobas

Vitros

  

Component

u/T

uT/T

uH/M

 uH/M*

CVf

CVa

CVt

90%CI

Ns

CVf

CVa

CVt

90%CI

Ns

CVf

CVa

CVt

90%CI

Ns

CVf

CVa

CVt

90%CI

Ns

 D
Albumin 3.3 % 3.3 % 0.2 %

0.0 %

1.1%

1.1%

0.3%

0.0 %

0.7 %

69

0.8%

0.9%

0.0%

0.0 %

0.5 %

31

1.0%

1.1%

0.0%

0.0 %

0.7 %

23

1.9%

1.7%

0.7%

0.0 %

1.7 %

18

-3
Bilirubin     2.2 %

2.0 %

4.7%

3.5%

3.2%

2.2 %

4.1 %

74

5.5%

4.0%

3.7%

1.9 %

5.4 %

30

4.0%

2.9%

2.8%

1.3 %

4.2 %

22

3.7%

3.2%

1.9%

0.0 %

3.4 %

22

0
Ca 0.6 % 0.2 % 0.6 %

0.4 %

1.2%

0.8%

0.9%

0.6 %

1.1 %

69

0.9%

0.7%

0.6%

0.2 %

0.9 %

28

1.0%

0.9%

0.4%

0.0 %

0.9 %

20

0.9%

1.0%

0.0%

0.0 %

0.7 %

18

3
Cholesterol 0.5 % 0.2 % 0.5 %

0.6 %

1.2%

1.0%

0.7%

0.4 %

1.0 %

75

1.2%

0.9%

0.9%

0.5 %

1.2 %

32

0.9%

0.9%

0.1%

0.0 %

0.7 %

23

1.5%

1.2%

0.9%

0.0 %

1.6 %

19

1
Creatinin 1.3 % 0.4 % 1.2 %

0.4 %

2.2%

1.3%

1.8%

1.4 %

2.2 %

70

1.3%

1.3%

0.2%

0.0 %

1.0 %

30

3.3%

1.5%

2.9%

2.1 %

3.9 %

20

1.0%

0.8%

0.6%

0.0 %

1.0 %

19

1
Fe 1.4 % 1.4 % 0.0 %

0.2 %

1.1%

1.1%

0.0%

0.0 %

0.7 %

45

0.9%

1.0%

0.0%

0.0 %

0.7 %

21

0.6%

0.6%

0.3%

0.0 %

0.7 %

12

2.5%

1.8%

1.8%

0.5 %

2.9 %

13

-1
Glucose 0.6 % 0.4 % 0.4 %

0.0 %

1.1%

0.9%

0.6%

0.3 %

0.9 %

65

1.1%

1.0%

0.4%

0.0 %

0.9 %

26

1.2%

0.8%

0.9%

0.5 %

1.3 %

21

0.7%

0.8%

0.0%

0.0 %

0.4 %

17

1
HDL     0.8 %

1.0 %

1.8%

1.4%

1.1%

0.6 %

1.5 %

64

1.9%

1.4%

1.4%

0.8 %

1.9 %

36

1.5%

1.4%

0.4%

0.0 %

1.2 %

27

            

1
K 0.4 % 0.3 % 0.3 %

0.2 %

0.9%

0.8%

0.4%

0.0 %

0.6 %

73

0.8%

0.7%

0.3%

0.0 %

0.7 %

30

0.7%

0.6%

0.3%

0.0 %

0.6 %

21

1.0%

1.0%

0.4%

0.0 %

0.9 %

21

1
Mg 0.8 % 0.4 % 0.7 %

0.5 %

1.6%

1.3%

1.0%

0.5 %

1.4 %

54

1.8%

1.8%

0.0%

0.0 %

1.6 %

18

1.5%

1.3%

0.7%

0.0 %

1.4 %

19

1.4%

1.3%

0.7%

0.0 %

1.4 %

19

-2
Na 0.4 % 0.3 % 0.3 %

0.3 %

0.6%

0.4%

0.4%

0.3 %

0.6 %

66

0.6%

0.4%

0.5%

0.3 %

0.7 %

28

0.5%

0.3%

0.4%

0.2 %

0.6 %

20

0.5%

0.4%

0.3%

0.0 %

0.5 %

19

-1
P inorg     0.5 %

0.4 %

1.2%

0.9%

0.8%

0.5 %

1.0 %

67

1.0%

1.0%

0.1%

0.0 %

0.7 %

26

0.9%

0.7%

0.5%

0.0 %

0.9 %

20

1.2%

1.0%

0.7%

0.0 %

1.2 %

20

1
Protein     0.3 %

0.0 %

1.0%

0.9%

0.4%

0.0 %

0.7 %

53

0.5%

0.7%

0.0%

0.0 %

0.0 %

22

0.7%

0.7%

0.1%

0.0 %

0.6 %

15

1.2%

1.0%

0.6%

0.0 %

1.3 %

14

2
TIBC     0.0 %

0.5 %

1.4%

1.4%

0.0%

0.0 %

1.0 %

24

1.4%

1.3%

0.7%

0.0 %

1.3 %

20

1.1%

1.4%

0.0%

0.0 %

1.2 %

3

            

1
Trigly     0.4 %

0.5 %

1.2%

1.0%

0.6%

0.2 %

0.9 %

58

1.0%

0.9%

0.4%

0.0 %

0.9 %

22

1.0%

0.8%

0.6%

0.0 %

1.1 %

19

1.1%

1.1%

0.4%

0.0 %

1.1 %

16

1
Urea 0.7 % 0.5 % 0.5 %

0.0 %

1.6%

1.4%

0.7%

0.0 %

1.2 %

69

1.6%

1.5%

0.7%

0.0 %

1.3 %

32

1.2%

1.4%

0.0%

0.0 %

0.6 %

19

2.0%

1.5%

1.4%

0.5 %

2.2 %

20

-2
Uric acid 1.1 % 0.9 % 0.6 %

0.4 %

1.3%

0.9%

0.9%

0.7 %

1.2 %

71

0.9%

0.7%

0.6%

0.2 %

0.8 %

30

1.3%

1.1%

0.7%

0.0 %

1.2 %

19

0.8%

0.8%

0.1%

0.0 %

0.7 %

20

2

In the table CV (relative standard deviation) have been used instead of S which have been used in the text, but the subscripts are the same.

uH/M: relative standard uncertainty for X other than analytical variation (i.e. between tube variation)

uH/M*: As uH/M, but here is uH/M calculated from CVt chosen from the instrument groups with the best precision

uT/T: relative standard uncertainty for X by transferrence from IMEP 17-1.

u/T: Combined standard uncertainty (square root of sum of squares)

CVf – relative standard deviation of all Mx/Mc

CVa - calculated expected relative standard deviation from within series variation.

CVt – common variance component for X and CAL that can not be attributed to analytical variation: (CVf2 – CVa2)1/2 . Denoted as 0 in table if CVf2 – CVa2 < 0.

90% CI – 90 % confidence interval for CVt

Ns - number of series used in calculations

D – (last column) is the difference between series for "All" and the sum of Hitachi, Cobas and Vitros. The reason that the difference is not always 0, is that the tests give different results when the 3 instrument groups are treated separately than when they are all together.

Discussion

The extra variance components are low for all components and have small practical importance.

The variance components can be added to existing uncertainty for target value for X as a combined between tube and preanalytical standard uncertainty.

Because bias between method groups may be the reason for CVt to be greater than necessary, it is alternatively mede an attempt to calculate CVt for the instrument group with the best precision. Only 5 components of 17 got higher CVt, but it is only for creatinin that the change is of any importance. It may be concluded that 1.8% for creatinin more is a reflection of method variation than actual inhomogeneity.

Values for three components in the table have green background:

Creatinin: Cobas is the reason for St= 1.8% and not <0.6%.

TIBC: St = 0% in spite of Hitachi with St=0.7% with 20 series and Cobas 0.0% with 3 series. The method differences for Cobas and Hitachi seems to be the most likely explanation, i.e. 0.7% as the most correct value.

Uric acid: St=0.9% in spite of all instrument groups is <0.7%. There are two more series in "All" that have been eliminated by the tests when the instrument groups are evaluated separately.