Scandinavian Journal of Clinical and Laboratory Investigation
ISSN: 0036-5513 (Print) 1502-7686 (Online) Journal homepage: http://www.tandfonline.com/loi/iclb20
Allowable systematic difference between two instruments measuring the same analyte Arne Åsberg, Kristine Bodal Solem & Gustav Mikkelsen To cite this article: Arne Åsberg, Kristine Bodal Solem & Gustav Mikkelsen (2015) Allowable systematic difference between two instruments measuring the same analyte, Scandinavian Journal of Clinical and Laboratory Investigation, 75:7, 631-632, DOI: 10.3109/00365513.2015.1057900 To link to this article: http://dx.doi.org/10.3109/00365513.2015.1057900
Published online: 18 Aug 2015.
Submit your article to this journal
Article views: 111
View related articles
View Crossmark data
Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=iclb20 Download by: [FU Berlin]
Date: 27 January 2017, At: 03:46
Scandinavian Journal of Clinical & Laboratory Investigation, 2015; 75: 631–632
LETTER TO THE EDITOR
Allowable systematic difference between two instruments measuring the same analyte
ARNE ÅSBERG, KRISTINE BODAL SOLEM & GUSTAV MIKKELSEN Department of Clinical Chemistry, Trondheim University Hospital, Trondheim, Norway
SIR: We think Petersen et al. [1] have misunderstood certain aspects in our article from 2014 [2]. In clinical chemistry many laboratories have two working instruments for the same analyte, in order to ensure operation in case one instrument fails. Let us name these instruments I1 and I2. A certain sample from one patient may be analyzed on I1 or I2, and the probability that the sample is analyzed on I1 may be different from 0.5 if I1 and I2 are loaded with a different number of samples per day. In the long run, the clinician monitoring the patient receives many analytical results of the same analyte, some from I1 and some from I2. When comparing any two analytical results, the clinician does not know whether both of the results are from I1 or both from I2, or if one result is from I1 and the other from I2. In this situation, a systematic difference between I1 and I2 is seen by the clinician as an increase in the analytical imprecision. That is the scenario we have modeled in the article from 2014, as clearly stated [2]. That is not the scenario Petersen et al. have modeled in their article from 1992 [3], whose results are restated in the letter from Petersen et al. in this issue of The Scandinavian Journal of Clinical & Laboratory Investigation [1]. Although not explicitly described in their letter [1], they rather seem to have modeled a scenario where the clinician always compares one analytical result from I1 with one analytical result from I2. That would certainly not be a common situation for clinicians monitoring patients with analytical results from most laboratories, as clinical laboratories often use more than one instrument for the same analyte (i.e. commonly used clinical chemistry analytes). We did not, as Petersen et al. claim, ‘propose that the allowable ΔB should be larger under the same conditions’ [1], because it is not the same conditions.
So, is our model wrongly stated? We derived a formula for the total analytical variance if the same sample could be analyzed an infinite number of times on two instruments, given as SDa_total2 ⫽ p⋅[(1 ⫺ p)⋅ds]2 ⫹ (1 ⫺ p)⋅(p⋅ds)2 ⫹ p⋅SDa12 ⫹ (1 ⫺ p)⋅SDa22, where SDa1 and SDa2 are the analytical standard deviation of I1 and I2, respectively, ds is the constant mean difference between I1 and I2, and p is the probability that the sample is analyzed on I1 [2]. Then we used the traditional claim that SDa_total2 ⬍ 0.25⋅SDw2, or SDa_total ⬍ 0.5⋅SDw, where SDw is the standard deviation describing withinsubject biological variability. Petersen et al. [1] think that we have wrongly formulated the component of the variance that is due to the constant mean difference between I1 and I2. We disagree. The population variance of analytical results coming from two analytical instruments with equal probability and whose analytical standard deviations are zero, is the mean sum of the squared differences from their mean, which is n⋅[(ds/2)2]/n ⫽ (ds/2)2, in accordance with our statement in [2]. In their letter [1], Petersen et al. cited only half our sentence and gave a formula for ‘the variance on the constant ds’, which is not appropriate in our model. Our formula for the total analytical variance if the same sample could be analyzed an infinite number of times on two instruments may easily be tested by computer simulation. For instance, if the mean analytical result is 100 with I1 and 104 with I2 (ds ⫽ 4), SDa1 ⫽ 2, SDa2 ⫽ 3, and the probability (p) that a certain sample is being analyzed on I1 is 0.7, then the total analytical variance is
Correspondence: Arne Åsberg, Department of Clinical Chemistry, Trondheim University Hospital, N-7006 Trondheim, Norway. E-mail: [email protected] (Received 13 May 2015 ; accepted 31 May 2015) ISSN 0036-5513 print/ISSN 1502-7686 online © 2015 Informa Healthcare DOI: 10.3109/00365513.2015.1057900
632
A. Åsberg et al.
SDa_total2 ⫽ 0.7⋅[(1 ⫺ 0.7)⋅4]2 ⫹ (1 ⫺ 0.7)⋅(0.7⋅4)2 ⫹ 0.7⋅22 ⫹ (1 ⫺ 0.7)⋅32 ⫽ 8.86, compared to 8.858 using computer simulation with two million analytical results. Accordingly, we do not think our model is wrongly stated. Nevertheless, our model is a model of the reality, not reality itself. It should not be used outside the scenario for which it was designed, and even then it has several limitations which are discussed in the article [2]. Neither is the model of Petersen et al. universally applicable, making the conclusion in their letter [1] far too simplistic. Why don’t we adjust for the difference between I1 and I2 and be done with it? We would if we could, and we are certainly trying. However, even if I1 and I2 were identical instruments and they were calibrated with the same calibration material, a small difference would remain due to calibration uncertainty. To determine whether the difference is acceptable may require a high number of measurements on both instruments [4].
In conclusion, our modeling and its results are different from those of Petersen et al. because we have studied two different scenarios. Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper. References [1] Petersen PH, Fraser CG, Lund F, Sölétormos G. Validation of analytical performance characteristics required for the reference change value applied in patient monitoring. Scand J Clin Lab Invest 2015;75:000–000. [2] Åsberg A, Solem KB, Mikkelsen G. Allowable systematic difference between two instruments measuring the same analyte. Scand J Clin Lab Invest 2014;74:588–90. [3] Petersen PH, Fraser CG, Westgard JO, Larsen ML. Analytical goal-setting for monitoring patients when two analytical methods are used. Clin Chem 1992;38:2256–60. [4] Åsberg A, Solem KB, Mikkelsen G. Determining sample size when assessing mean equivalence. Scand J Clin Lab Invest 2014;74:713–5.
ISSN: 0036-5513 (Print) 1502-7686 (Online) Journal homepage: http://www.tandfonline.com/loi/iclb20
Allowable systematic difference between two instruments measuring the same analyte Arne Åsberg, Kristine Bodal Solem & Gustav Mikkelsen To cite this article: Arne Åsberg, Kristine Bodal Solem & Gustav Mikkelsen (2015) Allowable systematic difference between two instruments measuring the same analyte, Scandinavian Journal of Clinical and Laboratory Investigation, 75:7, 631-632, DOI: 10.3109/00365513.2015.1057900 To link to this article: http://dx.doi.org/10.3109/00365513.2015.1057900
Published online: 18 Aug 2015.
Submit your article to this journal
Article views: 111
View related articles
View Crossmark data
Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=iclb20 Download by: [FU Berlin]
Date: 27 January 2017, At: 03:46
Scandinavian Journal of Clinical & Laboratory Investigation, 2015; 75: 631–632
LETTER TO THE EDITOR
Allowable systematic difference between two instruments measuring the same analyte
ARNE ÅSBERG, KRISTINE BODAL SOLEM & GUSTAV MIKKELSEN Department of Clinical Chemistry, Trondheim University Hospital, Trondheim, Norway
SIR: We think Petersen et al. [1] have misunderstood certain aspects in our article from 2014 [2]. In clinical chemistry many laboratories have two working instruments for the same analyte, in order to ensure operation in case one instrument fails. Let us name these instruments I1 and I2. A certain sample from one patient may be analyzed on I1 or I2, and the probability that the sample is analyzed on I1 may be different from 0.5 if I1 and I2 are loaded with a different number of samples per day. In the long run, the clinician monitoring the patient receives many analytical results of the same analyte, some from I1 and some from I2. When comparing any two analytical results, the clinician does not know whether both of the results are from I1 or both from I2, or if one result is from I1 and the other from I2. In this situation, a systematic difference between I1 and I2 is seen by the clinician as an increase in the analytical imprecision. That is the scenario we have modeled in the article from 2014, as clearly stated [2]. That is not the scenario Petersen et al. have modeled in their article from 1992 [3], whose results are restated in the letter from Petersen et al. in this issue of The Scandinavian Journal of Clinical & Laboratory Investigation [1]. Although not explicitly described in their letter [1], they rather seem to have modeled a scenario where the clinician always compares one analytical result from I1 with one analytical result from I2. That would certainly not be a common situation for clinicians monitoring patients with analytical results from most laboratories, as clinical laboratories often use more than one instrument for the same analyte (i.e. commonly used clinical chemistry analytes). We did not, as Petersen et al. claim, ‘propose that the allowable ΔB should be larger under the same conditions’ [1], because it is not the same conditions.
So, is our model wrongly stated? We derived a formula for the total analytical variance if the same sample could be analyzed an infinite number of times on two instruments, given as SDa_total2 ⫽ p⋅[(1 ⫺ p)⋅ds]2 ⫹ (1 ⫺ p)⋅(p⋅ds)2 ⫹ p⋅SDa12 ⫹ (1 ⫺ p)⋅SDa22, where SDa1 and SDa2 are the analytical standard deviation of I1 and I2, respectively, ds is the constant mean difference between I1 and I2, and p is the probability that the sample is analyzed on I1 [2]. Then we used the traditional claim that SDa_total2 ⬍ 0.25⋅SDw2, or SDa_total ⬍ 0.5⋅SDw, where SDw is the standard deviation describing withinsubject biological variability. Petersen et al. [1] think that we have wrongly formulated the component of the variance that is due to the constant mean difference between I1 and I2. We disagree. The population variance of analytical results coming from two analytical instruments with equal probability and whose analytical standard deviations are zero, is the mean sum of the squared differences from their mean, which is n⋅[(ds/2)2]/n ⫽ (ds/2)2, in accordance with our statement in [2]. In their letter [1], Petersen et al. cited only half our sentence and gave a formula for ‘the variance on the constant ds’, which is not appropriate in our model. Our formula for the total analytical variance if the same sample could be analyzed an infinite number of times on two instruments may easily be tested by computer simulation. For instance, if the mean analytical result is 100 with I1 and 104 with I2 (ds ⫽ 4), SDa1 ⫽ 2, SDa2 ⫽ 3, and the probability (p) that a certain sample is being analyzed on I1 is 0.7, then the total analytical variance is
Correspondence: Arne Åsberg, Department of Clinical Chemistry, Trondheim University Hospital, N-7006 Trondheim, Norway. E-mail: [email protected] (Received 13 May 2015 ; accepted 31 May 2015) ISSN 0036-5513 print/ISSN 1502-7686 online © 2015 Informa Healthcare DOI: 10.3109/00365513.2015.1057900
632
A. Åsberg et al.
SDa_total2 ⫽ 0.7⋅[(1 ⫺ 0.7)⋅4]2 ⫹ (1 ⫺ 0.7)⋅(0.7⋅4)2 ⫹ 0.7⋅22 ⫹ (1 ⫺ 0.7)⋅32 ⫽ 8.86, compared to 8.858 using computer simulation with two million analytical results. Accordingly, we do not think our model is wrongly stated. Nevertheless, our model is a model of the reality, not reality itself. It should not be used outside the scenario for which it was designed, and even then it has several limitations which are discussed in the article [2]. Neither is the model of Petersen et al. universally applicable, making the conclusion in their letter [1] far too simplistic. Why don’t we adjust for the difference between I1 and I2 and be done with it? We would if we could, and we are certainly trying. However, even if I1 and I2 were identical instruments and they were calibrated with the same calibration material, a small difference would remain due to calibration uncertainty. To determine whether the difference is acceptable may require a high number of measurements on both instruments [4].
In conclusion, our modeling and its results are different from those of Petersen et al. because we have studied two different scenarios. Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper. References [1] Petersen PH, Fraser CG, Lund F, Sölétormos G. Validation of analytical performance characteristics required for the reference change value applied in patient monitoring. Scand J Clin Lab Invest 2015;75:000–000. [2] Åsberg A, Solem KB, Mikkelsen G. Allowable systematic difference between two instruments measuring the same analyte. Scand J Clin Lab Invest 2014;74:588–90. [3] Petersen PH, Fraser CG, Westgard JO, Larsen ML. Analytical goal-setting for monitoring patients when two analytical methods are used. Clin Chem 1992;38:2256–60. [4] Åsberg A, Solem KB, Mikkelsen G. Determining sample size when assessing mean equivalence. Scand J Clin Lab Invest 2014;74:713–5.
