2 We would like to compare the results of two papers recently issued on two international scientific journals:Both papers have been issued in 2009.
3 Let’s start with Linear Regressions Linear Regression is a way to study the strength of the correlation between two methods, not their agreementthe closer to 1,0 is the value of correlation coefficient - that is the closer the slope of the regression line is to 45° (line of equivalence) - the more two methods are in agreementIn comparing method it is important to detect the biasBias is a source of systematic difference between two methods of measurements:FIXED BIAS: when one of the methods gives resulta that higher or lower of than those of the other by a constant amountPROPORTIONAL BIAS: one method gives values that are lower (or higher) than those from the other by an amount that is proportional to the level of the measured variable.From Ludbrook J (1997) Clin Exp Pharmacol Physiol. 24,
4 Let’s start with Linear Regressions Ves-Matic Cube 200 vs WestergrenLinear Regression according to Passing – Bablok(ρ = 0.946; P < 0.001; y = - 0,0435x + 1,0435)Test-1 vs WestergrenLinear Regression(r2 = 0.386; P < .0005; y = 0.547x )By comparing the values it is clear that the Ves-Matic Cube correlates with the Westergren method better than the Test-1 (ρ = compared with r2 = 0.386).In addition, the analysis of the graphs (scattergrams), highlights that the Ves-Matic Cube 200/Westergren points are closer to the regression line compared to those of Test-1/Westergren: this means that the dispersion of data is smaller, and means that the ESR values obtained by Ves-Matic Cube 200 are closer to those obtained with the reference method, in comparison to Test-1 values.Note also that the origin of the regression line for Ves-Matic Cube is from the 0 point, that means that the bias is very low, while in the Test-1 line, the origin is not from the 0 point.By comparing the values it is clear that the Ves-Matic Cube correlates with the Westergren method better than the Test-1 (ρ = compared with r2 = 0.386).
5 Let’s start with Linear Regressions LET’S SHOW THE TRICKPlease note that in Figure 1 - Test-1 graph - there are points (left side of the Test-1 vs Westergren graph) which show that the Test-1 has provided either very high ESR values, which resulted normal or slightly high with Westergren method, and falsely low values (around 20 mm), while with the Westergren method they were high (over 40 mm). Consider that different ESR levels may have a different clinical significance and thus address clinical decisions to one or another direction a graphic trick has been used to try and minimize the visual impact of the overestimation of ESR low values in the -Test-1/Westergren graph: point 20 has a different proportion on x and y axis (Figure 1 - Test-1 vs Westergren chart).Freely Falling Erythrocytes20 – 50 mm/h50 – 90 mm/h90 – 140 mm/hAlteration of plasma proteinsAnaemiaArthrosisGoutPregnancyPostpartumPeriodLymphomaReumatic feverRheumatoid arthritisHorton’s diseaseMyelomaLeukaemiaPolymialgia rheumaticaLESthrombophlebitisAcute infectionsCytomegalovirusToxoplasmosisrickettsiosisViral hepatitisInfectious mononucleosisGlomerulonephritisSubacute endocarditisPneumoniaCholangitisOsteomyelitisPyelonephritisAbscessesTissue necrosisCirrhosisUlceraticve colitisStrokeAMIChron’s diseasesEpatic metastasisSurgeryBreast carcinomaPulmonary carcinomaPulmonary infarctionESR values are used to determine the clinical status of the patient: how can doctors be comfortable with these results?
6 And now Bland and Altman’s plot The Bland-Altman plot is used for the comparison among methods because, compared to the correlation coefficient, it is able to detect if one of the methods is affected by systematic errors of inaccuracy or imprecision.Systematic error means that a measure system is prone to “constantly” overestimate or underestimate the true object of the measure.A systematic difference between the reported measures means that in the scatter diagram the points line up along a straight line at approximately 45° without giving any indications about the inaccuracy direction or entity.The Bland and Altman plot is now used for comparing methods of measurements because it takes more into account the bias of the methods, and it is a measure of the real agreement between methods.This method too is not perfect, as it cannot distinguish which one of the methods is affected by the bias, and also it cannot differentiate between fixed and proportional bias, nevertheless, it is very useful.
7 And now Bland and Altman’s plot The Bland and Altman method compares the difference between the paired measures performed with the two methods (Westergren - Ves-Matic Cube), with the average of these measures ((Westergren + Ves-Matic Cube)/2) starting from the premise that the more the two measures will be similar, the lower the difference between them will be, and therefore the more restricted will be the limits of agreement (dashed lines)At the limit, when the two measurements coincide, the difference is = 0.From the analysis of the two comparison graphs (Figure 2), we can say that:first of all the limits of agreement of the comparison Ves-Matic Cube 200/Westergren appear "narrower" compared to those of the Test-1/Westergren, and this means that the Ves-Matic Cube 200 provides data closer to those of the reference method compared to Test-1. Concerning the bias, this is only -0.5 mm/h in our system and about -11 mm/h in the Test-1, index of a general tendency to underestimate of this last method
8 And now Bland and Altman’s plot Limits of agreement (-13,9 to 12,9 mm/h)Bias: - 0,5 mm/hLimits of agreement (-29,9 to 51,8 mm/h)Bias: -10,95 mm/h
9 Take home messagesThe analysis of scattergraphs (that "measure" the strength of the correlation between two methods, not their agreement, i.e. if the two methods give very similar data) suggests that the Ves-Matic Cube 200 correlates much better than the Test-1 with the Westergren method. This can be deduced because the value of the coefficient of correlation is equal to 0,946, while the value of coefficient of correlation of the Test-1 value is equal to 0,386. Important: the closer to 1 is the value of the correlation coefficient, the more two methods are correlated.
10 Take home messagesThe Bland-Altman method "measures" the real agreement between two methods. The lesser is the difference between the two compared measures, the higher is the two data agreement (in fact, if the two measures are equal, their difference is equal to zero). he Bland-Altman method indicates the limits of agreement between the two methods: the narrower is the interval between the two limits (i.e. the closer to zero is the difference between the two measures) the greater will be the agreement between methods.Ves-Matic Cube 200 limits of agreement: mm/h (total 26,8 mm/h)Test 1 limits of agreement: mm/h (total 81,7 mm/h)As you can see, the Ves-Matic Cube 200 limit of agreement is closer than the Test-1’s.In addition to the agreement, the Bland-Altman method gives also indication about the bias or deviation between the real value and the one measured by the system under evaluation:Ves-Matic Cube 200 Bias : - 0,50 mm/hTest-1 Bias : ,95 mm/hThe average deviation of the Ves-Cube values from the real one is only – 0,5 mm/h, while the Test-1 is about -11 mm/h, which means that the instrument has a general tendency to underestimation.
11 Take home messagesIn the Korean paper it is stated that the results of the test-1 have a better correlation with inflammation markers than the Westergren ESR doesIf indeed the Test-1 data correlate differently from ESR according to Westergren (which is the original and reference method used as clinical datum by physicians for decades) with inflammation markers, this means that Test-1 datum is NOT ESR, and therefore it is unfairly reimbursed.