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# Bland-Altman Plot (Bias and Limit of Agreement)

Figure 27.31. Bland-Altman diagram with 95% confidence limits with gradual increase in differences and heteroscedasticity. Left field: Conventional chart with average (dotted line), best fit line, and 95% confidence limits. Right field: Tolerance to heteroscedasticity, with better adaptation to data. You can also view the differences graphically* Then, the limit values ±1.96 × SD difference are on both sides of the predicted value. The scatter plot with 95% confidence limits is shown in Figure 27.31. The boundaries are drawn by calculating the SD difference at two averages and connecting it to a straight line. A new method can be validated against an existing method using regression analysis, as described earlier in this chapter. The distortion can be calculated based on the slope analysis or the Bland-Altman diagram. However, in some cases the distortion between the two methods may be significant and, in this case, a laboratory professional needs to know whether the values of an analyte determined by the reference method differ significantly from the values determined with the new method. This can be calculated by the mean of two sets of values and the standard deviation from Student`s t-test: Since the compliance limits previously indicated for the Bland-Altman diagram are point estimates, Bland and Altman (1999, 2003) also recommended setting confidence intervals above these limits. They used 3s2N as an approximation of the standard error, where s was the standard deviation of the differences and N was the total number of comparisons.

So if, as in one of them used, the mean difference of 231 comparisons was 0.2 mm with s = 3 mm, and the 95% match limits were − 5.8 to + 6.1 mm, then the default error would be 332231 = 0.34, and the 95% confidence interval is ± 1.96 × 0.34 = 0.67, so the 95% confidence intervals are for the limits: lower limit = − 5.8 ± 0.67 = − 5.13 to − 6.47 and for the upper limit = 6.1 ± 0.67 = 5.43 to 6.77. Instead of the term 95% compliance limits, it prefers the concept of 95% tolerance limits with 95% certainty. Ludbrook modified the graph of the difference from the mean to show the mean difference (as in the usual Bland-Altman diagram) and two pairs of boundary lines; The inner pair is the upper and lower limit of 95% confidence for the population, and the outer pair are the 95% tolerance limits with 95% confidence. For inner limits, he suggested using a slightly more precise formula: Xdiff ̄±t0.05N−1sdiff1+1N. For the example used above, the 95% population confidence limits are 0.2+ ̄1.96×31+1231=0.2+ ̄5.89=6.09bis−5.69. These are slightly different from those calculated according to the simpler formula. For the tolerance limits, Ludbrook used the mean difference ± ksdiff, where k is taken from the tolerance tables mentioned in Chapter 7. For N = 231, k ~ 2.131, and the tolerance limits are 0.2 ± 2.131 × 3 = 6.56 to − 6.16. If the differences increase in proportion to the size of the measurement, Ludbrook recommends that instead of logarithms, perform a regression of the differences from the Model I means, and then calculate the 95% hyperbolic limits for the points. it is essentially about tolerance limits.

Figure 15.2 shows a Bland-Altman diagram from Clinic 104 against laboratory data on warfarin inr values in DB13. Three of the abnormalities identified in Figure 15.1 can be observed. The average is offset and is greater than zero, indicating an average distortion. The data cluster is stronger at the top left and the cluster moves down when we move from left to right, suggesting that the average distortion is greater for smaller INR values. No data are above the upper confidence limit (2 or 3, about 2.5%, would be expected), but more than 7.5% are below the lower bound, suggesting bias in the data. These are slightly different from those calculated according to the simpler formula. For the tolerance limits, Ludbrook used the mean difference ±ksdiff, where k is taken from the tolerance tables mentioned in Chapter 7. For N = 231, k is ∼2.131 and the tolerance limits are 0.2 ± 2.131 × 3 = 6.56 to −6.16. If the differences increase in proportion to the size of the measurement, Ludbrook recommends that instead of logarithms, perform a regression of the differences from the Model I means, and then calculate the 95% hyperbolic limits for the points. it is essentially about tolerance limits. The Bland-Altman chart shows four types of data misconduct. These types are (1) systematic error (mean shift), (2) proportional error (trend), (3) inconsistent variability, and (4) excessive or irregular variability.

It is recommended (Stöckl et al., 2004; Abu-Arafeh et al., 2016) to enter a value for the “Maximum allowable difference between methods” and select the “95% IC of match limits” option. The Abbott Architect ci8200 and Cobas e411 rock were used to analyze 120 serum samples for active vitamin B12. The results covered the range of 100 pmol/L. The comparison of the method was carried out using weight regression and Bland-Altman diagrams. Regent batches have also been evaluated against WHO standard 03/178. Roche`s Cobas method showed a small, constant bias of 9 pmol/L compared to the Abbott Architect test with a proportional bias of up to 23 pmol/L at the clinical decision point. The accuracy of the Roche method was also evaluated according to CLSI-EP5 A3 and showed an intrarun accuracy of < 4% and an interrun accuracy of < 6%.41 The Bland-Altman analysis is a data graph also known as the difference graph, which is used to analyze the correspondence between two different variables X and Y. The Bland-Altman (1983) diagram is formed by representing the differences in the individual pair values of X and Y on the vertical axis compared to the average values of the individual pair values ((X + Y) / 2) on the horizontal axis. There are three horizontal lines in the graph, the mean distortion (d ̄), which is calculated as a linear regression, and the Pearson correlation coefficient are essential tests for accuracy and performance; however, both are influenced by dispersion.

The Bland-Altman difference graph, also known as the Tukey mean difference graph, provides a graphical representation of the agreement between two trials.20 Similar to the t-test, Pearson correlation, and linear regression, the results of the matched tests are presented in automated spreadsheet columns. This formula is applied: to compare the differences between the two sets of samples regardless of their average, it is more appropriate to consider the ratio of the pairs of measurements. [4] The logarithmic transformation (base 2) of the measurements before analysis allows the use of the standard approach; The diagram is therefore given by the following equation: Keywords: Bland-Altman diagram, agree line, two measures If the differences are not related to size, the mean of the differences provides an estimate of the average bias between the methods. Compliance limits estimate the interval within which a certain proportion of the differences between the measures are likely to occur. Limitations can be used to determine whether the methods can be used interchangeably or whether a new method can replace an old method without changing the interpretation of the results. A Bland–Altman diagram is a useful representation of the relationship between two paired variables using the same scale. It allows you to perceive a phenomenon, but does not test it, that is, it does not give you a probability of error in a decision on variables as in a test. Like the Student t-Test, ANOVA is available in computer tables. The operator enters the data in one column per record (group or sample) and applies the ANOVA formula. The test ratios between groups df (the number of groups – 1) and those of group df (sum of data points – 1 per group). The test also calculates and reports the sum of the squares within and between groups, the total sum of the squares, the middle squares within and between groups, and the F statistic.

Spreadsheets compare the F statistics with the table of critical F values and report the P value, which the operator then compares with the P-value limit selected to determine significance. Table 2.5 presents the typical results of ANOVA. Tuning limits (LoA) are defined as the mean difference ± differences of 1.96 SD. If these limits do not exceed the maximum permissible difference between the Δ methods (the differences in the mean ± AND 1.96 are not clinically significant), the two methods are considered consistent and can be used interchangeably. Compliance limits estimate an interval of -73.9 to 78.1, suggesting that the Mini Wright meter can measure up to 73.9 l/min below and 78.1 l/min above the large meter. .