Bland-Altman Test

A Bland-Altman Test is a data visualization procedure in comparing different methods of measurements.

• AKA: Bland-Altman Plot, Tukey Mean Difference Test.
• Context:
  • It is usually used for clinical measurement comparisons.
• See: Tukey's Method, Statistical Test, Multiple Comparisons Problem, MA Plot.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Bland–Altman_plot Retrieved 2016-08-28
  • A Bland–Altman plot (Difference plot) in analytical chemistry and biostatistics is a method of data plotting used in analyzing the agreement between two different assays. It is identical to a Tukey mean-difference plot, the name by which it is known in other fields, but was popularised in medical statistics by J. Martin Bland and Douglas G. Altman [1][2].

(...)Consider a set of n samples (for example, objects of unknown volume). Both assays (for example, different methods of volume measurement) are performed on each sample, resulting in 2n data points. Each of the n samples is then represented on the graph by assigning the mean of the two measurements as the abscissa (x-axis) value, and the difference between the two values as the ordinate (y-axis) value.

Hence, the Cartesian coordinates of a given sample S with values of [math]\displaystyle{ S_1 }[/math] and [math]\displaystyle{ S_2 }[/math] determined by the two assays is

[math]\displaystyle{ S(x,y)=\left( \frac{S_1+S_2}{2}, S_1-S_2 \right). }[/math]

For comparing the dissimilarities between the two sets of samples independently from their mean values, it is more appropriate to look at the ratio of the pairs of measurements[3]. Log transformation (base 2) of the measurements before the analysis will enable the standard approach to be used; hence the plot will be given by the following equation:

[math]\displaystyle{ S(x,y)=\left( \frac{\log_2{S_1}+\log_2{S_2}}{2}, \log_2{S_1}-\log_2{S_2} \right). }[/math]

(...) One primary application of the Bland–Altman plot is to compare two clinical measurements that each provide some errors in their measure. It can also be used to compare a new measurement technique or method with a gold standard, as even a gold standard does not - or should not - imply it to be without error.

1986

• (Bland & Altman, 1986) ⇒ Bland, J. M., & Altman, D. (1986). Statistical methods for assessing agreement between two methods of clinical measurement. The lancet, 327(8476), 307-310. doi:10.1016/S0140-6736(86)90837-8
  • In clinical measurement comparison of a new measurement technique with an established one is often needed to see whether they agree sufficiently for the new to replace the old. Such investigations are often analysed inappropriately, notably by using correlation coefficients. The use of correlation is misleading. An alternative approach, based on graphical techniques and simple calculations, is described, together with the relation between this analysis and the assessment of repeatability.

1983

• (Altman & Bland, 1968) ⇒ Altman, D. G., & Bland, J. M. (1983). Measurement in medicine: the analysis of method comparison studies. The statistician, 307-317. doi:10.2307/2987937
  • Summary: Methods of analysis used in the comparison of two methods of measurement are reviewed. The use of correlation, regression and the difference between means is criticized. A simple parametric approach is proposed based on analysis of variance and simple graphical methods.

The problem: In medicine we often want to compare two different methods of measuring some quantity, such as blood pressure, gestational age, or cardiac stroke volume. Sometimes we compare an approximate or simple method tithe very precise one. This is a calibration problem, and we shall not discuss it further here. Frequently, however, we cannot regard either method as giving the true value of the quantity being measured. In this case we want to know whether the methods give answers which are, in some sense, comparable. For example, we may wish to see whether a new, cheap and quick method produces answers that agree with those from an established method sufficiently well for clinical purposes. Many such studies, using a variety of statistical techniques, have been reported. Yet few really answer the question "Do the two methods of measurement agree sufficiently closely?" In this pa, we shall describe what is usually done, show why this is inappropriate, suggest a better approach, and ask why such studies are done to badly. We will restrict our consideration to the comparison of two methods of measuring a continuous variable, although similar problems can arise with categorical variables.

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