**Measuring agreement (April 19, 2005)**

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Someone reviewing a paper asked me about all the "weird statistics" being used in the paper, such as the Bland-Altman plot and Deming regression.

The Bland-Altman plot is a fairly standard way to compare the agreement between two measures of the clinical outcome.

**Statistical methods for assessing agreement between two methods of clinical measurement.**Bland JM, Altman DG. Lancet 1986: 1(8476); 307-10. [Medline] [Full text]

Here's an example of a Bland-Altman plot

that compares functional residual capacity by two approaches: rebreathing of sulphur hexafluoride and by computed tomography. The two measures appear to be reasonably close to one another, and the degree of agreement is about the same across the full range of the data. This graph appears in

**Uneven distribution of ventilation in acute respiratory distress syndrome.**Rylander C, Tylen U, Rossi-Norrlund R, Herrmann P, Quintel M, Bake B. Crit Care 2005: 9(2); R165-71. [Medline] [Abstract] [Full text] [PDF]

which is an open source journal.

Deming regression is just the same thing as linear regression except that an adjustment is made for measurement error in the independent variable.

**General deming regression for estimating systematic bias and its confidence interval in method-comparison studies.**Martin RF. Clin Chem 2000: 46(1); 100-4. [Medline] [Abstract] [Full text] [PDF]

As an example of Deming regression, two immunoassays for human glandular kallikrein were compared using Deming regression. The slope was 0.79 (95% confidence interval 0.67 to 0.92) and the intercept was 0.014 (95% CI 0.004 to 0.025) with an R-squared value of 0.67. This line (the solid line in the graph below) differs from the ideal line with slope=1 and intercept=0 (the dotted line) and has a weak correlation, since one assay can only account for 2/3 of the variation in the other assay.

[Permission received on April 25, 2005 to reproduce this image.]

**Standardization of two immunoassays for human glandular kallikrein 2.**Haese A, Vaisanen V, Finlay JA, Pettersson K, Rittenhouse HG, Partin AW, Bruzek DJ, Sokoll LJ, Lilja H, Chan DW. Clin Chem 2003: 49(4); 601-10. [Medline] [Abstract] [Full text] [PDF]

The authors may have also used something called Lin's Concordance Coefficient.

**Validating Mathematical Models of Biological Systems: Application of the Concordance Correlation Coefficient [PDF]**. St-Pierre NR. Accessed on 2005-04-19. library.lanl.gov/cgi-bin/getdoc?event=SAMO2004&document=samo04-41.pdf

An example of Lin's concordance coefficient appears in a study of joint space narrowing and erosion scores in plain versus digitized x-rays. The erosion concordance score is 0.89 and the graph below shows good agreement between the regression line (solid) and the line of perfect agreement (dashed).

In contrast, the joint space narrowing has a concordance score of only 0.36 and notice how the regression line is not even close to the line of perfect agreement.

These data and figures come from

**Internet hand x-rays: A comparison of joint space narrowing and erosion scores (Sharp/Genant) of plain versus digitized x-rays in rheumatoid arthritis patients.**Arbillaga HO, Montgomery GP, Cabarrus LP, Watson MM, Martin L, Edworthy SM. BMC Musculoskelet Disord 2002: 3(1); 13. [Medline] [Abstract] [Full text] [PDF]

which is an open source journal.

These tools are little publicized because the measurement of agreement does not fit into the classical statistical models. There is no research hypothesis, for example, but rather the goal of the research is to assess how strongly two measures agree with one another.

**Further reading**

**Statistical validation criteria for drinking-water microbiological methods [PDF]**. McBride G, published by the Ministry of Health, National Institute of Water & Atmospheric Research Ltd, February 2003. Accessed on 2005-04-19. www.moh.govt.nz/moh.nsf/wpg_Index/Publications-Statistical+validation+criteria+for+drinking-water+microbiological+methods**Points of Care in Using Statistics in Method-Comparison Studies**. Westgard JO, This is an annotated version of an editorial that appeared in the 1998 November issue of Clinical Chemistry, volume 44, pages 2240-2242. This version includes links to supporting materials available on this website. Accessed on 2005-04-19. www.westgard.com/essay19.htm**Method Validation: The Frequently-Asked-Questions**. Westgard JO. Accessed on 2005-04-19. www.westgard.com/quest11.htm