An assumption of the Bland-Altman limits of agreement is that the differences (or
residuals, when fitting a regression) are normally distributed. In many cases, there will
not be a big impact on the limits of agreement when the distribution of the differences is
not normal. However, there may be cases where it is preferable to estimate the limits using
a nonparametric method.
A histogram of the differences is useful for assessing the
assumption of normality. If the distribution is skewed or has very long tails, the
assumption of normality may not be valid.
To illustrate these concepts, we will
use another example from Bland & Altman’s 1999 paper. This example shows the
differences in systolic blood pressure measurements by a device and those by
The difference plot shows the limits of agreement estimated using the 2.5th and
97.5th percentiles and the average bias estimated as the median of the
(click to enlarge)(click to enlarge)
The limits of agreement estimated by the nonparametric method are wider than the
limits estimated using the parametric method. Roughly 2.5% of the observations are
above, with a similar percentage below the limits of agreement. In contrast, the
narrower parametric-based limits of agreement show all observations outside the
lower limits of agreement and none above the upper limit.