A third element of the Bland-Altman approach, an interval known as
limits of agreement' is introduced in @BA86 (sometimes referred to in literature as 95\% limits of agreement). Limits of agreement are used to assess whether the two methods of measurement can be used interchangeably. @BA86 refer to this as theequivalence’
of two measurement methods. The specific question to which limits of
agreement are intended as the answer to must be established clearly.
comment that the limits of agreement show `how far apart measurements by
the two methods were likely to be for most individuals’, a definition
echoed in their 1999 paper:
The limits of agreement (LoA) are computed by the following
formula:
\begin{equation}
LoA = \bar{d} \pm 1.96 S(d)
\end{equation}
with $\bar{d}$ as the estimate of the inter method bias, $S(d)$ as
the standard deviation of the differences and 1.96 is the 95\%
quantile for the standard normal distribution. (However, in some
literature, 2 standard deviations are used instead for
simplicity.) The limits of agreement methodology assumes a constant level of bias throughout the range of measurements. As @BA86 point out this may not be the case. Bland and Altman advises on how to calculate of confidence intervals for the inter-method bias and the limits of agreement.
Importantly the authors recommend prior determination of what would and would constitute acceptable agreement, and that sample sizes should be predetermined to give an accurate conclusion.
\begin{quote}
`How far apart measurements can be without causing difficulties
will be a question of judgment. Ideally, it should be defined in
advance to help in the interpretation of the method comparison and
to choose the sample size.'\citep{BA86}
\end{quote}However highlight inadequacies in the correct application of limits of agreement, resulting in contradictory estimates of limits of agreement in various papers.