A framework for the meta-analysis of Bland–Altman studies based on a limits of agreement approach

Bland–Altman method comparison studies are common in the medical sciences and are used to compare a new measure to a gold-standard (often costlier or more invasive) measure. The distribution of these differences is summarized by two statistics, the ‘bias’ and standard deviation, and these measures are combined to provide estimates of the limits of agreement (LoA). When these LoA are within the bounds of clinically insignificant differences, the new non-invasive measure is preferred. Very often, multiple Bland–Altman studies have been conducted comparing the same two measures, and random-effects meta-analysis provides a means to pool these estimates. We provide a framework for the meta-analysis of Bland–Altman studies, including methods for estimating the LoA and measures of uncertainty (i.e., confidence intervals). Importantly, these LoA are likely to be wider than those typically reported in Bland–Altman meta-analyses. Frequently, Bland–Altman studies report results based on repeated measures designs but do not properly adjust for this design in the analysis. Meta-analyses of Bland–Altman studies frequently exclude these studies for this reason. We provide a meta-analytic approach that allows inclusion of estimates from these studies. This includes adjustments to the estimate of the standard deviation and a method for pooling the estimates based upon robust variance estimation. An example is included based on a previously published meta-analysis.