Why correlation is a misleading metric for measuring scientific agreement
In short: When scientists compare two new medical tests, they often reach for correlation coefficients. But a high correlation doesn't prove two methods agree. To find the truth about measurement bias and error, researchers turn to a more nuanced tool: the Bland–Altman plot.
In clinical laboratories, assessing whether a new measurement method can replace an old one is a common challenge. Traditionally, researchers used the Pearson correlation coefficient (r) to show how closely two variables relate. However, correlation only measures the strength of a linear relationship, not the agreement between methods. A high correlation can be a mere byproduct of using a wide range of samples, even if the two methods produce significantly different results.
Proposed by Altman and Bland in 1983—building on earlier work by Eksborg in 1981—the Bland–Altman plot offers a superior alternative. Instead of looking at how variables move together, it focuses on the differences between them. The plot typically displays the mean of the two measurements on the x-axis and the difference between them on the y-axis. This allows researchers to identify 'bias'—the average difference between the two systems—and establish 'limits of agreement.'
The 95% limits of agreement define an interval where most differences between the methods are expected to fall. A positive mean difference suggests the new method produces larger values than the gold standard, while a negative difference suggests lower values. Crucially, the plot itself does not determine if these limits are acceptable; that threshold must be defined a 'a priori' based on clinical necessity or biological considerations.
Modern applications continue to refine this technique. For instance, when dealing with 'censored' data—where some values fall below detection limits—simple substitutions can introduce bias, necessitating more complex multiple imputation approaches. In cardiovascular medicine, researchers are even moving toward quantile regression to address instances where agreement worsens at specific ranges, such as lower fractional flow reserve values.
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Sources
- Summary by Intellect · source: Understanding Bland Altman analysis - PMC
- Also: Bland–Altman plot
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