Key result
Fractional polynomial regression models Bland-Altman limits of agreement for Agatston scores when standard assumptions fail.
Why the study?
Standard Bland-Altman analysis requires normally distributed differences, constant bias, and variance homogeneity, which are often violated when evaluating agreement for metrics like the Agatston score.
Fractional polynomial regression provides a robust alternative for Bland-Altman analysis when standard assumptions of variance homogeneity and constant bias are violated, as demonstrated with Agatston score data.
May improve agreement analysis for heterogeneous data like Agatston scores; leaves open prospective validation in cardiovascular method comparisons.
Bland–Altman limits of agreement are very popular in method comparison studies on quantitative outcomes. However, a straightforward application of Bland–Altman analysis requires roughly normally distributed differences, a constant bias, and variance homogeneity across the measurement range. If one or more assumptions are violated, a variance-stabilizing transformation (e.g., natural logarithm, square root) may be sufficient before Bland–Altman analysis can be performed. Sometimes, fractional polynomial regression has been used when the choice of variance-stabilizing transformation was unclear and increasing variability in the differences was observed with increasing mean values. In this case, regressing the absolute differences on a function of the average and applying fractional polynomial regression to this end were previously proposed. This review revisits a previous inter-rater agreement analysis on the Agatston score for coronary calcification. We show the inappropriateness of a straightforward Bland–Altman analysis and briefly describe the nonparametric limits of agreement of the original investigation. We demonstrate the application of fractional polynomials, use the Stata packages fp and fp_select, and discuss the use of degree-2 (the default setting) and degree-3 fractional polynomials. Finally, we discuss conditions for evaluating the appropriateness of nonstandard limits of agreement.
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Gerke et al. (2023) conducted a review in Coronary calcification. Fractional polynomial regression vs. Standard Bland-Altman analysis was evaluated on Appropriateness of nonstandard limits of agreement. Fractional polynomial regression (degree-2 and degree-3) can model Bland-Altman limits of agreement when standard assumptions are violated, as demonstrated with the Agatston score.
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