An Alternative to the Bland-Altman Repeated-Measures Correlation to Account for Variability of Slopes Across Persons

The Bland-Altman repeated-measures correlation (rmcorr) is widely used to estimate within-person correlations between two variables in repeated-measures data. However, it assumes the same slope for all subjects, which can be misleading when slopes vary. To propose an alternative method, the weighted mean within-person correlation (wmcorr), which calculates the average of all within-person correlations, weighted by the square root of the number of observations for each person. The wmcorr method was applied to real data examples and compared to the Bland-Altman rmcorr. Simulations (5,000) were run to compare the mean significance levels (p-values) of rmcorr and wmcorr and to determine the relationship between estimated rmcorrs and wmcorrs. In most cases, rmcorr and wmcorr yielded similar results. However, in cases where subjects had at least moderately varying slopes, wmcorr provided a more visually intuitive estimate of the within-person correlation. Conflicting significance levels or opposite directions of rmcorr and wmcorr served as "warning signs" for potential data quality issues or the need for further data collection. The wmcorr method is proposed as an alternative to the Bland-Altman rmcorr for estimating within-person correlations in repeated-measures data. Researchers are encouraged to estimate both wmcorr and rmcorr, as discrepancies between the two can alert researchers to data patterns that warrant closer inspection before drawing conclusions about within-person relationships.