Anchored Minimal Clinically Important Difference Metrics: Considerations for Bias and Regression to the Mean

Abstract

Minimal clinically important differences (MCIDs) are used to understand clinical relevance. However, repeated observations produce biased analyses unless one accounts for baseline observation, known as regression to the mean (RTM). Using an International Knee Documentation Committee (IKDC) survey dataset, we can demonstrate the effect of RTM on MCID values by (1) MCID-estimate dependence on baseline observation and (2) MCID-estimate bias being higher when the posttest-pretest data correlation is lower. We created 10 IKDC datasets with 5000 patients and a specific correlation under both equal and unequal variances. For each 10-point increase in baseline IKDC, MCID decreased by 3.5, 2.7, 1.9, 1.2, and 0.7 points when posttest-pretest correlations were 0.10, 0.25, 0.50, 0.75, and 0.90, respectively, under equal variances. Not accounting for RTM resulted in a static 20-point MCID. Minimal clinically important difference estimates may be unreliable. Minimal clinically important difference calculations should include the correlation and variances between posttest and pretest data, and researchers should consider using a baseline covariate-adjusted receiver operating characteristic curve analysis to calculate MCID.

Keywords: patient-reported outcomes; statistics; validity.

Figure 1

Plots of the Δ (posttest−pretest = Δ) against the observed baseline data (ie, pretest data) for various levels of posttest-pretest data correlation under the scenario of equal variances. A, 0.10 correlation. B, 0.25 correlation. C, 0.50 correlation. D, 0.75 correlation. E, 0.90 correlation. The linear regression lines and equations are plotted to depict that the slope of the correlation is higher when the posttest-pretest data correlation is lower.

Figure 2

Plots of the Δ (posttest−pretest = Δ) against the observed baseline data (ie, pretest data) for various levels of posttest-pretest data correlation under unequal variances. A, 0.10 correlation. B, 0.25 correlation. C, 0.50 correlation. D, 0.75 correlation. E, 0.90 correlation. The linear regression line and equation are plotted to depict that the slope of the correlation is generally higher when the posttest-pretest data correlation is lower, although both D and E approximate a slope of zero.

Figure 3

Simulated minimal clinically important differences (MCIDs) are demonstrated with increasing levels of correlation under the scenario of equal variances. A, 0.10 correlation. B, 0.25 correlation. C, 0.50 correlation. D, 0.75 correlation. E, 0.90 correlation. Lower levels of data correlation result in a greater rate of change in the MCID estimate as well as a wider range of MCIDs as a function of the observed baseline data. The regression equations are for a linear regression fit to the data (MCID and observed baseline measurement) and not for the plotted data and bootstrapped 95% CIs.

Figure 4

Simulated minimal clinically important differences (MCIDs) are demonstrated with increasing levels of correlation under unequal variances. A, 0.10 correlation. B, 0.25 correlation. C, 0.50 correlation. D, 0.75 correlation. E, 0.90 correlation. Lower levels of data correlation result in a greater rate of change in the MCID estimate as well as a wider range of MCIDs as a function of the observed baseline data, although both D and E approximate a slope of zero. The regression equations are for a linear regression fit to the data (MCID and observed baseline measurement) and not the plotted data and bootstrapped 95% CIs.