Weighted Repeated Measures Correlation Coefficient: A New Correlation Coefficient for Handling Missing Data With Repeated Measures.

The relationship between two variables measured multiple times per individual has often been evaluated in clinical studies. These data are not independent; therefore, the Pearson correlation coefficient is inappropriate, and some correlation coefficients for these data have been proposed. However, in the presence of missing data, the existing methods can be biased. In this article, we proposed a weighted repeated measures correlation coefficient that provides an accurate estimate, even with missing data, in a study in which participants ideally have the same number of measurements. We also provided a bootstrap confidence interval for the weighted repeated measures correlation coefficients. We evaluated the performance of the proposed and existing methods (i.e., simple Pearson correlation coefficient, the Pearson correlation coefficient for average, average of the Pearson correlation coefficient, correlation coefficient based on analysis of covariance, and correlation coefficient based on the linear mixed-effects model) through simulations and application to actual data. In numerical evaluations using simulations, the proposed method consistently outperformed existing methods. We recommend using a weighted repeated measures correlation coefficient to handle missing values in multiple-measurement data.