Partial correlation coefficient for a study with repeated measurements

Abstract

Repeated data are increasingly collected in studies to investigate the trajectory of change in measurements over time. Determining a link between one repeated measurement with another that is considered as the biomarker for disease progression, may provide a new target for drug development. When a third variable is associated with one of the two measurements, partial correlation after eliminating the effect of that variable is able to provide reliable estimate for association as compared to the existing raw correlation for repeated data. We propose using linear regression models to compute residuals by modeling a relationship between each measurement and a third variable. The computed residuals are then used in a linear mixed model (implemented by SAS Proc Mixed) to compute partial correlation for repeated data. Alternatively, the partial correlation may be computed as the average of partial correlations at each visit. We provide two real examples to illustrate the application of the proposed partial correlation, and conduct extensive numerical studies to compare the proposed partial correlation coefficients.

Keywords: Alzheimer’s disease; Parkinson’s disease; Partial correction; Proc Mixed; Repeated measurements.

Fig. 1

Simulated partial correlation between two repeated measurements after controlling for age given the raw correlation between these two measurements from 0.3 to 0.9 when n = 20. Correlations between age and the average of measurements from −0.8 to 0.8 are studied.

Fig. 2

Simulated partial correlation between two repeated measurements after controlling for age given the raw correlation between these two measurements from 0.3 to 0.9 when n = 60. Correlations between age and the average of measurements from −0.8 to 0.8 are studied.

Fig. 3

Simulated partial correlation between two repeated measurements after controlling for age given the raw correlation between these two measurements from 0.3 to 0.9 when n = 20. Correlations between age and the average of measurements from −0.8 to 0.8 are studied. The standard deviation of age is 10 (left) and 40 (right) under the dependent assumption.