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 evaluate the proposed partial correlation coefficients.

Keywords:

• Alzheimer’s disease
• Parkinson’s disease
• Partial correction
• Proc Mixed
• Repeated measurements

Acknowledgments

The authors are very grateful to editor, associate editor, and three reviewers for their insightful comments that help to improve the article significantly.

Additional information

Funding

Shan’s research is partially supported by grants from the National Institute of General Medical Sciences from the National Institutes of Health: P20GM109025. Data used in the preparation of this article were obtained from the Parkinson’s Progression Markers Initiative (PPMI) database (www.ppmi-info.org/data). For up-to-date information on the study, visit www.ppmi-info.org. PPMI—a public-private partnership—is funded by the Michael J. Fox Foundation for Parkinson’s Research and funding partners, including Abbvie, Allergan, Avid, Biogen, Biolegend, Bristol-Myers Squibb, Jenali, GE Healthcare, Genetnetch, GlaxoSmithKline, Lilly, Lundbeck, Merck, MesoScale Discovery, Pfizer, Piramal, Prevail, Roche, SanofiGenzyme, Servier, Takeda, Teva, and UCB.