The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Assessing Correlation between Two Variables in Repeated Measurements using Mixed Effect Models

혼합모형을 이용한 반복 측정된 변수들 간의 상관분석

  • Han, Kyunghwa (Yonsei Biomedical Research Center, Department of Radiology, Research Institute of Radiological Science, Yonsei University College of Medicine) ;
  • Jung, Inkyung (Department of Biostatistics and Medical Informatics, Yonsei University College of Medicine)
  • 한경화 (연세대학교 의과대학 연세의생명연구원, 영상의학교실, 방사선의과학연구소) ;
  • 정인경 (영상의학교실)
  • Received : 2015.03.13
  • Accepted : 2015.04.06
  • Published : 2015.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

Repeated measurements on each variables of interest often arise in bioscience or medical research. We need to account for correlations among repeated measurements to assess the correlation between two variables in the presence of replication. This paper reviews methods to estimate a correlation coefficient between two variables in repeated measurements using the variance-covariance matrix of linear mixed effect models. We analyze acoustic radiation force impulse imaging (ARFI) data to assess correlation between three shear wave velocity (SWV) measurements in liver or spleen and spleen length by ultrasonography. We present how to obtain parameter estimates for the variance-covariance matrix and correlations in mixed effects models using PROC MIXED in SAS.

생명과학 또는 의학 연구에서는 반복 측정된 변수들 간의 상관 관계를 보고자 하는 경우가 발생한다. 반복 측정된 것을 고려하지 않으면 상관관계를 과소 추정하는 경향이 나타나므로 이를 고려해야 하며, 선형혼합모형의 분산-공분산 행렬을 이용하여 상관관계를 추정할 수 있다. 본 연구에서는 변수들의 반복 측정이 동시에 된 경우와 그렇지 않은 경우로 나누어 혼합모형을 이용한 상관계수의 추정방법을 소개한다. 고속 음향 복사력 임펄스 영상(acoustic radiation force impulse imaging; ARFI)으로 간과 비장에서 각각 세 번씩 전단파 속도를 반복 측정하고 복부 초음파 검사로 비장 길이를 측정한 자료에서 전단파 속도와 비장 길이 간의 상관 관계를 분석하기 위해 본 논문에서 소개한 방법들을 적용하였고 SAS의 PROC MIXED를 이용하는 방법을 제시하였다.

Keywords

References

  1. Bland, J. M. and Altman, D. G. (1994). Correlation, regression, and repeated data, British Medical Journal, 308, 896. https://doi.org/10.1136/bmj.308.6933.896
  2. Bland, J. M. and Altman, D. G. (1995a). Calculating correlation coefficients with repeated observations:Part 1-Correlation within subjects, British Medical Journal, 310, 446. https://doi.org/10.1136/bmj.310.6977.446
  3. Bland, J. M. and Altman, D. G. (1995b). Calculating correlation coefficients with repeated observations:Part 2-Correlation between subjects, British Medical Journal, 310, 633. https://doi.org/10.1136/bmj.310.6980.633
  4. Hamlett, A., Ryan, L., Serrano-Trespalacios, P. and Wol nger, R. (2003). Mixed models for assessing correlation in the presence of replication, Journal of the Air & Waste Management Association, 53, 442-450. https://doi.org/10.1080/10473289.2003.10466174
  5. Hamlett, A., Ryan, L. and Wolnger, R. (2004). On the use of PROC MIXED to estimate correlation in the presence of repeated measures, SAS Users Group International, Proceedings of the Statistics and Data Analysis Section, 1-7.
  6. Kenward, M. G. and Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood, Biometrics, 983-997.
  7. Lam, M., Webb, K. A. and O'Donnell, D. E. (1999). Correlation between two variables in repeated measures, American Statistical Association, Proceedings of the Biometric Section, 213-218.
  8. Roy, A. (2006). Estimating correlation coefficient between two variables with repeated observations using mixed effects model, Biometrical Journal, 48, 286-301. https://doi.org/10.1002/bimj.200510192
  9. SAS Institute Inc. (2008). SAS/STAT 9.2 User's Guide. Cary, NC: SAS Institute Inc.