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Bootstrap confidence intervals for correlation between continuous repeated measures

Author

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  • Guogen Shan

    (University of Nevada, Las Vegas)

  • Hua Zhang

    (Zhejiang Gongshang University)

  • Jim Barbour

    (Experian Information Solutions, Inc.)

Abstract

Repeated measures designs are widely used in practice to increase power, reduce sample size, and increase efficiency in data collection. Correlation between repeated measurements is one of the first research questions that needs to be addressed in a repeated-measure study. In addition to an estimate for correlation, confidence interval should be computed and reported for statistical inference. The asymptotic interval based on the delta method is traditionally calculated due to its simplicity. However, this interval is often criticized for its unsatisfactory performance with regards to coverage and interval width. Bootstrap could be utilized to reduce the interval width, and the widely used bootstrap intervals include the percentile interval, the bias-corrected interval, and the bias-corrected with acceleration interval. Wilcox (Comput Stat Data Anal 22:89–98,1996) suggested a modified percentile interval with the interval levels adjusted by sample size to have the coverage probability close to the nominal level. For a study with repeated measures, more parameters in addition to sample size would affect the coverage probability. For these reasons, we propose modifying the percentiles in the percentile interval to guarantee the coverage probability based on simulation studies. We analyze the correlation between imaging volumes and memory scores from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study to illustrate the application of the considered intervals. The proposed interval is exact with the coverage probability guaranteed, and is recommended for use in practice.

Suggested Citation

  • Guogen Shan & Hua Zhang & Jim Barbour, 2021. "Bootstrap confidence intervals for correlation between continuous repeated measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1175-1195, October.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:4:d:10.1007_s10260-020-00555-1
    DOI: 10.1007/s10260-020-00555-1
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    References listed on IDEAS

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    1. Wilcox, Rand R., 1996. "Confidence intervals for the slope of a regression line when the error term has nonconstant variance," Computational Statistics & Data Analysis, Elsevier, vol. 22(1), pages 89-98, June.
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    Cited by:

    1. Natalie DelRocco & Yipeng Wang & Dongyuan Wu & Yuting Yang & Guogen Shan, 2023. "New Confidence Intervals for Relative Risk of Two Correlated Proportions," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 1-30, April.

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