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Nonparametric estimation of Spearman's rank correlation with bivariate survival data

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  • Svetlana K. Eden
  • Chun Li
  • Bryan E. Shepherd

Abstract

We study rank‐based approaches to estimate the correlation between two right‐censored variables. With end‐of‐study censoring, it is often impossible to nonparametrically identify the complete bivariate survival distribution, and therefore it is impossible to nonparametrically compute Spearman's rank correlation. As a solution, we propose two measures that can be nonparametrically estimated. The first measure is Spearman's correlation in a restricted region. The second measure is Spearman's correlation for an altered but estimable joint distribution. We describe population parameters for these measures and illustrate how they are similar to and different from the overall Spearman's correlation. We propose consistent estimators of these measures and study their performance through simulations. We illustrate our methods with a study assessing the correlation between the time to viral failure and the time to regimen change among persons living with HIV in Latin America who start antiretroviral therapy.

Suggested Citation

  • Svetlana K. Eden & Chun Li & Bryan E. Shepherd, 2022. "Nonparametric estimation of Spearman's rank correlation with bivariate survival data," Biometrics, The International Biometric Society, vol. 78(2), pages 421-434, June.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:2:p:421-434
    DOI: 10.1111/biom.13453
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    References listed on IDEAS

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    1. Dabrowska, Dorota M., 1989. "Kaplan-Meier estimate on the plane: Weak convergence, LIL, and the bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 29(2), pages 308-325, May.
    2. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    3. Chun Li & Bryan E. Shepherd, 2012. "A new residual for ordinal outcomes," Biometrika, Biometrika Trust, vol. 99(2), pages 473-480.
    4. M. J. Van Der Laan, 1997. "Nonparametric estimators of the bivariate survival function under random censoring," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 51(2), pages 178-200, July.
    5. Qi Liu & Chun Li & Valentine Wanga & Bryan E. Shepherd, 2018. "Covariate†adjusted Spearman's rank correlation with probability†scale residuals," Biometrics, The International Biometric Society, vol. 74(2), pages 595-605, June.
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