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Extensions of the absolute standardized hazard ratio and connections with measures of explained variation and variable importance

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  • Michael R. Crager

    (Exact Sciences Corporation)

Abstract

The absolute standardized hazard ratio (ASHR) is a scale-invariant scalar measure of the strength of association of a vector of covariates with the risk of an event. It is derived from proportional hazards regression. The ASHR is useful for making comparisons among different sets of covariates. Extensions of the ASHR concept and practical considerations regarding its computation are discussed. These include a new method to conduct preliminary checks for collinearity among covariates, a partial ASHR to evaluate the association with event risk of some of the covariates conditioning on others, and the ASHR for interactions. To put the ASHR in context, its relationship to measures of explained variation and other measures of separation of risk is discussed. A new measure of the contribution of each covariate to the risk score variance is proposed. This measure, which is derived from the ASHR calculations, is interpretable as variable importance within the context of the multivariable model.

Suggested Citation

  • Michael R. Crager, 2020. "Extensions of the absolute standardized hazard ratio and connections with measures of explained variation and variable importance," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 872-892, October.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:4:d:10.1007_s10985-020-09504-2
    DOI: 10.1007/s10985-020-09504-2
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    References listed on IDEAS

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    1. Johan Bring, 1995. "Variable importance by partitioningR 2," Quality & Quantity: International Journal of Methodology, Springer, vol. 29(2), pages 173-189, May.
    2. Michael Schemper & Robin Henderson, 2000. "Predictive Accuracy and Explained Variation in Cox Regression," Biometrics, The International Biometric Society, vol. 56(1), pages 249-255, March.
    3. Michael R. Crager, 2012. "Generalizing the standardized hazard ratio to multivariate proportional hazards regression, with an application to clinical~genomic studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 399-417, May.
    4. Zuber Verena & Strimmer Korbinian, 2011. "High-Dimensional Regression and Variable Selection Using CAR Scores," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, July.
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