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Updated: Dec 14, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
Published on: July 3, 2020
Extensions of the absolute standardized hazard ratio and connections with measures of explained variation and
1Department of Biostatistics, Exact Sciences Corporation, 301 Penobscot Drive, Redwood City, CA, 94063, USA. mcrager@exactsciences.com.
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.
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