Generalized Concept of Relative Risk and Wider Applications of the Proportional Hazards Model and the Kaplan–Meier Estimator

Abstract

The concepts of relative risk and hazard ratio are generalized for ordinary ordinal and continuous response variables, respectively. Under the generalized concepts, the Cox proportional hazards model with the Breslow's and Efron's methods can be regarded as generalizations of the Mantel–Haenszel estimator for dealing with broader types of covariates and responses. When ordinal responses can be regarded as discretized observations of a hypothetical continuous variable, the estimated relative risks from the Cox model reflect the associations between the responses and covariates. Examples are given to illustrate the generalized concepts and wider applications of the Cox model and the Kaplan–Meier estimator.

Keywords:

• Cox proportional hazards model
• Hazard ratio
• Kaplan–Meier estimator
• Mantel–Haenszel estimator
• Relative risk

Mathematics Subject Classification:

• Primary: 62 Statistics; Secondary: 62N99