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

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Bojuan Zhao*
• Companies: Tianjin University of Finance and Economics
• Keywords: Cox proportional hazards model ; Kaplan-Meier estimator ; Mantel- Haenszel estimator ; relative risk ; hazard ratio

Abstract

The concepts of relative risk and hazard ratio are generalized for ordinary ordinal and continuous response variables respectively. Under the generalized concepts, the estimated relative risks obtained from the Cox proportional hazards model with the Breslow's and the Efron's methods are weighted averages of certain observed relative risks, with formats that are similar to the Mantel-Haenszel estimator, but with an unknown parameter in the weights. The Cox proportional hazards model with the Breslow's and the Efron's methods can be regarded as generalizations of the Mantel-Haenszel estimator for dealing with broader types of covariates and response variables. When ordinary ordinal or countable responses can be regarded as discretized observations of a hypothetical continuous variable, the estimated relative risk from the proportional hazards model can be used to reflect the association(s) between the response variable and the covariate(s). Examples are given to illustrate the generalized concepts and wider applications of the proportional hazards model and the Kaplan-Meier estimator.