On a Correspondence between Models in Binary Regression Analysis and in Survival Analysis

A one-to-one correspondence between models in binary data analysis and continuous time survival analysis is spelled out and a correspondence between survival analysis models and linear transformation models is described.

Abstract

Summary A one-to-one correspondence between models in binary data analysis and continuous time survival analysis is spelled out. A correspondence between survival analysis models and linear transformation models is also described. Despite these correspondences, the models considered natural in one field often were unknown or did not find early acceptance in corresponding fields. For example, although Berkson's Logit model for binary response data was introduced in the 1940's, the equivalent 'proportional odds' model in regression survival analysis was not formulated until the late 1970's. In addition to describing a variety of corresponding models, we also discuss such disparities in model development.