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Relating Cox's Proportional Hazard Model to the Exponential Model for Survival
Author(s) -
Maller R. A.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290220
Subject(s) - covariate , proportional hazards model , mathematics , exponential function , representation (politics) , statistics , hazard , survival analysis , hazard ratio , simple (philosophy) , econometrics , mathematical analysis , confidence interval , philosophy , chemistry , organic chemistry , epistemology , politics , political science , law
An approximate representation is given for the partial likelihood estimate of the regression coefficient in Cox's proportional hazard model which indicates how it measures the association between survival time and covariate. The case of a single covariate is concentrated on. The representation is closely related to the first step of a Newton‐Raphson iteration, i.e. to the score test. A similar representation for the Feigl‐Zelen exponential model shows that a similar type of association is being measured, if observed lifetimes are interpreted as expected lifetimes of ordered exponentials. Necessary and sufficient conditions for the existence of Cox's estimate in the simple case are also written down.