CPR Working Paper Series No. 68
Cox-McFadden Partial and Marginal
Likelihoods for the Proportional Hazard Model with Random Effects
Jan Ondrich
August 2005
Abstract
In survival analysis, Cox’s name is associated with the partial likelihood
technique that allows consistent estimation of proportional hazard scale
parameters
without specifying a duration dependence baseline. In discrete choice
analysis,
McFadden’s name is associated with the generalized extreme-value (GEV) class
of
logistic choice models that relax the independence of irrelevant
alternatives assumption.
This paper shows that the mixed class of proportional hazard specifications
allowing
consistent estimation of scale and mixing parameters using partial
likelihood is
isomorphic to the GEV class. Independent censoring is allowed and I discuss
approximations to the partial likelihood in the presence of ties. Finally,
the partial
likelihood score vector can be used to construct log-rank tests that do not
require the
independence of observations involved.
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