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Título

PRIOR SPECIFCATIONS TO HANDLE MONOTONE LIKELIHOOD IN THE COX REGRESSION MODEL

Resumo

The phenomenon of monotone likelihood is observed in the fi tting process of
a Cox model when the likelihood converges to a finite value while at least one parameter
estimate diverges to infi nity. Monotone likelihood primarily occurs in samples with sub-
stantial censoring of survival times and associated to categorical covariates. In particular
and more frequent, it occurs when one level of a categorical covariate has not experienced
any failure. A solution suggested by Heinze and Schemper (2001) is an adaptation of a
procedure by Firth (1993) originally developed to reduce the bias of maximum likelihood
estimates. The method leads to finite parameter estimates by means of penalized maxi-
mum likelihood estimation. In this case, the penalty might be interpreted as a Je reys
type of prior well known in Bayesian inference. However, this approach has some draw-
backs, especially biased estimators and high standard errors. In this paper, we explore
other penalties for the partial likelihood function in the flavor of Bayesian prior distribu-
tions. An empirical study of the suggested procedures confi rms satisfactory performance
of both estimation and inference. We also explore a real analysis related to a melanoma
skin data set to evaluate the impact of the different prior distributions as penalizations.

Palavras-chave

Firth correction, MCMC, Partial likelihood, Survival analysis.

Área

Análise de Sobrevivência

Autores

Frederico Machado Almeida, Enrico Antonio Colosimo, Vinícius Diniz Mayrink