Penalized likelihood in Cox regression

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Abstract
In a Cox regression model, instability of the estimated regression coefficients can be reduced by maximizing a penalized partial log‐likelihood, where a penalty function of the regression coefficients is substracted from the partial log‐likelihood. In this paper, we choose the optimal weight of the penalty function by maximizing the predictive value of the model, as measured by the crossvalidated partial log‐likelihood. Our methods are illustrated by a study of ovarian cancer survival and by a study of centre effects in kidney graft survival.

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