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Title: Adjusted score functions to solve monotone likelihood problems in the Cox regression model Authors:  Euloge Clovis Kenne Pagui - University of Padova (Italy) [presenting]
Abstract: Standard inference procedures for the Cox model involve maximizing the partial likelihood function. A phenomenon well known as monotone likelihood might be observed when fitting the partial hazard model to particular data sets. Monotone likelihood mainly occurs in samples with substantial censoring of survival times and is associated with categorical covariates. In particular, and more frequently, it usually happens when one level of a categorical covariate has just experienced censoring times. One way to overcome this problem is to use of adjusted partial likelihood score aiming at mean bias reduction. The procedure is effective in preventing infinite estimates. As an alternative solution, we propose an approach based on the adjusted score function for median bias reduction. This procedure also solves the infinite estimate problem and has an additional advantage of being invariant under component-wise reparameterizations. This latter aspect is fundamental under the Cox model since hazards ratio interpretation is obtained by exponentiating parameter estimates. Extensive numerical studies of the proposed method suggest better inference properties than those of the mean bias reduction. A real data application related to a melanoma skin data set is used as an illustration for a comparison basis of the methods.