# Likelihood approaches for proportional likelihood ratio model with right-censored data.Stat Med 2014; 33(14):2467-79SM

Regression methods for survival data with right censoring have been extensively studied under semiparametric transformation models such as the Cox regression model and the proportional odds model. However, their practical application could be limited because of possible violation of model assumption or lack of ready interpretation for the regression coefficients in some cases. As an alternative, in this paper, the proportional likelihood ratio model introduced by Luo and Tsai is extended to flexibly model the relationship between survival outcome and covariates. This model has a natural connection with many important semiparametric models such as generalized linear model and density ratio model and is closely related to biased sampling problems. Compared with the semiparametric transformation model, the proportional likelihood ratio model is appealing and practical in many ways because of its model flexibility and quite direct clinical interpretation. We present two likelihood approaches for the estimation and inference on the target regression parameters under independent and dependent censoring assumptions. Based on a conditional likelihood approach using uncensored failure times, a numerically simple estimation procedure is developed by maximizing a pairwise pseudo-likelihood. We also develop a full likelihood approach, and the most efficient maximum likelihood estimator is obtained by a profile likelihood. Simulation studies are conducted to assess the finite-sample properties of the proposed estimators and compare the efficiency of the two likelihood approaches. An application to survival data for bone marrow transplantation patients of acute leukemia is provided to illustrate the proposed method and other approaches for handling non-proportionality. The relative merits of these methods are discussed in concluding remarks.

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*Statistics in Medicine,*vol. 33, no. 14, 2014, pp. 2467-79.

*Stat Med*. 2014;33(14):2467-79.

*Statistics in Medicine,*

*33*(14), pp. 2467-79. doi:10.1002/sim.6105.

*Stat Med.*2014 Jun 30;33(14):2467-79. PubMed PMID: 24500821.