In this article, we consider methods for assessing covariate effects on survival outcome in the target population when data are collected under prevalent sampling. We investigate a flexible semiparametric density ratio model without the constraints of the constant disease incidence rate and discrete covariates as required in Shen and others 2012. For inference, we introduce two likelihood approaches with distinct computational algorithms. We first develop a full likelihood approach to obtain the most efficient estimators by an iterative algorithm. Under the density ratio model, we exploit the invariance property of uncensored failure times from the prevalent cohort and also propose a computationally convenient estimation procedure that uses a conditional pairwise likelihood. The empirical performance and efficiency of the two approaches are evaluated through simulation studies. The proposed methods are applied to the Surveillance, Epidemiology, and End Results Medicare linked data for women diagnosed with stage IV breast cancer.