Abstract
In this article, we study nonlinear temproal trends in survival for prevalent cohort data.For dealing with this situation, we model the failure time to truncation time via the partially linear transformation models. In order to propose the estimation of the partially linear transformation models for left truncated survival data, we extend a system of martingale-representation estimating equations (Lu and Zhang, 2010), and the resampling method is used to estimate asymptotic variances of estimators. More- over, testing temporal trends are linear or nonlinear reasonably is essential. For this issue, a bootstrap testing is proposed. Simulation studies for left truncated survival data with and without nonlinear temporal trends are present. A breast cancer data is analyzed to illustrate the proposed methodlogy.