Joint models are frequently used in survival analysis to assess the relationship between time-to-event data and time-dependent covariates, which are measured longitudinally but often with errors. Routinely, a linear mixed-effects model is used to describe the longitudinal data process, while the survival times are assumed to follow the proportional hazards model. However, in some practical situations, individual covariate profiles may contain changepoints. In this article, we assume a two-phase polynomial random effects with subject-specific changepoint model for the longitudinal data process and the proportional hazards model for the survival times. Our main interest is in the estimation of the parameter in the hazards model. We incorporate a smooth transition function into the changepoint model for the longitudinal data and develop the corrected score and conditional score estimators, which do not require any assumption regarding the underlying distribution of the random effects or that of the changepoints. The estimators are shown to be asymptotically equivalent and their finite-sample performance is examined via simulations. The methods are applied to AIDS clinical trial data. Copyright © 2010 John Wiley & Sons, Ltd.