Progression-free survival (PFS) is a commonly used surrogate endpoint in oncology trials. Quantities of interest in this context are the correlation coefficient between PFS and OS as well as the survival function for OS. Fleischer et al. (2009) and Li and Zhang (2015) use a latent-time illness-death model without recovery to jointly model PFS and OS and based on this model, derive parametric point estimates for the correlation between PFS and OS and the survival function of OS. They either assume exponential or Weibull transition hazards with a common shape parameter. We generalize their approach by showing that the latent time assumption is not necessary, derive parametric and nonparametric point estimates as well as inference methods for the transition hazards, the correlation between PFS and OS, as well as the survival function of OS. We do this by relaxing the equal shape parameter assumption and under various assumptions on the stochastic process underpinning the multistate model, namely time-homogeneous and non-homogeneous Markov as well as non-Markov. Our results shed light on the implicit assumptions in Fleischer et al (2009) and Li and Zhang (2015). The methods are illustrated using a large Phase 3 oncology clinical trial.