Tools that provide personalized risk prediction of outcomes after surgical procedures help patients make preference-based decisions among the available treatment options. However, it is unclear which modeling approach provides the most accurate risk estimation. We constructed and compared several parametric and nonparametric models for predicting prosthesis survivorship after knee replacement surgery for osteoarthritis. We used 430,455 patient-procedure episodes between April 2003 and September 2015 from the National Joint Registry for England, Wales, Northern Ireland, and the Isle of Man. The flexible parametric survival and random survival forest models most accurately captured the observed probability of remaining event-free. The concordance index for the flexible parametric model was the highest (0.705, 95% confidence interval (CI): 0.702, 0.707) for total knee replacement and was 0.639 (95% CI: 0.634, 0.643) for unicondylar knee replacement and 0.589 (95% CI: 0.586, 0.592) for patellofemoral replacement. The observed-to-predicted ratios for both the flexible parametric and the random survival forest approaches indicated that models tended to underestimate the risks for most risk groups. Our results show that the flexible parametric model has a better overall performance compared with other tested parametric methods and has better discrimination compared with the random survival forest approach.