Estimating an Individual's Probability of Revision Surgery After Knee Replacement: A Comparison of Modeling Approaches Using a National Data Set

Abstract

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.

Figure 1.

Observed and predicted probabilities of remaining event-free, using different models and data from the National Joint Registry for England, Wales, Northern Ireland, and the Isle of Man, 2003–2015. A) Total knee replacement; B) unicondylar knee replacement; C) patellofemoral replacement. Predicted probabilities of remaining event-free were obtained from different models: exponential model, Weibull model, log-logistic model, flexible parametric model (FPM), and random survival forest (RFS). The observed probability of remaining event-free was obtained from the Kaplan-Meier estimator.

Figure 2.

Hazard estimates for different parametric models, using data from the National Joint Registry for England, Wales, Northern Ireland, and the Isle of Man, 2003–2015. A) Total knee replacement; B) unicondylar knee replacement; C) patellofemoral replacement. FPM, flexible parametric model.

Figure 3.

Calibration plots of prosthesis revision showing predicted risks (black bars) and observed risks (white bars) for different risk groups, using data from the National Joint Registry for England, Wales, Northern Ireland, and the Isle of Man, 2003–2015. A) Total knee replacement, results from the flexible parametric model; B) unicondylar knee replacement, results from the flexible parametric model; C) patellofemoral replacement, results from the flexible parametric model; D) total knee replacement, results from the random survival forest; E) unicondylar knee replacement, results from the random survival forest; F) patellofemoral replacement, results from the random survival forest.