Prediction of Multiple Recurrent Events: A Comparison of Extended Cox Models in Bladder Cancer

Recurrence of bladder cancer can occur repeatedly in the same patient after treatment of the primary tumor. Models predicting the risk of a next recurrence may inform individualized decision-making on surveillance frequency. We aimed to assess the usefulness of extensions of the Cox proportional hazards model for repeated events in this context. We analyzed 531 Dutch patients with bladder cancer (1990-2012) with information on 7 prespecified predictors at the time of diagnosis of the primary and recurrent tumors. We considered 3 aspects of model variants: how to model time to the repeated events (calendar time, gap time, elapsed time); the number of preceding events (predictor, stratum variable); and the within-subject correlation (ignored in a simple Cox model, robust standard errors in a variance-correction model, random effect in a frailty model). First to fourth recurrences of bladder cancer occurred in 313, 174, 103, and 66 patients, respectively, with median calendar follow-up times of 1.1, 2.5, 3.8, and 4.5 years, respectively. We focused on gap time in the detailed analyses, allowing for clinically meaningful predictions. Variance-correction models may be useful if predictor selection is part of the model development. Frailty models may be useful when within-subject correlation is strong.