A dynamic model for the risk of bladder cancer progression

Núria Porta, M. Luz Calle, Núria Malats and Guadalupe Gómez have a new paper in Statistics in Medicine. This develops a model for progression of bladder cancer with particular emphasis on predicting future risk given events up to a certain point in time.

In many ways the paper is taking a similar approach to Cortese and Andersen in explicitly modelling a time dependent covariate (here recurrence) in order to obtain predictions.
They fit a semi-parametric Cox Markov multi-state model to the data and define a prediction process


where is the time of the second event, is the type of the second event where P denotes progression and represents the history of the process up to time t. Analogously to outcome measures like the cumulative incidence functions, this predictive process is a function of the transition intensities. They also consider time dependent ROC curves to assess the improvement in classification accuracy that can be achieved by taking into account past history in addition to baseline characteristics.