Dynamic Predictions and Predictimands for Salvage Therapy in Recurrent Prostate Cancer Using Joint Models

Prostate cancer patients with biochemical recurrence (BCR) face a decision of whether to start salvage therapy (ST), which may reduce the probability of metastatic progression at the cost of side effects. To inform the decision to start ST at or after BCR, models that make counterfactual predictions incorporating treatment are highly desirable. However, estimation of such models using observational data requires care due to time-varying confounding by the longitudinal biomarker prostate-specific antigen (PSA). Moreover, a careful definition of the estimands of interest, referred to as "predictimands", is required due to the possibility of delayed initiation of treatment after biochemical recurrence. In this study, we utilize the framework of joint longitudinal and survival models to tackle these issues, estimating a model for pre-ST PSA trajectories and risk of metastasis that incorporates the effect of ST, from a dataset of 2075 patients with BCR. We define relevant predictimands for a new patient after BCR under three scenarios: Immediately treated, never treated, and treatment under a dynamic regime, where ST is started when PSA is observed to exceed a pre-specified threshold. We propose a Monte Carlo scheme for computing these predictimands, adapting previous work on dynamic predictions from joint models to account for treatment timing. This methodology is applied to an example patient and validated in a simulation study. This methodology could be adapted to a wide variety of applications requiring counterfactual predictions in the presence of time-varying treatments and biomarkers. Code to implement such analyses is available in the R package JMbayes2.