A joint frailty model to assess the relationship between time to curative treatment and biochemical recurrence in prostate cancer patients

Conflicting evidence exists regarding the effect of delaying prostate cancer (PCa) treatment on outcomes after curative treatment. Ideally, modelling this would require a joint analysis of the time to treatment initiation and the time to PCa recurrence. However, traditional Cox models are limited to analysing a single time-to-event outcome. In this study, we build a joint frailty model to assess the effect of delayed or expedited primary curative treatment (surgery or radiotherapy) on the risk of biochemical recurrence (BCR). We used HUS (Helsinki Metropolitan Hospital District) data lake for data mining and to categorise PCa patients by Gleason grade group (1-5), treatment, and biochemical recurrence for a final sample size of n=9934 patients (1993–2019). A broader definition of BCR was established considering secondary treatments as an additional indicator of relapse alongside traditional PSA cut-offs. We applied the INLA method for Bayesian inference, utilising the INLAJoint R package, to fit a shared frailty joint survival model. This model was used to analyse the relationship between the time from diagnosis to curative treatment (treatment risk) and the time from diagnosis to biochemical recurrence (relapse risk). Conditional on covariates, including age at diagnosis and Gleason grade group, our joint survival model revealed a significant association γ = -1.32 [-1.50, -1.14] between the risk of treatment and risk of BCR. As an example, regardless of the grade group, patients within the top 5% with the lowest risk of receiving treatment (i.e., the longest time to treatment) exhibited an HR=5.27 [4.28, 6.62] fold (increased) risk of recurrence compared to the average patient. We successfully employed a joint frailty model to simultaneously model the effect of time to curative primary treatment on time to biochemical recurrence. We show that the time to curative treatment is associated with the risk of relapse. Patients of the same age, same diagnostic PSA, and same grade group who are treated early are less likely to develop biochemical recurrence.