Biomarker series can indicate disease progression and predict clinical endpoints. When a treatment is prescribed depending on the biomarker, confounding by indication might be introduced if the treatment modifies the marker profile and risk of failure.

The two-stage model fitted within a Bayesian Markov Chain Monte Carlo framework is particularly flexible to account for such data. Prostate-specific antigens in prostate cancer patients treated with external beam radiation therapy can be monitored. In the presence of rising prostate-specific antigens after external beam radiation therapy, salvage hormone therapy can be prescribed to reduce both the prostate-specific antigens concentration and the risk of clinical failure, an illustration of confounding by indication. The prognostic value of hormone therapy and prostate-specific antigens trajectory on the risk of failure based on a two-stage model within a Bayesian framework to assess the role of the prostate-specific antigens profile on clinical failure while accounting for a secondary treatment prescribed by indication. the aim of this research is to model prostate specific antigens using a hierarchical piecewise linear trajectory with a random changepoint. Residual prostate-specific antigens variability can be expressed as a function of prostate-specific antigens concentration. Covariates in the survival model can include : hormone therapy, baseline characteristics, and individual predictions of the prostate-specific antigens nadir and timing and prostate-specific antigens slopes before and after the nadir as provided by the longitudinal process.

The two-stage modeling approach allows estimation of the regression coefficients in a time-dependent Cox model, while addressing the limitations with the knowledge of the true marker trajectory. In the first stage, the longitudinal process is modeled using a repeated measures component model, such as a random effects model. In the second stage, estimated characteristics of the longitudinal marker trajectory, such as slopes, are included as covariates in a survival model to assess their prognostic value.

Our aim was to highlight the flexibility of a two-stage model fitted within a Bayesian Markov Chain Monte Carlo (MCMC) framework. We applied this model to assess the prognostic value of the prostate-specific antigens (PSA) profile (level and timing of the nadir; pre- and post-nadir slopes) as well as salvage hormonal treatment (HT) on the risk of clinical failure following external beam radiation therapy (EBRT) in the presence of confounding by indication. We first present the longitudinal hierarchical PSA model that we developed earlier. This model was particularly flexible since it allowed us to account for the presence of a random changepoint as well as the modeling of the residual variability as a function of the PSA concentration. We next extend the longitudinal model to a two-stage model by using estimated parameters of the longitudinal process as covariates in a Cox proportional hazards model to assess prognostic factors of clinical failure including baseline characteristics, PSA trajectory, and HT.

Inclusion Criteria:

• clinically localized prostate cancer
• Clinical stage T1 to T4
• Node and metastasis negative
• Treated with external beam radiation therapy (RT).

Exclusion Criteria:

• Patients with baseline or planned hormonotherapy

Dataset of 2384 men included in three cohorts: University of Michigan, Ann Arbor, MI, USA (UM); Radiation Therapy Oncology Group (RTOG 9406); and William Beaumont Hospital, Detroit, MI, USA.

up to 10 years following initiation of radiotherapy

This study is a retrospective analysis focussing on the association between the longitudinal PSA trajectory and the time to clinical failure. As such, we did not report on safety.

Serious and Other (Not Including Serious) Adverse Events were not monitored/assessed.