A two-stage model in a Bayesian framework to estimate a survival endpoint in the presence of confounding by indication

Background 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. Objective Our aim was to highlight the flexibility of a two-stage model fitted within a Bayesian Markov Chain Monte Carlo framework. For this purpose, we monitored the prostate-specific antigens in prostate cancer patients treated with external beam radiation therapy. 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. We focused on the assessment of the prognostic value of hormone therapy and prostate-specific antigens trajectory on the risk of failure. Methods We used 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. We modeled prostate-specific antigens using a hierarchical piecewise linear trajectory with a random changepoint. Residual prostate-specific antigens variability was expressed as a function of prostate-specific antigens concentration. Covariates in the survival model included 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. Results We showed positive associations between an increased prostate-specific antigens nadir, an earlier changepoint and a steeper post-nadir slope with an increased risk of failure. Importantly, we highlighted a significant benefit of hormone therapy, an effect that was not observed when the prostate-specific antigens trajectory was not accounted for in the survival model. Conclusion Our modeling strategy was particularly flexible and accounted for multiple complex features of longitudinal and survival data, including the presence of a random changepoint and a time-dependent covariate.