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.
