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A hierarchical conditional autoregressive model for colorectal cancer survival data

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In this article, we propose a Bayesian hierarchical linear mixed model to cancer data with geographical characteristics. The spatial effects are captured via a conditional autoregressive (CAR) model. The survival model is introduced to analyze the survival pattern of colorectal cancer based on geographical factors and patients' disease conditions. We propose a special case of the classic Cox model with Weibull hazard as well as a cure rate model. A CAR prior is used to capture the spatial effects, which are determined based on counties the survival subjects belong to. The computation is done via Gibbs sampling. The ratio‐of‐uniforms method is used to sample from a nonstandard conditional posterior density, and the adaptive rejection method is used to sample from log‐concave densities. The model is applied to the Colon & Rectum Cancer incidences in Iowa from the Surveillance, Epidemiology, and End Results (SEER) database. Computation is implemented in Intel Fortran on Linux platform. WIREs Comput Stat 2014, 6:37–44. doi: 10.1002/wics.1283

Conflict of interest: The authors have declared no conflicts of interest for this article.

Acceptance region with the ratio‐of‐uniforms method when sampling α for the cure rate model.
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The survival estimates for stages with different causes of death, the x‐axis t is the survival years, and the y‐axis s is the survival estimates. (a) Alive, (b) dead, CRC cancer, (c) dead, other cancer, and (d) dead, non‐cancer.
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Estimated spatial effects.
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Posterior densities of the factors: (a) Historic stages effect, (b) tumor size, and (c) positive regional nodes.
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