Bayesian approach to cancer-trend analysis using age-stratified Poisson regression models.

Annual Percentage Change (APC) summarizes trends in age-adjusted cancer rates over short time-intervals. This measure implicitly assumes linearity of the log-rates over the intervals in question, which may not be valid, especially for relatively longer time-intervals. An alternative is the Average Annual Percentage Change (AAPC), which computes a weighted average of APC values over intervals where log-rates are piece-wise linear. In this article, we propose a Bayesian approach to calculating APC and AAPC values from age-adjusted cancer rate data. The procedure involves modeling the corresponding counts using age-specific Poisson regression models with a log-link function that contains unknown joinpoints. The slope-changes at the joinpoints are assumed to have a mixture distribution with point mass at zero and the joinpoints are assumed to be uniformly distributed subject to order-restrictions. Additionally, the age-specific intercept parameters are modeled nonparametrically using a Dirichlet process prior. The proposed method can be used to construct Bayesian credible intervals for AAPC using age-adjusted mortality rates. This provides a significant improvement over the currently available frequentist method, where variance calculations are done conditional on the joinpoint locations. Simulation studies are used to demonstrate the success of the method in capturing trend-changes. Finally, the proposed method is illustrated using data on prostate cancer incidence.