Research Article Received 4 June 2009, Accepted 2 August 2010 Published online 14 September 2010 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/sim.4077 Bayesian approach to cancer-trend analysis using age-stratified Poisson regression models Pulak Ghosh, a Kaushik Ghosh b ∗ † and Ram C. Tiwari c 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. Copyright © 2010 John Wiley & Sons, Ltd. Keywords: cancer mortality; cancer incidence; cancer surveillance; joinpoint regression; SEER program; Dirichlet process prior 1. Introduction Cancer has long been, and continues to be a major health concern in the United States, contributing to the second-highest number of deaths, exceeded only by heart disease. The American Cancer Society (ACS) in its annual publication Cancer Facts and Figures, 2008 (available online at http://www.cancer.org) reports that in 2008, about 1.4 million new cancer cases are expected to be diagnosed, and approximately 565 650 persons are expected to die of cancer in the United States. Many public and private agencies dealing with cancer and related issues depend on the rates of cancer deaths or new cancer cases as an estimate of cancer burden for planning and resource allocation. Monitoring the trends in various cancer rates is a significant aspect of cancer surveillance studies. For example, in Cancer Facts & Figures, 2008, ACS reports that for a number of cancer sites (such as breast, stomach, colon and rectum, lung and bronchus, leukemia, etc.), the age-adjusted cancer mortality rates have been decreasing over the recent years. The Surveillance, Epidemiology, and End Results (SEER) Program of the National Cancer Institute (NCI) periodically publishes similar reports on cancer trends, which can be found at http://seer.cancer.gov/csr. SEER is the most authoritative and comprehensive source of information about cancer incidence in the United States—currently it collects and publishes cancer incidence data from population-based cancer registries covering approximately over a quarter of the entire US population. The US cancer mortality data are available from the National Center for Health Statistics (NCHS) and can also be obtained from the SEER program. As part of the surveillance aspect of its program, SEER routinely monitors and compares trends in cancer mortality and incidence rates across geographic regions or over different time periods. The data are analyzed by the SEER*Stat software (available at http://seer.cancer.gov/seerstat) maintained by the NCI. Indeed, this surveillance task has important a Department of Quantitative Methods and Information Systems, Indian Institute of Management, Bannerghatta Road, Bangalore 560076, India b Department of Mathematical Sciences, University of Nevada Las Vegas, Las Vegas, NV 89154-4020, U.S.A. c Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug Administration, 10903 New Hampshire Avenue, Silver Spring, MD 20993-0002, U.S.A. ∗ Correspondence to: Kaushik Ghosh, Department of Mathematical Sciences, University of Nevada Las Vegas, 4505 Maryland Parkway, Box 454020, Las Vegas, NV 89154-4020, U.S.A. † E-mail: kaushik.ghosh@unlv.edu Copyright © 2010 John Wiley & Sons, Ltd. Statist. Med. 2011, 30 127–139 127