Three closely related projects were undertaken to improve standard confidence limits for estimating age-specific and age-adjusted cancer incidence and mortality rates. The first project investigated methods of generalizing standard Poisson variance methods to allow extra-Poisson variation in the calculation of confidence limits. We investigated a non- parametric nearest-neighbor estimate of the variance that does not need to rely on any assumed regression model and found it to give an approximately unbiased estimate of the overdispersion parameter for a wide class of true regression models. Once the overdispersion is non- parametrically estimated, the resulting variance estimate provides a more robust confidence interval estimate of the cancer rates. A paper on these methods has been published. The second project investigated confidence intervals for age-adjusted rates under the Poisson assumption. We found that the normal approximations, as well as a recently proposed approximation, do not perform well when the number of counts is small and the adjustment weights vary substantially across the different ages. We propose an approximation which gives exact intervals whenever the age-adjusted rate reduces to a weighted Poisson random variable. For other cases, we compare our approximation to other methods by simulations and show that it has better coverage properties. A paper has been published on this method. The third project creates confidence intervals for risk ratio estimators using similar methods to the second project. A manuscript on this last project is being prepared. Another project is to model an adjustment for the Surveillance, Epidemiology, and End Results (SEER) Program incidence rates. Incidence rates are first reported two years after the diagnosis year. In subsequent years, the rates for that diagnosis year tend to rise slightly due to delays in reporting. We are developing a model to adjust the initial incidence rates that accounts for these reporting delays. These models are being programmed by Information Management Services, Inc. Finally, in collaboration with Syracuse University, we are studying tests for detecting linear changes in the cancer trends, using permutation methods. These tests are similar to the nonparametric bootstrap, except we sample without replacement .
