Statistical methods for analyzing disease incidence and mortality data over time and geographical regions have gained considerable interest in recent years due to increasing concerns of public health, health disparity and legitimate resource allocation. Trend analysis of cancer incidence and mortality rates is essential for subsequent public health investigations. For example, the National Cancer Institute provides software for fitting statistical models to track changes in cancer curves. Currently available models for detecting trend changes over time are designed for a single curve. When multiple curves are available, current methods could be applied multiple times, however, this may not be efficient in the statistical sense. This paper proposes a statistical model that allows concurrent change-point estimation and grouping for multiple curves while maintaining local variabilities. The Bayesian analysis is carried out by eliciting a Dirichlet process prior on the relevant functional space to model change-points. Improper priors are elicited and the resulting posterior is shown to be valid and proper. The age-adjusted lung cancer mortality rates of U.S. states are analyzed to detect change-points and rates of change as well as clusters of states that share similar trends over time. The procedure is also compared with an approach that group states according to a penalized likelihood criterion.