A Bayesian semi-parametric model is proposed to capture the interaction among demographic effects (age and gender), spatial effects (county) and temporal effects of colorectal cancer incidences simultaneously. In particular, an extension of multivariate conditionally autoregressive (CAR) processes to a partially informative Gaussian demographic spatial temporal CAR (DSTCAR) process for a spatial–temporal setting is proposed. The precision matrix of the Gaussian DSTCAR process is the Kronecker product of several components. The spatial component is modelled with a CAR prior. A pth order intrinsic autoregressive prior (IAR(p)) is implemented for the temporal component to estimate a smoothed and non-parametric temporal trend. The demographic component is modelled with a Wishart prior. Data analysis shows significant spatial correlation only exists in the age group of 50–59. Males and females in their 50s and 60s show fairly strong correlation. The hypothesis testing based on Bayes factor suggests that gender correlation cannot be ignored in this model. Copyright © 2006 John Wiley & Sons, Ltd.