Massive data sets with complex spatiotemporal structures are common in environmental studies. In order to account for such spatiotemporal structures, spatially and temporally correlated random effects are often incorporated into generalized linear models for such data. The estimation of these models often poses theoretical and computational challenges. We propose an orthodox best linear unbiased predictor (BLUP) approach to these models. Our approach is illustrated with application to Ohio lung cancer data where the annual lung cancer deaths for 88 counties were obtained from 1968-1988. With estimated spatial and temporal random effects, we will also discuss the identification of high/low risk areas, spatial clustering as well as temporal trend. An adaptation of this approach to analysing spatially correlated survival data will also be illustrated with application to American Cancer Society data.