In automobile insurance studies, car accident data are often partially cross-classified by location and agent. One research question of great interest is to link time to the occurrence of car accidents with various factors. An appropriate analysis of such data needs to account for location and agent effects. In this talk, we incorporate partially crossed random effects into Cox proportional hazards models for such data and propose a Poisson modeling approach to model estimation. We predict the random effects using the orthodox best linear unbiased predictor method, and obtain consistent estimators for the regression parameters. This estimating method relies on only the first and second moments of the random effects. Our approach is illustrated with a collection of large automobile insurance data. Another potential application of our approach is to study clinical data partially cross-classified by residential areas and medical service providers.