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An important statistical task in disease mapping problems is to identify divergent regions with unusually high or low risk of disease. Leave‐one‐out cross‐validatory (LOOCV) model assessment is the gold standard for estimating predictive p‐values that can flag such divergent regions. However, actual LOOCV is time‐consuming because one needs to rerun a Markov chain Monte Carlo analysis for each posterior distribution in which an observation is held out as a test case. This paper introduces a new method, called integrated importance sampling (iIS), for estimating LOOCV predictive p‐values with only Markov chain samples drawn from the posterior based on a full data set. The key step in iIS is that we integrate away the latent variables associated the test observation with respect to their conditional distribution without reference to the actual observation. By following the general theory for importance sampling …