Table 4 summarizes the probabilities of false-positive results for the three models. For BYM and L1-BYM, the probabilities stay below 10% with no discernible pattern for Simu 1 and Simu 2. The error rates are clearly smaller and around 3% for Simu 3. In this scenario, the background relative risk is shifted below 1, so a decision rule with R0 = 1 is, in effect, a more stringent rule than in the case of Simu 1 and Simu 2 where the background relative risks are close to 1. For the MIX model, the false-positive rates are quite low for Simu 1 and Simu 2 and stay mostly below 3%. However, as shown in the last line of Table 4, these rates have greatly increased for the Simu 3 scenario, indicating that the decision rule D(0.05, 1.5) is no longer appropriate in this heterogeneous context. The heterogeneity creates a lot of uncertainty, with some background areas being grouped with nearby high-risk areas; consequently, the rule D(0.05, 1.5) is not stringent (specific) enough. Thus, we have investigated a series of rules D(c, 1.5) for c = 0.1–0.4 for the MIX model in the Simu 3 scenario. As c increases, the probability of false positive decreases; for D(0.4, 1.5), the probability is, on average, around 3% and always below 7% (Table 5).