The results for the MIX model given in Table 3 show a different pattern than those for the BYM or L1-BYM.
Having many heterogeneous clusters as in Simu 3 does not improve the MIX performance as much as that of BYM.
We first discuss rules adapted to the autoregressive BYM and L1-BYM models.
Furthermore, the spread of this distribution is less than the corresponding one for the BYM or L1-BYM models, as noted by Green and Richardson (2002).
For BYM and L1-BYM, the probabilities stay below 10% with no discernible pattern for Simu 1 and Simu 2.
Concerning the detection of truly increased relative risks and sensitivity, we first discuss the results for the BYM and L1-BYM models.
There is no clear pattern of difference between the results for BYM and L1-BYM; overall, the sensitivity is similar.
For Simu 1 and Simu 2 the sensitivity is generally below that of the BYM model and especially when the true relative risk is 1.
For the BYM model, decision rules based on computing the probability that the relative risk is above 1 with a cutoff between 70 and 80% gives a specific rule.
We found no notable difference in performance between the BYM model, which uses a Gaussian distribution, and the L1 BYM version, which uses a heavier-tailed, double-exponential distribution.
Figure B 1 shows three different loss functions representing weighted tradeoffs between the two types of errors: false positive and false negative, associated with the D(c, 1) decision rule for detecting raised-risk areas using the BYM model, plotted against cutoff c.
8) for all the BYM and L1-BYM results presented in this article.