Combining models of health and exposure data: the SAVIAH study”, in Spatial Epidemiology
- N. G. Best, K. Ickstadt, R. L. Wolpert, D. J. Briggs
- Methods and Applications,
The prior choice that each of the three risk categories contribute with equal fractions of the overall disease rate is somewhat arbitrary and may be too influential. We now imagine having prior information on the means for β0, β1 and β2, which happen to correspond to the fractions of disease rates attributed aposteriori to each risk category by the original model. This is achieved by setting τ0 = 15α0 Ȳ , τ1 = 5.4α1Z̄ Ȳ and τ2 = 1.4α2 Ȳ . Of course, the variances are also affected by this change. The local prior variances of β0 and β1 decrease, while the variance of β2 increases. The π and ψ functions are the same as for the original SAVIAH model, as seen in the paper. The local critique plots for this alternative model (SAVIAH2) can be seen in Figure 1 and 2. We see that the marginal posterior distributions of β0 and β1 are now using almost all of their local priors. The posterior samples of β2 are still located only in a small part of its local prior, but not as far out in the tail as before. The marginal posterior distribution of β0 has changed substantially compared to the one for the original SAVIAHmodel, with the posterior mean, median and standard deviation approximately halved from SAVIAH to SAVIAH2. The marginal posterior distributions of β1 and β2 are relatively unchanged (results not shown). The local critique plots for the γj’s are very similar to those seen for SAVIAH in the paper.