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Modifications of BME Analysis 185

Figure 9.7. (a) Death-rate D data available at regions Ri. (b) Continu-
ously distributed death rates, (c) Death-rate values D* assigned at the
centroids of unobserved regions.

causation at the individual level and are generally very difficult to establish.
Most studies of environmental epidemiology are concerned with stochastic
exposure-effect associations at the population level. While stochastic associa-
tions do not usually imply necessary and sufficient causation criteria, they offer
useful insight into a very complicated situation of tremendous public-health
significance (see, e.g., Rothman and Greenland, 1998). Epidemiologic studies
of the determinants of disease in a population involve a variety of techniques,
including visual comparisons of the patterns exhibited by the disease and envi-
ronmental factors and statistical analysis of population exposure-disease occurr
rence across a geographic area (Glattre, 1989; Krewski et al., 1989; Blot and
Mclaughlin, 1995). A useful means for evaluating exposure-effect associations
is the stochastic physico-epidemiologic predictability (PEP) criterion—also
called the "scalar vs. vector prediction (SVP) criterion"—that is expressed by
the following postulate.

POSTULATE 9.1: An exposure-effect association at the population
level is supported if the health-effect predictions obtained from vector