Geography Reference
In-Depth Information
Among the most common rates for disease mapping are the incidence, preva-
lence and standardized mortality (morbidity) ratio (SMR). Prevalence in epidemi-
ology is the total number of cases of a given disease or disorder in a specified
population at a specified time regardless of when the illness began (Earickson
2009 ). Thus, the prevalence of salmonella in the Czech Republic since 2010
includes the cumulative number of citizens suffering from the disease since that
year. On the other hand, prevalence is often confused with incidence , which refers
to only new cases diagnosed during a particular year. SMR is the ratio of the number
of deaths (or cases) observed in the study group or population to the number that
would be expected if the study population had the same specific rates as the
standard population, multiplied by 100 and usually expressed as a percentage
(Last and Abramson 2001 ). SMR also represents an estimate of the relative risk
(Bivand et al. 2008 ). SMRs should not be directly compared as they are not based
on the same standard population, but comparisons of SMRs between geographical
areas will be misleading only if the age and sex structure of the populations are
extremely disparate, which very rarely occurs in practice (Goldman and Brender
2000 ; Jarup 2004 ).
Bayesian Mapping and Smoothing
Presenting disease rates in area units as choropleth maps can inadvertently provide
misleading information. This fact is well known mainly in the case of small-area
studies that introduce an extra source of variability into the map because of random
variation. Typically, sparsely populated areas with few (or zero) cases can generate
extreme values of the SMR (and also prevalence), as the variance of the SMR is
inversely related to the expected number of cases, and small populations have large
variability in the estimated rates (Elliott and Wartenberg 2004 ), which is why risk
estimates and other rates are rather unstable.
Bayesian methods provide a solution for this kind of bias. They use probability
models to obtain smoothed estimates consisting of a compromise between the
observed rate for each region and an estimate from a larger collection of cases
and persons at risk (e.g., the rate observed over the entire study area or over a
collection of neighbouring regions) (Waller and Gotway 2004 ). The basic principle
of Bayesian methods is that uncertain data can be strengthened by combining them
with prior information (Pfeiffer et al. 2008 ). In the case of empirical Bayes
estimation of spatially-varying disease risk, the posterior risk can be estimated
from a weighted combination of the local risk (also called the likelihood) and the
risk in surrounding areas, the latter representing the prior information (Clayton and
Bernardinelli 1996 ). Empirical Bayes calculations of disease risk come from the
following formula (Bailey and Gatrell 1995 ):
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