lognormalEB | R Documentation |
Smooth relative risks from a set of expected and observed number of cases
using a log-Normal model as proposed by Clayton and Kaldor (1987).
There are estimated by
\tilde{\beta}_i =\log((O_i+1/2)/E_i)
in order to prevent taking the logarithm of zero.
If this case, the log-relative risks are assumed be independant and to have a
normal distribution with mean \varphi
and variance
\sigma^2
. Clayton y Kaldor (1987) use the EM algorithm to
develop estimates of these two parameters which are used to compute the
Empirical Bayes estimate of b_i
. The formula is not listed here, but
it can be consulted in Clayton and Kaldor (1987).
lognormalEB(Observed, Expected, maxiter = 20, tol = 1e-05)
Observed |
Vector of observed cases. |
Expected |
Vector of expected cases. |
maxiter |
Maximum number of iterations allowed. |
tol |
Tolerance used to stop the iterative procedure. |
A list of four elements:
n |
Number of regions. |
phi |
Estimate of |
sigma2 |
Estimate of |
smthrr |
Vector of smoothed relative risks. |
Clayton, David and Kaldor, John (1987). Empirical Bayes Estimates of Age-standardized Relative Risks for Use in Disease Mapping. Biometrics 43, 671-681.
library(spdep)
data(nc.sids)
sids<-data.frame(Observed=nc.sids$SID74)
sids<-cbind(sids, Expected=nc.sids$BIR74*sum(nc.sids$SID74)/sum(nc.sids$BIR74))
smth<-lognormalEB(sids$Observed, sids$Expected)
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