epi.dgamma: Estimate the precision of a [structured] heterogeneity term

In epiR: Tools for the Analysis of Epidemiological Data

Estimate the precision of a [structured] heterogeneity term

Description

Returns the precision of a [structured] heterogeneity term after one has specified the amount of variation a priori.

Usage

epi.dgamma(rr, quantiles = c(0.05, 0.95))

Arguments

rr	the lower and upper limits of relative risk, estimated a priori.
quantiles	a vector of length two defining the quantiles of the lower and upper relative risk estimates.

Value

Returns the precision (the inverse variance) of the heterogeneity term.

References

Best, NG. WinBUGS 1.3.1 Short Course, Brisbane Australia, November 2000.

Examples

## EXAMPLE 1:
## Suppose we are expecting the lower 5% and upper 95% confidence interval 
## of relative risk in a data set to be 0.5 and 3.0, respectively. 
## A prior estimate of the precision of the heterogeneity term would be:

tau <- epi.dgamma(rr = c(0.5, 3.0), quantiles = c(0.05, 0.95))
tau

## The estimate of the precision of the heterogeneity term (tau) is 3.37. 
## This can be re-expressed using the gamma distribution. We set the mean of the 
## distribution as tau and specify a large variance (that is, we are not 
## certain about tau).

mean <- tau; var <- 1000
shape <- mean^2 / var
inv.scale <- mean / var

## In WinBUGS the precision of the heterogeneity term is parameterised 
## as tau ~ dgamma(shape, inv.scale). Plot the probability density function
## of tau:

z <- seq(0.01, 10, by = 0.01)
fz <- dgamma(z, shape = shape, scale = 1 / inv.scale)
plot(x = z, y = fz, type = "l", ylab = "Probability density of tau")

epiR documentation built on Sept. 30, 2024, 9:16 a.m.