epi.dgamma {epiR} R Documentation

## 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, 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

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")

```

[Package epiR version 2.0.38 Index]