epi.dgamma {epiR} | R Documentation |
Returns the precision of a [structured] heterogeneity term after one has specified the amount of variation a priori.
epi.dgamma(rr, quantiles = c(0.05, 0.95))
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. |
Returns the precision (the inverse variance) of the heterogeneity term.
Best, NG. WinBUGS 1.3.1 Short Course, Brisbane, November 2000.
## 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")