Funnel-plot control limits

The limits within which an area's ratio would fall, given its expected count, if it were no different from the overall experience. A funnel plot is the alternative to a league table: it shows directly that a small area's ratio can wander far from one without meaning anything.

Usage

funnel_limits(expected, target = 1, levels = c(0.95, 0.998))

Arguments

expected

Expected counts to compute limits at.

target

The ratio the limits are centred on. One is the overall experience.

levels

Two-sided coverage levels for the limit pairs.

Value

A data frame of expected, level, lower and upper on the ratio scale.

Details

The limits are exact Poisson quantiles divided by the expected count, so they are the discrete counterpart of the usual normal funnel and stay correct at the small expected counts where the normal version goes below zero.

References

Advanced Statistics in Criminology and Criminal Justice discusses the funnel plot as the display of the relationship between an estimate and the sample size behind it.

Lawson, A. B. Using R for Bayesian Spatial and Spatio-Temporal Health Modeling. Chapman and Hall/CRC, on the Poisson counts these limits are built from.

See also

sir(), eb_rates()

Examples

# The funnel narrows as the expected count grows, which is the whole
# point: a ratio of 2 means nothing at an expected count of 2 and a
# great deal at an expected count of 200.
funnel_limits(c(2, 20, 200))
#>   expected level lower upper
#> 1        2 0.950 0.000 2.500
#> 2       20 0.950 0.600 1.450
#> 3      200 0.950 0.865 1.140
#> 4        2 0.998 0.000 4.000
#> 5       20 0.998 0.400 1.750
#> 6      200 0.998 0.790 1.225