Standardised incidence ratio, with an exact interval

The ratio of observed to expected, with the exact Poisson interval for it. A ratio of one is the overall experience; above one is an excess.

Usage

sir(observed, expected, area = NULL, conf_level = 0.95)

Arguments

observed: Observed counts.
expected: Expected counts, from expected_counts().
area: Optional labels.
conf_level: Confidence level.

Value

A data frame with observed, expected, sir, lower, upper and excess – whether the interval excludes one.

Details

The interval is the exact Poisson one, from the relation between the Poisson and gamma distributions, and so is identical to stats::poisson.test 's. It is the interval to use here because the counts that matter are small: a normal approximation on an observed count of three is not an interval, it is a decoration.

References

Lawson, A. B. Using R for Bayesian Spatial and Spatio-Temporal Health Modeling. Chapman and Hall/CRC, Chapter 1.

Examples

sir(observed = c(30, 12, 3), expected = c(20, 14, 5),
    area = c("North", "South", "East"))
#>    area observed expected       sir     lower    upper excess
#> 1 North       30       20 1.5000000 1.0120437 2.141343   TRUE
#> 2 South       12       14 0.8571429 0.4428982 1.497256  FALSE
#> 3  East        3        5 0.6000000 0.1237344 1.753455  FALSE

# An observed count of three carries almost no information, and the
# interval says so rather than hiding it.
sir(3, 5)
#>   observed expected sir     lower    upper excess
#> 1        3        5 0.6 0.1237344 1.753455  FALSE