sirex

Indirect standardisation: standardised ratios with shrinkage

R

sirex(x, n, strat, grp, rates = NULL, level = 0.95)

The events observed in each group (an area, a police service) against those expected from stratum rates, the standardised incidence ratio (SIR) with its exact Poisson interval, funnel-plot limits for a ratio of 1 at its expected count, and the ratio shrunk towards the overall one by the empirical Bayes estimate of Marshall (a gamma prior fitted by moments), so that groups with little exposure are not ranked on noise.

Parameters

x

The events: numbers from 0; or a clpre list from clprep().

n

The exposure of each row: positive numbers.

strat

The stratum of each row: labels.

grp

The group of each row: labels.

rates

NULL for the stratum rates pooled over all groups, or the reference rate of each stratum: numbers from 0, named by stratum or in the order of the strata.

level

The confidence level of the intervals: one number strictly between 0 and 1.

Returns

An object of class sirex, a list: sir, a data frame (group, obs, expd, sir, lo, hi, eb the shrunk ratio, shr the share of the prior in it, flo, fhi the funnel limits, out TRUE outside them); prior, the prior’s mean and variance (a variance of 0 when the ratios vary no more than chance, and then every eb is the mean); and level.

References

Marshall, R. J. (1991). Mapping disease and mortality rates using empirical Bayes estimators. Journal of the Royal Statistical Society, Series C, 40(2), 283-294. doi:10.2307/2347593

Examples

d <- data.frame(area = rep(c("N", "S", "E"), each = 2),
                age = rep(c("young", "old"), 3),
                x = c(12, 3, 30, 9, 4, 1),
                n = c(4000, 2000, 8000, 3000, 1500, 900))
sirex(d$x, d$n, d$age, d$area)

Generated from the R help page: sirex in the R reference.