Expected counts under indirect standardisation

The count each area would have if it experienced the overall rate in every stratum, given its own composition. Comparing observed against this rather than against a raw rate removes the part of the difference that is explained by who the area holds.

Usage

expected_counts(counts, population, area, strata = NULL)

Arguments

counts

Observed counts.

population

Population at risk, the same length as counts.

area

Area label for each row.

strata

Optional stratum label for each row – an age band, a gender, or their interaction. With strata the standardisation is indirect in the usual sense: the overall stratum-specific rates are applied to each area's own stratum populations.

Value

A data frame with one row per area: observed, population and expected.

Details

Without strata the expected count is just the area's population times the overall rate, which adjusts for size but not for composition. The two are worth distinguishing: a region holding disproportionately many young men will show an excess on the first and may show none on the second, and only the second is evidence about the region.

References

Lawson, A. B. Using R for Bayesian Spatial and Spatio-Temporal Health Modeling. Chapman and Hall/CRC. Chapter 1 sets out the convention used here: the expected counts come from applying the overall population rate to each area, and the standardised incidence ratio is the ratio of count to expected.

Hedderich, J. and Sachs, L. (2020). Applied Statistics: Methods Using R. Springer, on the distinction between indirect standardisation, which applies the reference's stratum-specific rates to the study population, and direct standardisation, which does the reverse.

See also

sir(), eb_rates(), funnel_limits()

Examples

d <- data.frame(
  region = rep(c("North", "South", "East"), each = 2),
  age = rep(c("18 to 24", "25 to 49"), 3),
  n = c(30, 45, 12, 60, 8, 20),
  pop = c(1000, 6000, 900, 9000, 400, 3500)
)

# Adjusting for size only.
expected_counts(d$n, d$pop, d$region)
#>    area observed population expected
#> 1  East       28       3900 32.81250
#> 2 North       75       7000 58.89423
#> 3 South       72       9900 83.29327

# Adjusting for size AND age composition, which is the comparison
# that says something about the region.
expected_counts(d$n, d$pop, d$region, strata = d$age)
#>    area observed population expected
#> 1  East       28       3900 32.34430
#> 2 North       75       7000 62.27967
#> 3 South       72       9900 80.37603