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Directly Age-Standardized Rate

Source: R/age_standardize.R
age_standardize.Rd

Computes a directly age-standardized rate: the rate that would be observed in a population with the age structure of a chosen standard. Direct standardization removes the effect of differing age distributions, so rates from different populations (countries, sexes, time periods) become comparable.

Usage

age_standardize(
  count,
  pop,
  stdpop,
  per = 1e+05,
  ci = FALSE,
  conf_level = 0.95,
  na.rm = TRUE
)

Arguments

count

Numeric vector of event counts (e.g. deaths) per age group.

pop

Numeric vector of population denominators per age group, the same length as count. Must be positive.

stdpop

Numeric vector of standard-population weights per age group, the same length as count. Relative values only; normalized internally. Pass who_std_pop$std_million (or $weight) for the WHO World Standard, aggregated to your age groups.

per

Numeric. The rate is expressed per this many people. Default 1e5 (per 100,000). Use 1 for a proportion, 1000 for per-mille.

ci

Logical. Return a confidence interval (Fay-Feuer gamma method)? Default FALSE.

conf_level

Numeric in (0, 1). Confidence level for the interval. Default 0.95.

na.rm

Logical. Drop age groups with a missing count, pop, or stdpop before computing? Default TRUE. When FALSE, any missing value makes the result NA.

Value

When ci = FALSE, a numeric scalar: the standardized rate per per. When ci = TRUE, a named numeric vector with elements rate, lower, and upper, all per per. Returns NA (scalar or in each element) with a warning when no age groups remain after NA handling.

Details

The age-specific rate in group \(i\) is \(r_i = d_i / n_i\) (count / pop). With standard weights \(w_i\) (from stdpop, normalized to sum to 1), the standardized rate is $$R = \left(\sum_i w_i r_i\right) \times \mathrm{per}.$$ The three vectors count, pop, and stdpop must be aligned: element \(i\) of each refers to the same age group, in the same order. stdpop may be supplied as counts, a standard million, or percentages — only its relative values matter, because it is normalized internally. The built-in who_std_pop dataset supplies the WHO World Standard.

Confidence interval. With ci = TRUE, a confidence interval is returned using the gamma-distribution method of Fay and Feuer (1997), which has good coverage even when rates are based on small numbers of events. This is the method used by, for example, epitools. The interval requires the age-specific event counts, so it is only available when count and pop are supplied (not a pre-computed rate).

References

Ahmad OB, Boschi-Pinto C, Lopez AD, Murray CJL, Lozano R, Inoue M (2001). Age standardization of rates: a new WHO standard. GPE Discussion Paper Series No. 31. World Health Organization.

Fay MP, Feuer EJ (1997). Confidence intervals for directly standardized rates: a method based on the gamma distribution. Statistics in Medicine 16(7):791-801.

See also

who_std_pop for the WHO World Standard Population; geomean() for ratio-based aggregation.

Examples

# Deaths and population in five age groups, standardized to the WHO
# World Standard collapsed to the same five groups.
deaths <- c(20, 15, 40, 90, 220)
pop    <- c(12000, 11000, 9000, 7000, 3000)
w      <- c(0.35, 0.25, 0.20, 0.12, 0.08)   # standard weights

age_standardize(deaths, pop, w)             # per 100,000
#> [1] 922.2655
age_standardize(deaths, pop, w, per = 1000) # per 1,000
#> [1] 9.222655

# With a 95% confidence interval
age_standardize(deaths, pop, w, ci = TRUE)
#>      rate     lower     upper 
#>  922.2655  831.1569 1021.1368 

# Using the bundled WHO World Standard for standard five-year groups.
# Aggregate who_std_pop to whatever age groups your data use, keeping
# the same order, then pass the weights:
std5 <- who_std_pop$std_million[1:5]
age_standardize(deaths, pop, std5)
#> [1] 1812.645