Average Annual Rate of Reduction (AARR)

Computes the average annual rate of reduction of an indicator over time — the standard WHO / UNICEF metric for tracking progress in declining indicators such as maternal, neonatal, and under-five mortality, stunting prevalence, or premature NCD mortality.

Usage

aarr(year, value, method = c("regression", "endpoint"), na.rm = TRUE)

Arguments

year

Numeric vector of years.

value

Numeric vector of indicator values, the same length as year. Values must be positive (the computation is on the log scale); any zero or negative value yields NA_real_ with a warning.

method

Character. "regression" (default) or "endpoint". See Details.

na.rm

Logical. Should pairs with a missing year or value be removed before computation? Default TRUE. When FALSE, any missing element makes the result NA_real_.

Value

A numeric scalar: the average annual rate of reduction as a fraction (0.024 = 2.4% per year). Multiply by 100 to compare with published WHO / UNICEF tables, which print percentages. Returns NA_real_ (with a warning) when fewer than two distinct years remain after NA handling, when any value is zero or negative, or when year or value contains non-finite values.

Details

Two estimation methods are offered:

• "regression" (default; the UNICEF-recommended approach): an ordinary least-squares line is fitted to log(value) against year, and the AARR is 1 - exp(b), where b is the fitted slope. All observations contribute, so the estimate is robust to noise in individual years.

• "endpoint": only the earliest and latest years are used: 1 - (v1 / v0) ^ (1 / (y1 - y0)), where v0 and v1 are the values at the earliest year y0 and the latest year y1. Intermediate observations are ignored. If several observations share the earliest or latest year, their mean is used (but see the note on duplicated years below).

Sign convention. A positive AARR means the indicator is declining (progress, for a mortality-type indicator): 0.024 means an average decline of 2.4% per year. A negative AARR means the indicator is increasing. Note this is the reverse of a growth rate.

Duplicated years usually mean the data still mix several strata — for example both sexes plus male / female in dim1, or several series codes in data cleaned by gho_clean() / sdg_clean(). aarr() warns and proceeds (the regression pools the strata), but you almost always want to filter to a single stratum first.

Relation to published figures. Published WHO / UNICEF tables print the AARR as a percentage (4.4 meaning 4.4% per year); multiply the value returned by this function by 100 to compare. Note also that WHO's Trends in Maternal Mortality reports print a continuous-time rate, -log(v1 / v0) / (y1 - y0) (there called ARR), which agrees closely but not exactly with the discrete AARR computed here — small differences from those tables are expected.

See also

geomean() for ratio-based indicator aggregation.

Examples

# A perfectly exponential 2.4%/yr decline recovers exactly 0.024
years  <- 2000:2015
values <- 100 * (1 - 0.024) ^ (years - 2000)
aarr(years, values)                       # 0.024
#> [1] 0.024
100 * aarr(years, values)                 # 2.4 — as printed in reports
#> [1] 2.4

# Endpoint method uses only the earliest and latest years
aarr(years, values, method = "endpoint")  # also 0.024 here
#> [1] 0.024

# An increasing indicator gives a negative AARR
aarr(2010:2020, 50 * 1.01 ^ (0:10))       # about -0.01
#> [1] -0.01

# Back-of-envelope projection to 2030 at the observed AARR
r <- aarr(years, values)
values[length(values)] * (1 - r) ^ (2030 - 2015)
#> [1] 48.24969