Deaths avoided under a counterfactual exposure reduction

The expected number of deaths (or cases) a year that a given drop in exposure would avoid in a population, from the baseline rate and a log-linear concentration-response coefficient. This is the health-impact function used in regulatory benefit assessments, for questions such as "how many deaths would a 5 microgram cut in PM2.5 avoid in this city?".

Usage

mortality_displaced(
  exposure_delta,
  population,
  baseline_rate,
  beta_per_unit,
  rare_outcome = FALSE,
  high_rate = FALSE
)

Arguments

exposure_delta: Counterfactual reduction in exposure, in the unit of beta_per_unit (positive means the exposure goes down).
population: At-risk population, a non-negative number of persons.
baseline_rate: Baseline rate in cases per person-year (0.008 is 800 per 100,000).
beta_per_unit: Log relative risk per unit of exposure (per unit, not per 10), a single finite number.
rare_outcome, high_rate: TRUE to admit a baseline rate below 1e-5 (one per 100,000) or above 0.1 (10,000 per 100,000) per person-year; without them such a rate is refused, being also what a rate in the wrong unit looks like.

Value

A single number: the expected cases avoided per year (negative for an increase in exposure).

Details

The BenMAP-CE health-impact function (US EPA 2018; Anenberg et al. 2010): $$\Delta Y = y_0 N (1 - e^{-\beta \Delta x}),$$ with $y_0$ the baseline rate per person-year, $N$ the population, $\beta$ the log relative risk per unit of exposure and $\Delta x$ the reduction. A negative exposure_delta (an increase) gives a negative number, the extra cases. A coefficient published per 10 units must be divided by 10 first (for example log(1.08) / 10 for the PM2.5 all-cause RR of 1.08 per 10).

The baseline rate is per person-year, not per 100,000: 800 deaths per 100,000 a year is 0.008. A rate below 1e-5 or above 0.1 is refused unless rare_outcome or high_rate says it is meant, because it is also what a rate in the wrong unit looks like; a rate above 1, or below 1e-11, is always refused. Every input must be a single finite number, and the population and rate non-negative.

References

US EPA (2018). Environmental Benefits Mapping and Analysis Program - Community Edition, user manual. Anenberg, S. C. et al. (2010). An estimate of the global burden of anthropogenic ozone and fine particulate matter on premature human mortality using atmospheric modeling. Environmental Health Perspectives 118(9), 1189-1195.

Examples

# A 10-unit cut, a million people, 800 deaths per 100,000 a year.
mortality_displaced(10, 1e6, 0.008, 0.0039)
#> [1] 305.9943

# The PM2.5 all-cause coefficient is published per 10 micrograms.
mortality_displaced(5, 2.8e6, 0.0075, log(1.08) / 10)
#> [1] 792.7406

# A rare outcome must be declared.
mortality_displaced(5, 1e6, 5e-6, 0.01, rare_outcome = TRUE)
#> [1] 0.2438529

# A rate per 100,000 passed as a rate per person is refused.
try(mortality_displaced(10, 1e6, 800, 0.0039))
#> Error : `baseline_rate` is a rate per person-year, between 0 and 1 (0.008 is 800 per 100,000); 800 looks like a rate per 100,000, which only verify_pollution() takes