A concentration-response function (CRF) turns an air-pollution
concentration into the relative risk (RR) of a health outcome compared
with a counterfactual “clean air” level: an RR of 1.05 means 5% more
deaths (or cases) than at the reference concentration. These are the
first step of any burden estimate; polbrdn and
vrfpol call them for you.
Usage
crfpm25(expo, y = "allcause", refconc = 5.8)
crfno2(expo, y = "allcause", refconc = 10, betaper10 = NULL)Arguments
- expo
Ambient concentration in micrograms per cubic metre, a single non-negative number or a vector of them (one per area, day or person).
- y
PM2.5:
"allcause","ihd"or"stroke"(deaths). NO2:"allcause"and"respiratory"(deaths; Huangfu and Atkinson 2020, RR 1.02 and 1.03 per 10 micrograms per cubic metre) or"chiast"(incident cases, not deaths; Khreis et al. 2017, OR 1.05 per 4 micrograms per cubic metre, scaled to per 10).- refconc
Counterfactual concentration below which no excess risk is assumed. PM2.5 default 5.8, the lower bound of the GBD 2019 theoretical minimum risk exposure level (the WHO 2021 guideline is 5); NO2 default 10, the WHO 2021 guideline.
- betaper10
Optional log relative risk per 10 micrograms per cubic metre (a single finite number, e.g.
log(1.04)) overriding the NO2 outcome table;NULL(the default) uses the table.
Value
A list of class rmbl_crf (plot() draws the curve)
with: rr and logrr, the relative risk and its logarithm
at the exposure (their means over a vector of exposures);
rrlo and rrup, the RR at the published 95%
limits (NA where there are none); refconc;
expconc (the exposure, or the mean of a vector);
pollutant ("PM2.5" or "NO2"); citation
(the source as a string); and extra, a list with the
coefficient (betaper10 and betaper10ci for the
log-linear forms, alpha, gamma, delta for the
IER), form (PM2.5 only), outcome, and for a vector of
exposures rrperunit, the RR at each one.
Details
crfpm25() is log-linear for all-cause mortality with the pooled
cohort estimate of the WHO 2021 guideline review (Chen and Hoek 2020:
RR 1.08, 95% CI 1.06-1.09, per 10 micrograms per cubic metre),
$$RR(z) = \exp(\ln(1.08) (z - z_{cf}) / 10)$$
for \(z > z_{cf}\) and 1 otherwise; for the cause-specific outcomes
(ischaemic heart disease, stroke) it is the Integrated Exposure-Response
curve of Burnett et al. (2014, equation 1),
$$RR(z) = 1 + \alpha (1 - e^{-\gamma (z - z_{cf})^{\delta}}),$$
with the GBD 2013 parameter triples; the IER was fitted per cause and has no
all-cause form. crfno2() is the log-linear function of the WHO 2021
review (Huangfu and Atkinson 2020: RR 1.02, 95% CI 1.01-1.04, per 10
micrograms per cubic metre for all-cause mortality),
$$RR(z) = \exp(\beta (z - z_{cf}) / 10).$$
A vector of exposures gives the mean RR and log-RR. The per-unit
relative risks are then in extra$rrperunit.
Every function has zero excess risk at and below the reference
concentration (\(z \le z_{cf}\) gives RR 1). The published 95%
limits of the log-linear coefficients are carried through the same
curve into rrlo and rrup; the IER parameters come
without an interval, so those are NA for "ihd" and
"stroke", and also when betaper10 is supplied.
Refusals: an unknown y (the message lists the available
ones); an exposure that is missing, infinite, negative, logical or
empty; and a refconc (or betaper10) that is not
a single finite number, or a negative refconc. A supplied
betaper10 may be negative (a protective association) and
replaces the table, in which case y is only a label.
The functions are pure computations: no file, network or option is
used.
References
Chen, J. and Hoek, G. (2020). Long-term exposure to PM and all-cause and cause-specific mortality: a systematic review and meta-analysis. Environment International 143, 105974. Huangfu, P. and Atkinson, R. (2020). Long-term exposure to NO2 and O3 and all-cause and respiratory mortality: a systematic review and meta-analysis. Environment International 144, 105998. Khreis, H. et al. (2017). Exposure to traffic-related air pollution and risk of development of childhood asthma: a systematic review and meta-analysis. Environment International 100, 1-31. GBD 2019 Risk Factors Collaborators (2020). The Lancet 396(10258), 1223-1249. Burnett, R. T. et al. (2014). An integrated risk function for estimating the global burden of disease attributable to ambient fine particulate matter exposure. Environmental Health Perspectives 122(4), 397-403. WHO (2021). Global Air Quality Guidelines.
Examples
# All-cause mortality at an annual PM2.5 of 12 micrograms per cubic metre.
r <- crfpm25(12)
c(rr = r$rr, lower = r$rrlo, upper = r$rrup)
#> rr lower upper
#> 1.048873 1.036787 1.054883
# The cause-specific IER curve for ischaemic heart disease.
crfpm25(12, y = "ihd")$rr
#> [1] 1.553634
# NO2 and respiratory deaths; at or below the reference there is no
# excess risk.
crfno2(25, y = "respiratory")$rr
#> [1] 1.045336
crfno2(8)$rr
#> [1] 1
# A vector of exposures (one per area): the mean RR and each area's RR.
crfpm25(c(5, 12, 20))$extra$rrperunit
#> [1] 1.000000 1.048873 1.115480
# Your own coefficient: RR 1.04 per 10 micrograms per cubic metre.
crfno2(30, betaper10 = log(1.04))$rr
#> [1] 1.0816
# An outcome without a published function is refused.
try(crfpm25(12, y = "asthma"))
#> Error : Unknown outcome 'asthma'. Available: allcause, ihd, stroke