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Get the relative risk of an exposure level

Source: R/get_risk.R
get_risk.Rd

This function re-scales the relative risk from the increment value in the epidemiological study (e.g. for PM2.5 10 or 5 ug/m3) to the actual population exposure

Usage

get_risk(
  erf_shape = NULL,
  rr = NULL,
  rr_increment = NULL,
  erf_eq = NULL,
  cutoff = 0,
  exp
)

Arguments

erf_shape

String value specifying the exposure-response function shape to be assumed. Options (no default): "linear", log_linear", "linear_log", "log_log". Only applicable in RR pathways; not required if erf_eq_... argument(s) already specified.

rr

Numeric value or numeric vector specifying the relative risk estimate(s) and (optionally) the corresponding lower and upper 95% confidence interval bounds. Not required if the erf_eq argument is already specified.

rr_increment

Numeric value specifying the exposure increment for which the provided relative risk is valid. See Details for more info. Only applicable in RR pathways; not required if erf_eq_... argument(s) already specified.

erf_eq

String or function specifying the exposure-response function and (optionally) the corresponding lower and upper 95% confidence interval functions. See Details and Examples sections below.

cutoff

Numeric value specifying the exposure cut-off value (i.e. the exposure level below which no health effects occur) and (optionally) the corresponding lower and upper 95% confidence interval bounds.

exp

Numeric value or numeric vector specifying the exposure level(s) to the environmental stressor (e.g. annual population-weighted mean) and (optionally) the corresponding lower and upper bound of the 95% confidence interval.

Value

This function returns the numeric risk value(s) at the specified exposure level(s), referred to as rr_at_exp in the relative risk equations above.

Details

Function arguments

erf_eq

If the function is provided as string, it can only contain the variable c (exposure), e.g. "3+c+c^2". If the function is provided as a function, the object must be of the class function. If only the values of the x-axis (exposure) and y axis (relative risk) of the dots in the exposure-response function are available, a cubic spline natural interpolation can be assumed to get the function using, e.g., stats::splinefun(x, y, method="natural")

Equations for scaling of relative risk

linear ERF $$rr\_at\_exp = 1 + \frac{(rr - 1)}{rr\_increment} \cdot (exp - cutoff)$$

log-linear ERF

$$rr\_at\_exp = e^{\frac{\log(\mathrm{rr})}{\mathrm{rr\_increment}} \cdot (\mathrm{exp} - \mathrm{cutoff})}$$

log-log ERF

$$rr\_at\_exp = (\frac{exp + 1}{cutoff + 1})^{\frac{\log(\mathrm{rr})}{\log(\mathrm{rr\_increment + cutoff + 1}) - \log(cutoff + 1)}}$$

linear-log ERF

$$rr\_at\_exp = 1 + \frac{\log(\mathrm{rr - 1})}{\log(\mathrm{rr\_increment + cutoff + 1}) - \log(cutoff + 1)} \cdot \frac{\log(exp + 1)}{\log(cutoff + 1)}$$

Sources

For the log-linear, log-log and linear-log exposure-response function equations see Pozzer et al. 2022 (https://doi.org/10.1029/2022GH000711).

Author

Alberto Castro & Axel Luyten

Examples

# Goal: scale relative risk to observed exposure level
get_risk(
  rr = 1.05,
  rr_increment = 10,
  erf_shape = "linear",
  exp = 10,
  cutoff = 5
)
#> [1] 1.025

# Goal: determine the absolute risk for high annoyance at specific noise exposure levels
get_risk(
  erf_eq = "78.9270-3.1162*c+0.0342*c^2",
  exp = c(57.5, 62.5, 67.5, 72.5, 77.5)
)
#> [1] 12.81925 17.75825 24.40725 32.76625 42.83525

# Goal: attribute COPD cases to air pollution exposure by applying a user-defined exposure response function,
# e.g. MR-BRT curves from Global Burden of Disease study.
get_risk(
  erf_eq = splinefun(
    x = c(0, 5, 10, 15, 20, 25, 30, 50, 70, 90, 110),
    y = c(1.00, 1.04, 1.08, 1.12, 1.16, 1.20, 1.23, 1.35, 1.45, 1.53, 1.60),
    method = "natural"),
  exp = c(8, 9, 10)
)
#> [1] 1.063984 1.071987 1.080000