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Compare the attributable health impacts between two scenarios

Source: R/compare.R
compare.Rd

This function calculates the health impacts between two scenarios (e.g. before and after a intervention in a health impact assessments) using either the delta or pif approach.

Usage

compare(
  output_attribute_scen_1,
  output_attribute_scen_2,
  approach_comparison = "delta"
)

Arguments

output_attribute_scen_1

Scenario 1 as in the output of attribute()

output_attribute_scen_2

Scenario 2 as in the output of attribute()

approach_comparison

String showing the method of comparison. Options: "delta" or "pif".

Value

This function returns a list containing:

1) health_main (tibble) containing the main results from the comparison;

  • impact (numeric column) difference in attributable health burden/impact between scenario 1 and 2

  • impact_scen_1 (numeric column) attributable health impact of scenario 1

  • impact_scen_2 (numeric column) attributable health impact of scenario 2

  • And many more

2) health_detailed (list) containing detailed (and interim) results from the comparison.

  • results_raw (tibble) containing comparison results for each combination of input uncertainty for both scenario 1 and 2

  • results_by_geo_id_micro (tibble) containing comparison results for each geographic unit under analysis (specified in geo_id_micro argument)

  • results_by_geo_id_macro (tibble) containing comparison results for each aggregated geographic unit under analysis (specified in geo_id_macro argument))

  • input_table (list) containing the inputs to each relevant argument for both scenario 1 and 2

  • input_args (list) containing all the argument inputs for both scenario 1 and 2 used in the background

  • scen_1 (tibble) containing results for scenario 1

  • scen_2 (tibble) containing results for scenario 2

Details

Note that the PIF comparison approach assumes same baseline health data for scenario 1 and 2 (e.g. comparison of two scenarios at the same time).

Equations population impact fraction (PIF)

The Population Impact Fraction (PIF) is defined as the proportional change in disease or mortality when exposure to a risk factor is changed (for instance due to an intervention). The most general equation describing this mathematically is an integral form (WHO 2003a, https://www.who.int/publications/i/item/9241546204; WHO 2003b, https://doi.org/10.1186/1478-7954-1-1): $$PIF = \frac{\int RR(x)PE(x)dx - \int RR(x)PE'(x)dx}{\int RR(x)PE(x)dx}$$

Where:

x = exposure level

PE(x) = population distribution of exposure

PE'(x) = alternative population distribution of exposure

RR(x) = relative risk at exposure level compared to the reference level

If the population exposure is described as a categorical rather than continuous exposure, the integrals in equation (5) may be converted to sums, resulting in the following equations for the PIF (WHO 2003a, https://www.who.int/publications/i/item/9241546204; WHO 2003b, https://doi.org/10.1186/1478-7954-1-1): $$PIF = \frac{\sum RR_{i} \times PE_{i} - \sum RR_{i}PE'_{i}}{\sum RR_{i}PE_{i}}$$

Where:

i = is the exposure category (e.g. in bins of 1 \(\mu g/m^3\) PM2.5 or 5 dB noise exposure)

\(PE_i\) = fraction of population in exposure category i

\(PE'_i\) = fraction of population in category i for alternative (ideal) exposure scenario

\(RR_i\) = relative risk for exposure category level i compared to the reference level

Finally, if the exposure is provided as the population weighted mean concentration (PWC), the equation for the PIF is reduced to: $$PIF = \frac{RR_{PWC} - RR_{alt PWC}}{RR_{PWC}}$$

Where:

\(RR_{PWC}\) = relative risk associated with the population weighted mean exposure

\(RR_{PWC}\) = relative risk associated with the population weighted mean for the alternative exposure scenario

Delta comparison approach

With the delta comparison the difference between two scenarios is obtained by subtraction. The delta approach is suited for all comparison cases, and specifically for comparison of a situation now with a situation in the future.

Author

Alberto Castro & Axel Luyten

Examples

# Goal: comparison of two scenarios with delta approach
scenario_A <- attribute_health(
  exp_central = 8.85,   # EXPOSURE 1
  cutoff_central = 5,
  bhd_central = 25000,
  approach_risk = "relative_risk",
  erf_shape = "log_linear",
  rr_central = 1.118,
  rr_increment = 10
)
scenario_B <- attribute_health(
  exp_central = 6,     # EXPOSURE 2
  cutoff_central = 5,
  bhd_central = 25000,
  approach_risk = "relative_risk",
  erf_shape = "log_linear",
  rr_central = 1.118,
  rr_increment = 10
)
results <- compare(
approach_comparison = "delta",
output_attribute_scen_1 = scenario_A,
output_attribute_scen_2 = scenario_B
)
# Inspect the difference, stored in the \code{impact} column
results$health_main |>
  dplyr::select(impact, impact_scen_1, impact_scen_2) |>
  print()
#> # A tibble: 1 × 3
#>   impact impact_scen_1 impact_scen_2
#>    <dbl>         <dbl>         <dbl>
#> 1   774.         1051.          277.

# Goal: comparison of two scenarios with population impact fraction (pif) approach
output_attribute_scen_1 <- attribute_health(
  exp_central = 8.85,   # EXPOSURE 1
  cutoff_central = 5,
  bhd_central = 25000,
  approach_risk = "relative_risk",
  erf_shape = "log_linear",
  rr_central = 1.118, rr_lower = 1.060, rr_upper = 1.179,
  rr_increment = 10
)
output_attribute_scen_2 <- attribute_health(
  exp_central = 6,      # EXPOSURE 2
  cutoff_central = 5,
  bhd_central = 25000,
  approach_risk = "relative_risk",
  erf_shape = "log_linear",
  rr_central = 1.118, rr_lower = 1.060, rr_upper = 1.179,
  rr_increment = 10
)
results <- compare(
  output_attribute_scen_1 = output_attribute_scen_1,
  output_attribute_scen_2 = output_attribute_scen_2,
  approach_comparison = "pif"
)
# Inspect the difference, stored in the impact column
results$health_main$impact
#> [1]  782.2331  411.7377 1146.1450