Attributable cases

Calculates the number of attributable cases or the number of cases that would be averted under a counterfactual scenario for a given fraction (either paf or pif).

Usage

averted_cases(
  cases,
  pif,
  variance = 0,
  conf_level = 0.95,
  link = "identity",
  link_inv = NULL,
  link_deriv = NULL
)

attributable_cases(
  cases,
  paf,
  variance = 0,
  conf_level = 0.95,
  link = "identity",
  link_inv = NULL,
  link_deriv = NULL
)

Arguments

cases

The overall number of cases in the population.

pif

A potential impact fraction object created by pif, paf, pif_total, pif_ensemble, paf_total or paf_ensemble.

variance

The estimated variance for the cases (default = 0).

conf_level

Confidence level for the confidence interval (default 0.95).

link

Link function such that the case confidence intervals stay within the expected bounds (either log or identity).

link_inv

(Optional). If link is a function then yhe inverse of link. For example if link is logit this should be inv_logit.

link_deriv

Derivative of the link function. The function tries to build it automatically from link using Deriv::Deriv().

paf

A population attributable fraction object created by paf, paf_total or paf_ensemble.

Value

A cases_class object with the attributable cases.

Details

Negative cases are interpreted as cases that would be caused by the intervention.

Formulas

The attributable cases are calculated as: $$ \text{Attributable cases} = \textrm{PAF} \times \textrm{Cases} $$ and the averted cases are respectively: $$ \text{Averted cases} = \textrm{PIF} \times \textrm{Cases} $$

The variance is estimated using the product-variance formula: $$ \textrm{Var}[\text{Averted cases}] = \sigma^2_{\textrm{Cases}} \cdot \big( \textrm{PIF}\big)^2 + \sigma^2_{\textrm{PIF}} \cdot \big( \textrm{Cases} \big)^2 + \sigma^2_{\textrm{PIF}} \cdot \sigma^2_{\textrm{Cases}} $$

See also

pif(), paf()

Examples

frac <- paf(p = 0.499, beta = log(3.6), var_p = 0.002, var_beta = FALSE)
attributable_cases(100, paf = frac)
#> 
#> ── Attributable cases: [deltapif-275541757533686] ──
#> 
#> Attributable cases = 56.473 [95% CI: 52.155 to 60.790]
#> standard_deviation(attributable cases) = 220.300

frac <- pif(p = 0.499, beta = log(3.6), p_cft = 0.1, var_p = 0.002, var_beta = FALSE)
averted_cases(100, pif = frac)
#> 
#> ── Averted cases: [deltapif-00465313804441933] ──
#> 
#> Averted cases = 45.155 [95% CI: 39.715 to 50.596]
#> standard_deviation(averted cases) = 277.578