Extract confidence intervals for the potential impact fraction or the population attributable fraction

Usage

# S3 method for pif_class
confint(x, parm = NULL, level = 0.95, method = c("wald", "percentile"), ...)

Arguments

x

A pif_class object

parm

a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

(double) Confidence level for the uncertainty interval. Defaults to 0.95.

method

(string) either 'wald' (recommended) or 'percentile' for uncertainty intervals based upon the bootstrap's percentile or the Wald-type approximation (see confidence interval section)

...

additional methods to pass to mean() and stats::sd() if wald or stats::quantile() if percentile type intervals

Confidence Intervals

Confidence intervals are estimated via the two methods specified by Arnab (2017) .

1. Wald-type confidence intervals (which are more precise) are of the form: $$\widehat{\text{PIF}} \pm t_{1 - \alpha/2} \sqrt{\widehat{\text{Var}}_{\text{B}}\big[\widehat{\text{PIF}}\big]}$$ where $t_{1 - \alpha/2}$ stands for the percent points at level $1 - \alpha/2$ of Student's t-distribution, and $\widehat{\text{Var}}_{\text{B}}\big[\widehat{\text{PIF}}\big]$ represents the estimated variance (via bootstrap) of the potential impact fraction estimator.

2. Percentile confidence intervals (less precise) are of the form: $$\Big[\widehat{\text{PIF}}_{\text{B},\alpha/2}, \widehat{\text{PIF}}_{\text{B},1-\alpha/2}\Big]$$ where $\widehat{\text{PIF}}_{\text{B},k}$ represents the kth sample quantile from the bootstrap simulation of the potential impact fraction estimator.

Examples

#Example 1
data(ensanut)
options(survey.lonely.psu = "adjust")
design <- survey::svydesign(data = ensanut, ids = ~1, weights = ~weight, strata = ~strata)
rr <- function(X, theta) {
  exp(-2 +
    theta[1] * X[, "age"] + theta[2] * X[, "systolic_blood_pressure"] / 100)
}
cft <- function(X) {
  X[, "systolic_blood_pressure"] <- X[, "systolic_blood_pressure"] - 5
  return(X)
}
pifsim <- pif(design,
  theta = log(c(1.05, 1.38)), rr, cft,
  additional_theta_arguments = c(0.01, 0.03), n_bootstrap_samples = 10,
)
confint(pifsim)
#>     counterfactual   relative_risk potential_impact_fraction
#> 1 Counterfactual_1 Relative_Risk_1               -0.01341996
#> 2 Counterfactual_1 Relative_Risk_1                0.03826853
#>   average_relative_risk average_counterfactual        type
#> 1             -1697.331              -1645.505  Lower 2.5%
#> 2              2686.984               2606.830 Upper 97.5%