# paf.confidence.one2one: Approximate Confidence Intervals for the Population... In pifpaf: Potential Impact Fraction and Population Attributable Fraction for Cross-Sectional Data

## Description

Function that calculates approximate confidence intervals of the Population Attributable Fraction `paf` considering a one to one Relative Risk `rr` with unidimensional `theta` parameter values

## Usage

 ```1 2 3 4 5 6``` ```paf.confidence.one2one(X, thetahat, rr, thetalow, thetaup, weights = rep(1/nrow(as.matrix(X)), nrow(as.matrix(X))), confidence = 95, confidence_theta = 99, check_thetas = TRUE, deriv.method.args = list(), deriv.method = c("Richardson", "complex"), method = c("empirical", "approximate"), Xvar = var(X), check_exposure = TRUE, check_rr = TRUE, check_integrals = TRUE) ```

## Arguments

 `X` Random sample (`data.frame`) which includes exposure and covariates. `thetahat` Estimative of `theta` for the Relative Risk function `rr` Function for Relative Risk which uses parameter `theta`. The order of the parameters shound be `rr(X, theta)`. **Optional** `thetalow` Lower bound of the confidence interval. `thetaup` Upper bound of the confidence interval. `weights` Survey `weights` for the random sample `X`. `confidence` Confidence level % (default: `95`) `confidence_theta` Confidence level % of `theta` corresponding to the interval [`thetalow`, `thetaup`] (default: `99`%). `check_thetas` Check that thetas are correctly specified `deriv.method.args` `method.args` for `hessian`. `deriv.method` `method` for `hessian`. Don't change this unless you know what you are doing. `method` Either `"empirical"` (default) or `"approximate"`. `Xvar` Variance of exposure levels (for `"approximate"` method). `check_exposure` Check that exposure `X` is positive and numeric `check_rr` Check that Relative Risk function `rr` equals `1` when evaluated at `0` `check_integrals` Check that counterfactual and relative risk's expected values are well defined for this scenario

## Author(s)

Rodrigo Zepeda-Tello [email protected]

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35``` ```#Example 1: Exponential Relative Risk #-------------------------------------------- set.seed(18427) X <- data.frame(rnorm(1000, 3,.7)) thetahat <- 0.4 thetalow <- 0.1 thetaup <- 0.7 paf.confidence.one2one(X, thetahat, function(X, theta){exp(theta*X)}, thetalow, thetaup) #Approximate method: Xmean <- data.frame(mean(X[,1])) Xvar <- var(X[,1]) paf.confidence.one2one(Xmean, thetahat, function(X, theta){exp(theta*X)}, thetalow, thetaup, Xvar = Xvar, method = "approximate") #Example 2: Multivariate example #-------------------------------------------- set.seed(18427) X1 <- rnorm(1000,3,.7) X2 <- rnorm(1000,3,.7) X <- data.frame(X1,X2) thetahat <- c(0.12, 0.03) thetalow <- c(0.05, 0.01) thetaup <- c(0.25, 0.06) rr <- function(X, theta){exp(theta[1]*X[,1] + theta[2]*X[,2])} paf.confidence.one2one(X, thetahat, rr, thetalow, thetaup) #Approximate method: Xmean <- data.frame(t(colMeans(X))) Xvar <- var(X) paf.confidence.one2one(Xmean, thetahat, function(X, theta){exp(theta[1]*X[,1] + theta[2]*X[,2])}, thetalow, thetaup, Xvar = Xvar, method = "approximate") ```