# pif.confidence.approximate: 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 to the population attributable fraction

## Usage

 ```1 2 3 4 5 6 7``` ```pif.confidence.approximate(Xmean, Xvar, thetahat, thetavar, rr, cft = function(Xmean) { matrix(0, ncol = ncol(as.matrix(Xmean)), nrow = nrow(as.matrix(Xmean))) }, check_thetas = TRUE, check_cft = TRUE, check_xvar = TRUE, check_rr = TRUE, check_integrals = TRUE, check_exposure = TRUE, deriv.method.args = list(), deriv.method = c("Richardson", "complex"), nsim = 1000, confidence = 95, is_paf = FALSE) ```

## Arguments

 `Xmean` Mean value of exposure levels. `Xvar` Variance of exposure levels. `thetahat` Estimator (vector or matrix) of `theta` for the Relative Risk function `rr` `thetavar` Estimator of variance of `thetahat` `rr` Function for Relative Risk which uses parameter `theta`. The order of the parameters shound be `rr(X, theta)`. **Optional** `cft` Function `cft(X)` for counterfactual. Leave empty for the Population Attributable Fraction `paf` where counterfactual is 0 exposure. `check_thetas` Checks that theta parameters are correctly inputed `check_cft` Check if counterfactual function `cft` reduces exposure. `check_xvar` Check if it is covariance matrix. `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. `check_exposure` Check that exposure `X` is positive and numeric `deriv.method.args` `method.args` for `hessian`. `deriv.method` `method` for `hessian`. Don't change this unless you know what you are doing. `nsim` Number of simulations for estimation of variance `confidence` Concidence level (0 to 100) default = `95` % `is_paf` Force evaluation of paf

## Author(s)

Rodrigo Zepeda-Tello rzepeda17@gmail.com

 ``` 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``` ```## Not run: #Example 1: Exponential Relative risk #-------------------------------------------- set.seed(46987) rr <- function(X,theta){exp(X*theta)} cft <- function(X){0.5*X} X <- runif(1000) Xmean <- data.frame(mean(X)) Xvar <- var(X) theta <- 0.2 thetavar <- 0.015 pif.confidence.approximate(Xmean, Xvar, theta, thetavar, rr) pif.confidence.approximate(Xmean, Xvar, theta, thetavar, rr, cft) #Example 2: Multivariate example #-------------------------------------------- X1 <- rnorm(1000,3,.5) X2 <- rnorm(1000,4,1) X <- as.matrix(cbind(X1,X2)) Xmean <- data.frame(t(colMeans(X))) Xvar <- cov(X) theta <- c(0.12, 0.17) thetavar <- matrix(c(0.001, 0.00001, 0.00001, 0.004), byrow = TRUE, nrow = 2) rr <- function(X, theta){exp(theta[1]*X[,1] + theta[2]*X[,2])} pif.confidence.approximate(Xmean, Xvar, theta, thetavar, rr, cft = function(X){cbind(0.5*X[,1],0.4*X[,2])}) ## End(Not run) ```