# pif.empirical: Point Estimate of the Potential Impact Fraction via the... In pifpaf: Potential Impact Fraction and Population Attributable Fraction for Cross-Sectional Data

## Description

Function that calculates the potential impact fraction `pif` via the empirical method. That is: for a random sample `X`, a relative risk function `rr(X, thetahat)` with parameters `thetahat` the empirical estimator is given by:

PIF = 1 - ∑ rr(cft(X_i); θ)/∑ rr(X_i; θ)

## Usage

 ```1 2 3``` ```pif.empirical(X, thetahat, rr, cft = NA, weights = rep(1/nrow(as.matrix(X)), nrow(as.matrix(X))), check_exposure = TRUE, check_rr = TRUE, check_integrals = TRUE, is_paf = FALSE) ```

## Arguments

 `X` Random sample (`data.frame`) which includes exposure and covariates. or sample mean if approximate method is selected. `thetahat` Estimator (`vector`) 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** `cft` Function `cft(X)` for counterfactual. Leave empty for the Population Attributable Fraction `paf` where counterfactual is 0 exposure. `weights` Normalized survey `weights` for the sample `X`. `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. `is_paf` Boolean forcing evaluation of `paf`.

## Note

The empirical method converges for relative risk `rr` functions that are Lipschitz, convex or concave on `thetahat`. For stranger functions use `pif.kernel`.

## Author(s)

Rodrigo Zepeda-Tello [email protected]

`pif` which is a wrapper for all pif methods (`pif.empirical`, `pif.approximate`, `pif.kernel`).

For estimation of the Population Attributable Fraction see `paf`.

## Examples

 ``` 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``` ```#Example 1: Relative risk given by exponential #-------------------------------------------- set.seed(18427) X <- data.frame(rnorm(100,3,.5)) thetahat <- 0.12 rr <- function(X, theta){exp(theta*X)} pif.empirical(X, thetahat, rr, cft = function(X){ 0.5*X }) #Without counterfactual estimates PAF pif.empirical(X, thetahat, rr) #Example 2: Linear relative risk #-------------------------------------------- pif.empirical(X, thetahat, rr = function(X, theta){theta*X + 1}, cft = function(X){ 0.5*X }) #Example 3: Multivariate relative risk #-------------------------------------------- set.seed(18427) X1 <- rnorm(100,4,1) X2 <- rnorm(100,2,0.4) X <- data.frame(cbind(X1,X2)) thetahat <- c(0.12, 0.03) rr <- function(X, theta){exp(theta[1]*X[,1] + theta[2]*X[,2])} #Creating a counterfactual. As rr requires a bivariate input, cft should #return a two-column matrix cft <- function(X){ cbind(X[,1]/2, 1.1*X[,2]) } pif.empirical(X, thetahat, rr, cft) ```

pifpaf documentation built on Sept. 29, 2017, 1:03 a.m.