R/paf.R
In INSP-RH/pif: Potential Impact Fraction and Population Attributable Fraction for Cross-Sectional Data
#' @title Population Attributable Fraction
#'
#' @description Function for estimating the Population Attributable Fraction
#' \code{paf} from a cross-sectional sample of the exposure \code{X} with a
#' known Relative Risk function \code{rr} with meta-analytical parameter \code{theta}, where
#' the Population Attributable Fraction is given by: \deqn{ PAF =
#' \frac{E_X\left[rr(X;\theta)\right]-1}{E_X\left[rr(X;\theta)\right]} .}{ PAF
#' = mean(rr(X; theta) - 1)/mean(rr(X; theta)).}
#'
#' @param X Random sample (\code{data.frame}) which includes exposure
#' and covariates or sample \code{mean} if \code{"approximate"} method is
#' selected.
#'
#' @param thetahat Asymptotically consistent or Fisher consistent
#' estimator (\code{vector}) of \code{theta} for the Relative
#' Risk function \code{rr}.
#'
#' @param rr \code{function} for Relative Risk which uses parameter
#' \code{theta}. The order of the parameters should be \code{rr(X, theta)}.
#'
#'
#' \strong{**Optional**}
#'
#' @param weights Normalized survey \code{weights} for the sample \code{X}.
#'
#' @param method Either \code{"empirical"} (default), \code{"kernel"} or
#' \code{"approximate"}. For details on estimation methods see
#' \code{\link{pif}}.
#'
#' @param Xvar Variance of exposure levels (for \code{"approximate"}
#' method).
#'
#' @param deriv.method.args \code{method.args} for
#' \code{\link[numDeriv]{hessian}} (for \code{"approximate"} method).
#'
#' @param deriv.method \code{method} for \code{\link[numDeriv]{hessian}}.
#' Don't change this unless you know what you are doing (for
#' \code{"approximate"} method).
#'
#' @param ktype \code{kernel} type: \code{"gaussian"},
#' \code{"epanechnikov"}, \code{"rectangular"}, \code{"triangular"},
#' \code{"biweight"}, \code{"cosine"}, \code{"optcosine"} (for \code{"kernel"}
#' method). Additional information on kernels in \code{\link[stats]{density}}.
#'
#' @param bw Smoothing bandwith parameter (for
#' \code{"kernel"} method) from \code{\link[stats]{density}}. Default
#' \code{"SJ"}.
#'
#' @param adjust Adjust bandwith parameter (for \code{"kernel"}
#' method) from \code{\link[stats]{density}}.
#'
#' @param n Number of equally spaced points at which the density (for
#' \code{"kernel"} method) is to be estimated (see
#' \code{\link[stats]{density}}).
#'
#' @param check_integrals \code{boolean} Check that counterfactual \code{cft}
#' and relative risk's \code{rr} expected values are well defined for this
#' scenario.
#'
#' @param check_exposure \code{boolean} Check that exposure \code{X} is
#' positive and numeric.
#'
#' @param check_rr \code{boolean} Check that Relative Risk function
#' \code{rr} equals \code{1} when evaluated at \code{0}.
#'
#' @return paf Estimate of Population Attributable Fraction.
#'
#' @author Rodrigo Zepeda-Tello \email{rzepeda17@gmail.com}
#' @author Dalia Camacho-García-Formentí \email{daliaf172@gmail.com}
#'
#' @note \code{"approximate"} method should be the last choice. In practice
#' \code{"empirical"} should be preferred as convergence is faster in
#' simulations than \code{"kernel"}. In addition, the scope
#' of \code{"kernel"} is limited as it does not work with multivariate
#' exposures \code{X}.
#'
#' @note \code{\link{paf}} is a wrapper for \code{\link{pif}} with
#' counterfactual of theoretical minimum risk exposure (\code{rr} = 1).
#'
#' @note For more information on kernels see \code{\link[stats]{density}}.
#'
#' @note Do not use the \code{$} operator when using \code{"approximate"}
#' \code{method}.
#'
#' @details The Relative Risk function \code{rr} and counterfactual \code{cft}
#' should consider \code{X} to be a \code{data.frame}. Each row of
#' \code{X} is an "individual" and each column a variable (exposure or covariate)
#' of said individual.
#'
#' @examples
#'
#' #Example 1: Exponential Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rnorm(100,3,1))
#' thetahat <- 0.12
#' rr <- function(X, theta){exp(theta*X)}
#'
#' #Using the empirical method
#' paf(X, thetahat, rr)
#'
#' #Same example with kernel method
#' paf(X, thetahat, rr, method = "kernel")
#'
#' #Same example with approximate method
#' Xmean <- data.frame(Exposure = mean(X[,"Exposure"]))
#' Xvar <- var(X[,"Exposure"])
#' paf(Xmean, thetahat, rr, method = "approximate", Xvar = Xvar)
#'
#' #Additional options for approximate:
#' paf(Xmean, thetahat, rr, method = "approximate", Xvar = Xvar,
#' deriv.method = "Richardson", deriv.method.args = list(eps=1e-3, d=0.1))
#'
#' #Example 2: Linear Relative Risk with weighted sample
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rbeta(100,3,1))
#' weights <- runif(100)
#' normalized_weights <- weights/sum(weights)
#' thetahat <- 0.12
#' rr <- function(X, theta){theta*X^2 + 1}
#' paf(X, thetahat, rr, weights = normalized_weights)
#'
#'
#' #Additional options for kernel:
#' paf(X, thetahat, rr, weights = normalized_weights,
#' method = "kernel", ktype = "cosine", bw = "nrd0")
#'
#'
#' #Example 3: Multivariate Linear Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X1 <- rnorm(100,4,1)
#' X2 <- rnorm(100,2,0.4)
#' X <- data.frame(Exposure = X1, Covariate = X2)
#' thetahat <- c(0.12, 0.03)
#'
#' #When creating relative risks avoid using the $ operator
#' #as it doesn't work under approximate method
#' rr_not <- function(X, theta){
#' exp(theta[1]*X$Exposure + theta[2]*X$Covariate)
#' }
#' rr_better <- function(X, theta){
#' exp(theta[1]*X[,"Exposure"] + theta[2]*X[,"Covariate"])
#' }
#'
#' #For the empirical method it makes no difference:
#' paf(X, thetahat, rr_better)
#' paf(X, thetahat, rr_not)
#'
#'
#' #But the approximate method crashes due to operator
#' Xmean <- data.frame(Exposure = mean(X[,"Exposure"]),
#' Covariate = mean(X[,"Covariate"]))
#' Xvar <- var(X)
#'
#' paf(Xmean, thetahat, rr_better, method = "approximate", Xvar = Xvar)
#' \dontrun{
#' #Warning: $ operator in rr definitions don't work in approximate
#' paf(Xmean, thetahat, rr_not, method = "approximate", Xvar = Xvar)
#' }
#'
#'
#' \dontrun{
#' #Warning: Multivariate cases cannot be evaluated with kernel method
#' paf(X, thetahat, rr, method = "kernel")
#' }
#'
#' #Example 4: Categorical Relative Risk & Exposure
#' #--------------------------------------------
#' set.seed(18427)
#' mysample <- sample(c("Normal","Overweight","Obese"), 100,
#' replace = TRUE, prob = c(0.4, 0.1, 0.5))
#' X <- data.frame(Exposure = mysample)
#'
#' thetahat <- c(1, 1.2, 1.5)
#'
#' #Categorical relative risk function
#' rr <- function(X, theta){
#'
#' #Create return vector with default risk of 1
#' r_risk <- rep(1, nrow(X))
#'
#' #Assign categorical relative risk
#' r_risk[which(X[,"Exposure"] == "Normal")] <- thetahat[1]
#' r_risk[which(X[,"Exposure"] == "Overweight")] <- thetahat[2]
#' r_risk[which(X[,"Exposure"] == "Obese")] <- thetahat[3]
#'
#' return(r_risk)
#' }
#'
#' paf(X, thetahat, rr, check_rr = FALSE)
#'
#' #Example 5: Continuous Exposure and Categorical Relative Risk
#' #------------------------------------------------------------------
#' set.seed(18427)
#'
#' #Assume we have BMI from a sample
#' BMI <- data.frame(Exposure = rlnorm(100, 3.1, sdlog = 0.1))
#'
#' #Theoretical minimum risk exposure is at 20kg/m^2 in borderline "Normal" category
#' BMI_adjusted <- BMI - 20
#'
#' thetahat <- c(Malnourished = 2.2, Normal = 1, Overweight = 1.8,
#' Obese = 2.5)
#' rr <- function(X, theta){
#'
#' #Create return vector with default risk of 1
#' r_risk <- rep(1, nrow(X))
#'
#' #Assign categorical relative risk
#' r_risk[which(X[,"Exposure"] < 0)] <- theta[1] #Malnourished
#' r_risk[intersect(which(X[,"Exposure"] >= 0),
#' which(X[,"Exposure"] < 5))] <- theta[2] #Normal
#' r_risk[intersect(which(X[,"Exposure"] >= 5),
#' which(X[,"Exposure"] < 10))] <- theta[3] #Overweight
#' r_risk[which(X[,"Exposure"] >= 10)] <- theta[4] #Obese
#'
#' return(r_risk)
#' }
#'
#' paf(BMI_adjusted, thetahat, rr, check_exposure = FALSE)
#'
#' #Example 6: Bivariate exposure and rr ("classical PAF")
#' #------------------------------------------------------------------
#' set.seed(18427)
#' mysample <- sample(c("Exposed","Unexposed"), 1000,
#' replace = TRUE, prob = c(0.1, 0.9))
#' X <- data.frame(Exposure = mysample)
#' theta <- c("Exposed" = 2.5, "Unexposed" = 1.2)
#' rr <- function(X, theta){
#'
#' #Create relative risk function
#' r_risk <- rep(1, nrow(X))
#'
#' #Assign values of relative risk
#' r_risk[which(X[,"Exposure"] == "Unexposed")] <- theta["Unexposed"]
#' r_risk[which(X[,"Exposure"] == "Exposed")] <- theta["Exposed"]
#'
#' return(r_risk)
#' }
#'
#' paf(X, theta, rr)
#'
#' #Example 7: Continuous exposure, several covariates
#' #------------------------------------------------------------------
#' X <- data.frame(Exposure = rbeta(100, 2, 3),
#' Age = runif(100, 20, 100),
#' Sex = sample(c("M","F"), 100, replace = TRUE),
#' BMI = rlnorm(100, 3.2, 0.2))
#' thetahat <- c(-0.1, 0.05, 0.2, -0.4, 0.3, 0.1)
#'
#' rr <- function(X, theta){
#'
#' #Create risk vector
#' Risk <- rep(1, nrow(X))
#'
#' #Identify subpopulations
#' males <- which(X[,"Sex"] == "M")
#' females <- which(X[,"Sex"] == "F")
#'
#' #Calculate population specific rr
#' Risk[males] <- theta[1]*X[males,"Exposure"] +
#' theta[2]*X[males,"Age"]^2 +
#' theta[3]*X[males,"BMI"]/2
#'
#' Risk[females] <- theta[4]*X[females,"Exposure"] +
#' theta[5]*X[females,"Age"]^2 +
#' theta[6]*X[females,"BMI"]/2
#'
#' return(Risk)
#' }
#'
#' paf(X, thetahat, rr)
#'
#'
#' @seealso \code{\link{paf.confidence}} for confidence interval estimation,
#' \code{\link{pif}} for Potential Impact Fraction estimation.
#'
#' See \code{\link{paf.exponential}} and \code{\link{paf.linear}} for
#' fractions with ready-to-use exponential and linear Relative Risks
#' respectively.
#'
#' Sensitivity analysis plots can be done with \code{\link{paf.plot}}, and
#' \code{\link{paf.sensitivity}}.
#'
#'
#' @references Vander Hoorn, S., Ezzati, M., Rodgers, A., Lopez, A. D., &
#' Murray, C. J. (2004). \emph{Estimating attributable burden of disease from
#' exposure and hazard data. Comparative quantification of health risks:
#' global and regional burden of disease attributable to selected major risk
#' factors}. Geneva: World Health Organization, 2129-40.
#'
#' @importFrom stats var
#'
#' @export
paf <- function(X, thetahat, rr,
method = "empirical",
weights = rep(1/nrow(as.matrix(X)),nrow(as.matrix(X))),
Xvar = var(X),
deriv.method.args = list(),
deriv.method = "Richardson",
adjust = 1, n = 512,
ktype = "gaussian",
bw = "SJ",
check_exposure = TRUE, check_rr = TRUE,
check_integrals = TRUE){
#Estimation of PAF
.paf <- pif(X = X, thetahat = thetahat, rr = rr, cft=NA,
method = method, weights = weights,
Xvar = Xvar, deriv.method.args = deriv.method.args,
deriv.method = deriv.method, adjust = adjust, n = n,
ktype = ktype, bw = bw,
check_exposure = check_exposure, check_integrals = check_integrals,
check_rr = check_rr, is_paf = TRUE)
return(.paf)
}
INSP-RH/pif documentation built on May 7, 2019, 6:01 a.m.
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#' @title Population Attributable Fraction
#'
#' @description Function for estimating the Population Attributable Fraction
#' \code{paf} from a cross-sectional sample of the exposure \code{X} with a
#' known Relative Risk function \code{rr} with meta-analytical parameter \code{theta}, where
#' the Population Attributable Fraction is given by: \deqn{ PAF =
#' \frac{E_X\left[rr(X;\theta)\right]-1}{E_X\left[rr(X;\theta)\right]} .}{ PAF
#' = mean(rr(X; theta) - 1)/mean(rr(X; theta)).}
#'
#' @param X Random sample (\code{data.frame}) which includes exposure
#' and covariates or sample \code{mean} if \code{"approximate"} method is
#' selected.
#'
#' @param thetahat Asymptotically consistent or Fisher consistent
#' estimator (\code{vector}) of \code{theta} for the Relative
#' Risk function \code{rr}.
#'
#' @param rr \code{function} for Relative Risk which uses parameter
#' \code{theta}. The order of the parameters should be \code{rr(X, theta)}.
#'
#'
#' \strong{**Optional**}
#'
#' @param weights Normalized survey \code{weights} for the sample \code{X}.
#'
#' @param method Either \code{"empirical"} (default), \code{"kernel"} or
#' \code{"approximate"}. For details on estimation methods see
#' \code{\link{pif}}.
#'
#' @param Xvar Variance of exposure levels (for \code{"approximate"}
#' method).
#'
#' @param deriv.method.args \code{method.args} for
#' \code{\link[numDeriv]{hessian}} (for \code{"approximate"} method).
#'
#' @param deriv.method \code{method} for \code{\link[numDeriv]{hessian}}.
#' Don't change this unless you know what you are doing (for
#' \code{"approximate"} method).
#'
#' @param ktype \code{kernel} type: \code{"gaussian"},
#' \code{"epanechnikov"}, \code{"rectangular"}, \code{"triangular"},
#' \code{"biweight"}, \code{"cosine"}, \code{"optcosine"} (for \code{"kernel"}
#' method). Additional information on kernels in \code{\link[stats]{density}}.
#'
#' @param bw Smoothing bandwith parameter (for
#' \code{"kernel"} method) from \code{\link[stats]{density}}. Default
#' \code{"SJ"}.
#'
#' @param adjust Adjust bandwith parameter (for \code{"kernel"}
#' method) from \code{\link[stats]{density}}.
#'
#' @param n Number of equally spaced points at which the density (for
#' \code{"kernel"} method) is to be estimated (see
#' \code{\link[stats]{density}}).
#'
#' @param check_integrals \code{boolean} Check that counterfactual \code{cft}
#' and relative risk's \code{rr} expected values are well defined for this
#' scenario.
#'
#' @param check_exposure \code{boolean} Check that exposure \code{X} is
#' positive and numeric.
#'
#' @param check_rr \code{boolean} Check that Relative Risk function
#' \code{rr} equals \code{1} when evaluated at \code{0}.
#'
#' @return paf Estimate of Population Attributable Fraction.
#'
#' @author Rodrigo Zepeda-Tello \email{rzepeda17@gmail.com}
#' @author Dalia Camacho-García-Formentí \email{daliaf172@gmail.com}
#'
#' @note \code{"approximate"} method should be the last choice. In practice
#' \code{"empirical"} should be preferred as convergence is faster in
#' simulations than \code{"kernel"}. In addition, the scope
#' of \code{"kernel"} is limited as it does not work with multivariate
#' exposures \code{X}.
#'
#' @note \code{\link{paf}} is a wrapper for \code{\link{pif}} with
#' counterfactual of theoretical minimum risk exposure (\code{rr} = 1).
#'
#' @note For more information on kernels see \code{\link[stats]{density}}.
#'
#' @note Do not use the \code{$} operator when using \code{"approximate"}
#' \code{method}.
#'
#' @details The Relative Risk function \code{rr} and counterfactual \code{cft}
#' should consider \code{X} to be a \code{data.frame}. Each row of
#' \code{X} is an "individual" and each column a variable (exposure or covariate)
#' of said individual.
#'
#' @examples
#'
#' #Example 1: Exponential Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rnorm(100,3,1))
#' thetahat <- 0.12
#' rr <- function(X, theta){exp(theta*X)}
#'
#' #Using the empirical method
#' paf(X, thetahat, rr)
#'
#' #Same example with kernel method
#' paf(X, thetahat, rr, method = "kernel")
#'
#' #Same example with approximate method
#' Xmean <- data.frame(Exposure = mean(X[,"Exposure"]))
#' Xvar <- var(X[,"Exposure"])
#' paf(Xmean, thetahat, rr, method = "approximate", Xvar = Xvar)
#'
#' #Additional options for approximate:
#' paf(Xmean, thetahat, rr, method = "approximate", Xvar = Xvar,
#' deriv.method = "Richardson", deriv.method.args = list(eps=1e-3, d=0.1))
#'
#' #Example 2: Linear Relative Risk with weighted sample
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rbeta(100,3,1))
#' weights <- runif(100)
#' normalized_weights <- weights/sum(weights)
#' thetahat <- 0.12
#' rr <- function(X, theta){theta*X^2 + 1}
#' paf(X, thetahat, rr, weights = normalized_weights)
#'
#'
#' #Additional options for kernel:
#' paf(X, thetahat, rr, weights = normalized_weights,
#' method = "kernel", ktype = "cosine", bw = "nrd0")
#'
#'
#' #Example 3: Multivariate Linear Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X1 <- rnorm(100,4,1)
#' X2 <- rnorm(100,2,0.4)
#' X <- data.frame(Exposure = X1, Covariate = X2)
#' thetahat <- c(0.12, 0.03)
#'
#' #When creating relative risks avoid using the $ operator
#' #as it doesn't work under approximate method
#' rr_not <- function(X, theta){
#' exp(theta[1]*X$Exposure + theta[2]*X$Covariate)
#' }
#' rr_better <- function(X, theta){
#' exp(theta[1]*X[,"Exposure"] + theta[2]*X[,"Covariate"])
#' }
#'
#' #For the empirical method it makes no difference:
#' paf(X, thetahat, rr_better)
#' paf(X, thetahat, rr_not)
#'
#'
#' #But the approximate method crashes due to operator
#' Xmean <- data.frame(Exposure = mean(X[,"Exposure"]),
#' Covariate = mean(X[,"Covariate"]))
#' Xvar <- var(X)
#'
#' paf(Xmean, thetahat, rr_better, method = "approximate", Xvar = Xvar)
#' \dontrun{
#' #Warning: $ operator in rr definitions don't work in approximate
#' paf(Xmean, thetahat, rr_not, method = "approximate", Xvar = Xvar)
#' }
#'
#'
#' \dontrun{
#' #Warning: Multivariate cases cannot be evaluated with kernel method
#' paf(X, thetahat, rr, method = "kernel")
#' }
#'
#' #Example 4: Categorical Relative Risk & Exposure
#' #--------------------------------------------
#' set.seed(18427)
#' mysample <- sample(c("Normal","Overweight","Obese"), 100,
#' replace = TRUE, prob = c(0.4, 0.1, 0.5))
#' X <- data.frame(Exposure = mysample)
#'
#' thetahat <- c(1, 1.2, 1.5)
#'
#' #Categorical relative risk function
#' rr <- function(X, theta){
#'
#' #Create return vector with default risk of 1
#' r_risk <- rep(1, nrow(X))
#'
#' #Assign categorical relative risk
#' r_risk[which(X[,"Exposure"] == "Normal")] <- thetahat[1]
#' r_risk[which(X[,"Exposure"] == "Overweight")] <- thetahat[2]
#' r_risk[which(X[,"Exposure"] == "Obese")] <- thetahat[3]
#'
#' return(r_risk)
#' }
#'
#' paf(X, thetahat, rr, check_rr = FALSE)
#'
#' #Example 5: Continuous Exposure and Categorical Relative Risk
#' #------------------------------------------------------------------
#' set.seed(18427)
#'
#' #Assume we have BMI from a sample
#' BMI <- data.frame(Exposure = rlnorm(100, 3.1, sdlog = 0.1))
#'
#' #Theoretical minimum risk exposure is at 20kg/m^2 in borderline "Normal" category
#' BMI_adjusted <- BMI - 20
#'
#' thetahat <- c(Malnourished = 2.2, Normal = 1, Overweight = 1.8,
#' Obese = 2.5)
#' rr <- function(X, theta){
#'
#' #Create return vector with default risk of 1
#' r_risk <- rep(1, nrow(X))
#'
#' #Assign categorical relative risk
#' r_risk[which(X[,"Exposure"] < 0)] <- theta[1] #Malnourished
#' r_risk[intersect(which(X[,"Exposure"] >= 0),
#' which(X[,"Exposure"] < 5))] <- theta[2] #Normal
#' r_risk[intersect(which(X[,"Exposure"] >= 5),
#' which(X[,"Exposure"] < 10))] <- theta[3] #Overweight
#' r_risk[which(X[,"Exposure"] >= 10)] <- theta[4] #Obese
#'
#' return(r_risk)
#' }
#'
#' paf(BMI_adjusted, thetahat, rr, check_exposure = FALSE)
#'
#' #Example 6: Bivariate exposure and rr ("classical PAF")
#' #------------------------------------------------------------------
#' set.seed(18427)
#' mysample <- sample(c("Exposed","Unexposed"), 1000,
#' replace = TRUE, prob = c(0.1, 0.9))
#' X <- data.frame(Exposure = mysample)
#' theta <- c("Exposed" = 2.5, "Unexposed" = 1.2)
#' rr <- function(X, theta){
#'
#' #Create relative risk function
#' r_risk <- rep(1, nrow(X))
#'
#' #Assign values of relative risk
#' r_risk[which(X[,"Exposure"] == "Unexposed")] <- theta["Unexposed"]
#' r_risk[which(X[,"Exposure"] == "Exposed")] <- theta["Exposed"]
#'
#' return(r_risk)
#' }
#'
#' paf(X, theta, rr)
#'
#' #Example 7: Continuous exposure, several covariates
#' #------------------------------------------------------------------
#' X <- data.frame(Exposure = rbeta(100, 2, 3),
#' Age = runif(100, 20, 100),
#' Sex = sample(c("M","F"), 100, replace = TRUE),
#' BMI = rlnorm(100, 3.2, 0.2))
#' thetahat <- c(-0.1, 0.05, 0.2, -0.4, 0.3, 0.1)
#'
#' rr <- function(X, theta){
#'
#' #Create risk vector
#' Risk <- rep(1, nrow(X))
#'
#' #Identify subpopulations
#' males <- which(X[,"Sex"] == "M")
#' females <- which(X[,"Sex"] == "F")
#'
#' #Calculate population specific rr
#' Risk[males] <- theta[1]*X[males,"Exposure"] +
#' theta[2]*X[males,"Age"]^2 +
#' theta[3]*X[males,"BMI"]/2
#'
#' Risk[females] <- theta[4]*X[females,"Exposure"] +
#' theta[5]*X[females,"Age"]^2 +
#' theta[6]*X[females,"BMI"]/2
#'
#' return(Risk)
#' }
#'
#' paf(X, thetahat, rr)
#'
#'
#' @seealso \code{\link{paf.confidence}} for confidence interval estimation,
#' \code{\link{pif}} for Potential Impact Fraction estimation.
#'
#' See \code{\link{paf.exponential}} and \code{\link{paf.linear}} for
#' fractions with ready-to-use exponential and linear Relative Risks
#' respectively.
#'
#' Sensitivity analysis plots can be done with \code{\link{paf.plot}}, and
#' \code{\link{paf.sensitivity}}.
#'
#'
#' @references Vander Hoorn, S., Ezzati, M., Rodgers, A., Lopez, A. D., &
#' Murray, C. J. (2004). \emph{Estimating attributable burden of disease from
#' exposure and hazard data. Comparative quantification of health risks:
#' global and regional burden of disease attributable to selected major risk
#' factors}. Geneva: World Health Organization, 2129-40.
#'
#' @importFrom stats var
#'
#' @export
paf <- function(X, thetahat, rr,
method = "empirical",
weights = rep(1/nrow(as.matrix(X)),nrow(as.matrix(X))),
Xvar = var(X),
deriv.method.args = list(),
deriv.method = "Richardson",
adjust = 1, n = 512,
ktype = "gaussian",
bw = "SJ",
check_exposure = TRUE, check_rr = TRUE,
check_integrals = TRUE){
#Estimation of PAF
.paf <- pif(X = X, thetahat = thetahat, rr = rr, cft=NA,
method = method, weights = weights,
Xvar = Xvar, deriv.method.args = deriv.method.args,
deriv.method = deriv.method, adjust = adjust, n = n,
ktype = ktype, bw = bw,
check_exposure = check_exposure, check_integrals = check_integrals,
check_rr = check_rr, is_paf = TRUE)
return(.paf)
}
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