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#' @title Population Attributable Fraction with Linear Relative Risk Function
#'
#' @description Function that calculates the Population Attributable Fraction
#' \code{\link{paf}} with linear Relative Risk function \code{rr} given by
#' \deqn{
#' rr(X; \theta) = \theta_1 + \sum\limits_{i=1}^{n} \theta_{i+1} X_i.
#' }{
#' rr(X, theta) = theta[1] + theta[2]*X[,1] + theta[3]*X[,2] + ... + theta[n+1]*X[,n].
#' }
#'
#' @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}.
#'
#' \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 with linear
#' relative risk.
#'
#' @author Rodrigo Zepeda-Tello \email{rzepeda17@gmail.com}
#' @author Dalia Camacho-GarcĂa-FormentĂ \email{daliaf172@gmail.com}
#'
#' @note The \code{"approximate"} method should be the last choice. In practice
#' \code{"empirical"} should be preferred as convergence is faster than
#' \code{"kernel"} for most functions. In addition, the scope of
#' \code{"kernel"} is limited as it does not work with multivariate exposure
#' data \code{X}.
#'
#' @note \code{\link{paf.linear}} is a wrapper for \code{\link{paf}} with linear
#' relative risk.
#'
#'
#' @examples
#'
#' #Example 1: Univariate relative risk
#' #----------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rnorm(100,3,.5))
#' thetahat <- c(1, 0.12) #Linear risk given by 1 + 0.12*X
#' paf.linear(X, thetahat)
#'
#' #This is the same as doing:
#' paf(X, thetahat, rr = function(X, theta){X*theta[2] + theta[1]})
#'
#' #Same example with kernel method
#' paf.linear(X, thetahat, method = "kernel")
#'
#' #Same example with approximate method
#' Xmean <- data.frame(mean(X[,"Exposure"]))
#' Xvar <- var(X)
#' paf.linear(Xmean, thetahat, method = "approximate", Xvar = Xvar)
#'
#' #Example 2: Multivariate relative risk
#' #----------------------------------------
#' X <- data.frame(Exposure = rnorm(100,2,.7), Covariate = rnorm(100,4,1))
#' theta <- c(1, 0.3,0.1)
#' paf.linear(X, theta) #Linear risk given by 1 + 0.3*X1 + 0.1*X2
#'
#' #Example 3: Polynomial relative risk
#' #----------------------------------------
#' X <- runif(100)
#' X2 <- X^2
#' X3 <- X^3
#' matX <- data.frame(X,X2,X3)
#' theta <- c(1, 0.3,0.1, 0.4)
#' paf.linear(matX,theta) #Polynomial risk: 1 + 0.3*X + 0.1*X^2 + 0.4*X^3
#'
#' @seealso
#'
#' See \code{\link{paf}} for Population Attributable Fraction (with
#' arbitrary relative risk), and \code{\link{pif}} for Potential Impact Fraction
#' estimation.
#'
#' See \code{\link{paf.exponential}} for PAF with ready-to-use exponential
#' relative risk function.
#'
#' For more information on kernels see \code{\link[stats]{density}}.
#'
#' @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.
#'
#' @export
paf.linear <- function(X, thetahat,
method = "empirical",
weights = rep(1/nrow(as.matrix(X)),nrow(as.matrix(X))),
Xvar = var(X),
deriv.method.args = list(),
deriv.method = c("Richardson", "complex"),
adjust = 1, n = 512,
ktype = "gaussian",
bw = "SJ",
check_exposure = TRUE, check_rr = TRUE, check_integrals = TRUE){
#Convert exposure to matrix
.X <- as.data.frame(X)
#Check that there are parameters for every covariate
if(ncol(.X) != (length(thetahat) - 1)){
stop(paste0("The amount of parameters in theta must be equal to the number ",
"of exposure values and covariates + 1 in each observation"))
}
#Create function for linear relative risk
.rr <- function(.myX, .mytheta){
#Sum everyone
.expsol <- .mytheta[1]
for (.i in 1:ncol(.myX)){
.expsol <- .expsol + .mytheta[.i + 1]*.myX[,.i]
}
return(.expsol)
}
#Estimate Population attributable fraction
.paf <- paf(X = X, thetahat = thetahat, rr = .rr,
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_rr = check_rr,
check_integrals = check_integrals)
return(.paf)
}
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