R/pif_confidence.R
In INSP-RH/pif: Potential Impact Fraction and Population Attributable Fraction for Cross-Sectional Data
#' @title Confidence Intervals for the Potential Impact Fraction
#'
#' @description Function that estimates confidence intervals for the Potential
#' Impact Fraction \code{\link{pif}} from a cross-sectional sample of
#' the exposure \code{X} with a known Relative Risk function \code{rr} with
#' parameter \code{theta}, where the Potential Impact Fraction is given
#' by: \deqn{ PIF =
#' \frac{E_X\left[rr(X;\theta)\right] -
#' E_X\left[rr\big(\textrm{cft}(X);\theta\big)\right]}
#' {E_X\left[rr(X;\theta)\right]}. }{ PIF = (mean(rr(X; theta)) -
#' mean(rr(cft(X);theta)))/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{thetahat} should be asymptotically normal \code{(N(theta, var_of_theta))}
#' with mean \code{theta} and estimated variance \code{var_of_theta}.
#'
#' @param rr \code{function} for Relative Risk which uses parameter
#' \code{theta}. The order of the parameters shound be \code{rr(X, theta)}.
#'
#' @param thetavar Estimator of variance \code{var_of_theta}.
#'
#'
#' \strong{**Optional**}
#'
#' @param cft Function \code{cft(X)} for counterfactual. Leave empty for
#' the Population Attributable Fraction \code{\link{paf}} where
#' counterfactual is that of the theoretical minimum risk exposure \code{X0}
#' such that \code{rr(X0,theta) = 1}.
#'
#' @param weights Normalized survey \code{weights} for the sample \code{X}.
#'
#' @param nsim Number of simulations for estimation of variance.
#'
#' @param confidence Confidence level \% (default \code{95}).
#'
#' @param confidence_method Either \code{bootstrap} (default), \code{linear},
#' \code{loglinear}. See \code{\link{paf}} details for additional information.
#'
#' @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_thetas \code{boolean} Check that theta associated parameters are
#' correctly inputed for the model.
#'
#' @param check_exposure \code{boolean} Check that exposure \code{X} is
#' positive and numeric.
#'
#' @param check_cft \code{boolean} Check that counterfactual function
#' \code{cft} reduces exposure.
#'
#' @param check_xvar \code{boolean} Check \code{Xvar} is covariance matrix.
#'
#' @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_rr \code{boolean} Check that Relative Risk function \code{rr} equals
#' \code{1} when evaluated at \code{0}.
#'
#' @param is_paf Boolean forcing evaluation of \code{\link{paf}}. This forces
#' the \code{\link{pif}} function to ignore the inputed counterfactual and set
#' it to the theoretical minimum risk value of \code{rr = 1}.
#'
#' @return pifvec Vector with lower (\code{"Lower_CI"}), and upper
#' (\code{"Upper_CI"}) confidence bounds for the \code{\link{pif}} as well as
#' point estimate \code{"Point_Estimate"} and estimated variance
#' of \code{log(pif)} (if \code{confidence_method} is \code{"loglinear"}).
#'
#' @note For more information on kernels see \code{\link[stats]{density}}.
#'
#' @note Do not use the \code{$} operator when using \code{"approximate"}
#' \code{method}.
#'
#'
#' @author Rodrigo Zepeda-Tello \email{rzepeda17@gmail.com}
#' @author Dalia Camacho-García-Formentí \email{daliaf172@gmail.com}
#'
#' @seealso
#'
#' See \code{\link{paf.confidence}} for confidence interval estimation of
#' \code{\link{paf}}, and \code{\link{pif}} for only point estimate.
#'
#' Sensitivity analysis plots can be done with \code{\link{paf.plot}}, and
#' \code{\link{paf.sensitivity}}
#'
#' @examples
#' #Example 1: Exponential Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rnorm(100,3,1))
#' thetahat <- 0.12
#' thetavar <- 0.02
#' rr <- function(X, theta){exp(theta*X)}
#'
#'
#' #Counterfactual of halving exposure
#' cft <- function(X){ 0.5*X }
#'
#' #Using bootstrap method
#' pif.confidence(X, thetahat, rr, thetavar, cft)
#'
#' \dontrun{
#' #Same example with loglinear method
#' pif.confidence(X, thetahat, rr, thetavar, cft, confidence_method = "loglinear")
#'
#' #Same example with linear method (usually the widest and least precise)
#' pif.confidence(X, thetahat, rr, thetavar, cft, confidence_method = "linear")
#'
#'
#' #Example 2: Linear Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rbeta(100,3,1))
#' thetahat <- 0.17
#' thetavar <- 0.01
#' rr <- function(X, theta){theta*X + 1}
#' cft <- function(X){ 0.5*X }
#' weights <- runif(100)
#' normalized_weights <- weights/sum(weights)
#' pif.confidence(X, thetahat, rr, thetavar, cft, weights = normalized_weights)
#'
#' #Same example with more complex counterfactual that reduces
#' #only the values > 0.75 are halved
#' cft <- function(X){
#'
#' #Indentify the ones with "a lot" of exposure:
#' where_excess_exposure <- which(X[,"Exposure"] > 0.75)
#'
#' #Halve their exposure
#' X[where_excess_exposure, "Exposure"] <-
#' X[where_excess_exposure, "Exposure"]/2
#' return(X)
#' }
#' pif.confidence(X, thetahat, rr, thetavar, cft, weights = normalized_weights)
#'
#'
#' #Example 3: Multivariate Linear Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X1 <- rnorm(100,4,1)
#' X2 <- rnorm(100,2,0.4)
#' thetahat <- c(0.12, 0.03)
#' thetavar <- diag(c(0.01, 0.02))
#'
#' #But the approximate method crashes due to operator
#' Xmean <- data.frame(Exposure = mean(X1),
#' Covariate = mean(X2))
#' Xvar <- var(cbind(X1, X2))
#'
#' #When creating relative risks avoid using the $ operator
#' #as it doesn't work under approximate method of PAF
#' 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"])
#' }
#'
#' #Creating a counterfactual.
#' cft <- function(X){
#' Y <- X
#' Y[,"Exposure"] <- 0.5*X[,"Exposure"]
#' Y[,"Covariate"] <- 1.1*X[,"Covariate"] + 1
#' return(Y)
#' }
#'
#' pif.confidence(Xmean, thetahat, rr_better, thetavar, cft,
#' method = "approximate", Xvar = Xvar)
#' }
#'
#' \dontrun{
#' #Warning: $ operator in rr definitions don't work in approximate
#' pif.confidence(Xmean, thetahat, rr_not, thetavar, cft, method = "approximate", Xvar = Xvar)
#' }
#'
#' \dontrun{
#' #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)
#' thetavar <- diag(c(0.1, 0.2, 0.3))
#'
#' #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)
#' }
#'
#'
#' #Counterfactual of reducing all obesity to normality
#' cft <- function(X){
#' X[which(X[,"Exposure"] == "Obese"),] <- "Normal"
#' return(X)
#' }
#'
#' pif.confidence(X, thetahat, rr, thetavar, cft, check_rr = FALSE)
#'
#'
#' #Example 5: Categorical Relative Risk & continuous exposure
#' #----------------------------------------------------------
#' set.seed(18427)
#' BMI <- data.frame(Exposure = rlnorm(100, 3.1, sdlog = 0.1))
#'
#' #Theoretical minimum risk exposure is 20kg/m^2 in borderline "Normal" category
#' BMI_adjusted <- BMI - 20
#'
#' thetahat <- c(Malnourished = 2.2, Normal = 1, Overweight = 1.8,
#' Obese = 2.5)
#' thetavar <- diag(c(0.1, 0.2, 0.2, 0.1))
#'
#' 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)
#' }
#'
#' #Counterfactual of everyone in normal range
#' cft <- function(bmi){
#' bmi <- data.frame(rep(2.5, nrow(bmi)), ncol = 1)
#' colnames(bmi) <- c("Exposure")
#' return(bmi)
#' }
#'
#' pif.confidence(BMI_adjusted, thetahat, rr, thetavar, cft,
#' check_exposure = FALSE, method = "empirical")
#'
#'
#' #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)
#' thetavar <- matrix(c(0.04, 0.02, 0.02, 0.03), ncol = 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)
#' }
#'
#' #Counterfactual of reducing the exposure in half of the individuals
#' cft <- function(X){
#'
#' #Find out which ones are exposed
#' Xexp <- which(X[,"Exposure"] == "Exposed")
#'
#' #Use only half of the exposed randomly
#' reduc <- sample(Xexp, length(Xexp)/2)
#'
#' #Unexpose those individuals
#' X[reduc, "Exposure"] <- "Unexposed"
#'
#' return(X)
#' }
#'
#' pif.confidence(X, theta, rr, thetavar, cft)
#'
#' #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)
#'
#' #Create variance of theta
#' almostvar <- matrix(runif(6^2), ncol = 6)
#'
#' thetavar <- t(almostvar) %*% almostvar
#'
#' 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)
#' }
#'
#' #Counterfactual of reducing BMI
#' cft <- function(X){
#' excess_bmi <- which(X[,"BMI"] > 25)
#' X[excess_bmi,"BMI"] <- 25
#' return(X)
#' }
#'
#' pif.confidence(X, thetahat, rr, thetavar, cft)
#' }
#' @export
pif.confidence <- function(X, thetahat, rr, thetavar,
cft = NA,
method = "empirical",
confidence_method = "bootstrap",
confidence = 95,
nsim = 1000,
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_cft = TRUE, check_rr = TRUE,
check_xvar = TRUE, check_integrals = TRUE, check_thetas = TRUE,
is_paf = FALSE){
#Choose method
method <- method[1]
confidence_method <- confidence_method[1]
switch (method,
"kernel" = {
pif.confidence.bootstrap(X = X, thetahat = thetahat, thetavar = thetavar, rr = rr, cft = cft, weights = weights,
method = "kernel", nboost = nsim, n=n, adjust = adjust, confidence = confidence,
ktype = ktype, bw = bw, check_exposure = check_exposure, check_rr = check_rr,
check_integrals = check_integrals, check_thetas = check_thetas, is_paf = is_paf)
},
"approximate" = {
switch(confidence_method,
"linear" = {
pif.confidence.approximate(Xmean = X, Xvar = Xvar, thetahat = thetahat, thetavar = thetavar, rr = rr,
cft = cft, check_thetas = check_thetas, check_cft = check_cft,
check_xvar = check_xvar, check_rr = check_rr, check_integrals = check_integrals,
check_exposure = check_exposure, deriv.method.args = deriv.method.args,
deriv.method = deriv.method, nsim = nsim, confidence = confidence,
is_paf = is_paf)
},
{
pif.confidence.approximate.loglinear(Xmean = X, Xvar = Xvar, thetahat = thetahat, thetavar = thetavar, rr = rr,
cft = cft, deriv.method.args = deriv.method.args, deriv.method = deriv.method,
check_exposure = check_exposure, check_rr = check_rr, check_integrals = check_integrals,
nsim = nsim, confidence = confidence, check_thetas = check_thetas,
is_paf = is_paf)
}
)
},
{
switch (confidence_method,
"linear" = {
pif.confidence.linear(X = X, thetahat = thetahat, rr = rr, thetavar = thetavar, cft = cft, weights = weights,
confidence = confidence, nsim=nsim, check_thetas = check_thetas,
check_exposure = check_exposure, check_rr = check_rr,
check_integrals = check_integrals, is_paf = is_paf)
},
"loglinear" = {
pif.confidence.loglinear(X = X, thetahat = thetahat, thetavar = thetavar, rr = rr, cft = cft, weights = weights,
nsim = nsim, confidence=confidence, check_thetas = check_thetas,
check_exposure = check_exposure,
check_cft = check_cft, is_paf = is_paf)
},
{
pif.confidence.bootstrap(X = X, thetahat = thetahat, thetavar = thetavar, rr = rr, cft = cft, weights = weights,
method = "empirical", nboost = nsim, confidence = confidence,
check_exposure = check_exposure, check_rr = check_rr,
check_integrals = check_integrals, check_thetas = check_thetas,
is_paf = is_paf)
}
)
}
)
}
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#' @title Confidence Intervals for the Potential Impact Fraction
#'
#' @description Function that estimates confidence intervals for the Potential
#' Impact Fraction \code{\link{pif}} from a cross-sectional sample of
#' the exposure \code{X} with a known Relative Risk function \code{rr} with
#' parameter \code{theta}, where the Potential Impact Fraction is given
#' by: \deqn{ PIF =
#' \frac{E_X\left[rr(X;\theta)\right] -
#' E_X\left[rr\big(\textrm{cft}(X);\theta\big)\right]}
#' {E_X\left[rr(X;\theta)\right]}. }{ PIF = (mean(rr(X; theta)) -
#' mean(rr(cft(X);theta)))/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{thetahat} should be asymptotically normal \code{(N(theta, var_of_theta))}
#' with mean \code{theta} and estimated variance \code{var_of_theta}.
#'
#' @param rr \code{function} for Relative Risk which uses parameter
#' \code{theta}. The order of the parameters shound be \code{rr(X, theta)}.
#'
#' @param thetavar Estimator of variance \code{var_of_theta}.
#'
#'
#' \strong{**Optional**}
#'
#' @param cft Function \code{cft(X)} for counterfactual. Leave empty for
#' the Population Attributable Fraction \code{\link{paf}} where
#' counterfactual is that of the theoretical minimum risk exposure \code{X0}
#' such that \code{rr(X0,theta) = 1}.
#'
#' @param weights Normalized survey \code{weights} for the sample \code{X}.
#'
#' @param nsim Number of simulations for estimation of variance.
#'
#' @param confidence Confidence level \% (default \code{95}).
#'
#' @param confidence_method Either \code{bootstrap} (default), \code{linear},
#' \code{loglinear}. See \code{\link{paf}} details for additional information.
#'
#' @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_thetas \code{boolean} Check that theta associated parameters are
#' correctly inputed for the model.
#'
#' @param check_exposure \code{boolean} Check that exposure \code{X} is
#' positive and numeric.
#'
#' @param check_cft \code{boolean} Check that counterfactual function
#' \code{cft} reduces exposure.
#'
#' @param check_xvar \code{boolean} Check \code{Xvar} is covariance matrix.
#'
#' @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_rr \code{boolean} Check that Relative Risk function \code{rr} equals
#' \code{1} when evaluated at \code{0}.
#'
#' @param is_paf Boolean forcing evaluation of \code{\link{paf}}. This forces
#' the \code{\link{pif}} function to ignore the inputed counterfactual and set
#' it to the theoretical minimum risk value of \code{rr = 1}.
#'
#' @return pifvec Vector with lower (\code{"Lower_CI"}), and upper
#' (\code{"Upper_CI"}) confidence bounds for the \code{\link{pif}} as well as
#' point estimate \code{"Point_Estimate"} and estimated variance
#' of \code{log(pif)} (if \code{confidence_method} is \code{"loglinear"}).
#'
#' @note For more information on kernels see \code{\link[stats]{density}}.
#'
#' @note Do not use the \code{$} operator when using \code{"approximate"}
#' \code{method}.
#'
#'
#' @author Rodrigo Zepeda-Tello \email{rzepeda17@gmail.com}
#' @author Dalia Camacho-García-Formentí \email{daliaf172@gmail.com}
#'
#' @seealso
#'
#' See \code{\link{paf.confidence}} for confidence interval estimation of
#' \code{\link{paf}}, and \code{\link{pif}} for only point estimate.
#'
#' Sensitivity analysis plots can be done with \code{\link{paf.plot}}, and
#' \code{\link{paf.sensitivity}}
#'
#' @examples
#' #Example 1: Exponential Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rnorm(100,3,1))
#' thetahat <- 0.12
#' thetavar <- 0.02
#' rr <- function(X, theta){exp(theta*X)}
#'
#'
#' #Counterfactual of halving exposure
#' cft <- function(X){ 0.5*X }
#'
#' #Using bootstrap method
#' pif.confidence(X, thetahat, rr, thetavar, cft)
#'
#' \dontrun{
#' #Same example with loglinear method
#' pif.confidence(X, thetahat, rr, thetavar, cft, confidence_method = "loglinear")
#'
#' #Same example with linear method (usually the widest and least precise)
#' pif.confidence(X, thetahat, rr, thetavar, cft, confidence_method = "linear")
#'
#'
#' #Example 2: Linear Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X <- data.frame(Exposure = rbeta(100,3,1))
#' thetahat <- 0.17
#' thetavar <- 0.01
#' rr <- function(X, theta){theta*X + 1}
#' cft <- function(X){ 0.5*X }
#' weights <- runif(100)
#' normalized_weights <- weights/sum(weights)
#' pif.confidence(X, thetahat, rr, thetavar, cft, weights = normalized_weights)
#'
#' #Same example with more complex counterfactual that reduces
#' #only the values > 0.75 are halved
#' cft <- function(X){
#'
#' #Indentify the ones with "a lot" of exposure:
#' where_excess_exposure <- which(X[,"Exposure"] > 0.75)
#'
#' #Halve their exposure
#' X[where_excess_exposure, "Exposure"] <-
#' X[where_excess_exposure, "Exposure"]/2
#' return(X)
#' }
#' pif.confidence(X, thetahat, rr, thetavar, cft, weights = normalized_weights)
#'
#'
#' #Example 3: Multivariate Linear Relative Risk
#' #--------------------------------------------
#' set.seed(18427)
#' X1 <- rnorm(100,4,1)
#' X2 <- rnorm(100,2,0.4)
#' thetahat <- c(0.12, 0.03)
#' thetavar <- diag(c(0.01, 0.02))
#'
#' #But the approximate method crashes due to operator
#' Xmean <- data.frame(Exposure = mean(X1),
#' Covariate = mean(X2))
#' Xvar <- var(cbind(X1, X2))
#'
#' #When creating relative risks avoid using the $ operator
#' #as it doesn't work under approximate method of PAF
#' 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"])
#' }
#'
#' #Creating a counterfactual.
#' cft <- function(X){
#' Y <- X
#' Y[,"Exposure"] <- 0.5*X[,"Exposure"]
#' Y[,"Covariate"] <- 1.1*X[,"Covariate"] + 1
#' return(Y)
#' }
#'
#' pif.confidence(Xmean, thetahat, rr_better, thetavar, cft,
#' method = "approximate", Xvar = Xvar)
#' }
#'
#' \dontrun{
#' #Warning: $ operator in rr definitions don't work in approximate
#' pif.confidence(Xmean, thetahat, rr_not, thetavar, cft, method = "approximate", Xvar = Xvar)
#' }
#'
#' \dontrun{
#' #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)
#' thetavar <- diag(c(0.1, 0.2, 0.3))
#'
#' #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)
#' }
#'
#'
#' #Counterfactual of reducing all obesity to normality
#' cft <- function(X){
#' X[which(X[,"Exposure"] == "Obese"),] <- "Normal"
#' return(X)
#' }
#'
#' pif.confidence(X, thetahat, rr, thetavar, cft, check_rr = FALSE)
#'
#'
#' #Example 5: Categorical Relative Risk & continuous exposure
#' #----------------------------------------------------------
#' set.seed(18427)
#' BMI <- data.frame(Exposure = rlnorm(100, 3.1, sdlog = 0.1))
#'
#' #Theoretical minimum risk exposure is 20kg/m^2 in borderline "Normal" category
#' BMI_adjusted <- BMI - 20
#'
#' thetahat <- c(Malnourished = 2.2, Normal = 1, Overweight = 1.8,
#' Obese = 2.5)
#' thetavar <- diag(c(0.1, 0.2, 0.2, 0.1))
#'
#' 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)
#' }
#'
#' #Counterfactual of everyone in normal range
#' cft <- function(bmi){
#' bmi <- data.frame(rep(2.5, nrow(bmi)), ncol = 1)
#' colnames(bmi) <- c("Exposure")
#' return(bmi)
#' }
#'
#' pif.confidence(BMI_adjusted, thetahat, rr, thetavar, cft,
#' check_exposure = FALSE, method = "empirical")
#'
#'
#' #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)
#' thetavar <- matrix(c(0.04, 0.02, 0.02, 0.03), ncol = 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)
#' }
#'
#' #Counterfactual of reducing the exposure in half of the individuals
#' cft <- function(X){
#'
#' #Find out which ones are exposed
#' Xexp <- which(X[,"Exposure"] == "Exposed")
#'
#' #Use only half of the exposed randomly
#' reduc <- sample(Xexp, length(Xexp)/2)
#'
#' #Unexpose those individuals
#' X[reduc, "Exposure"] <- "Unexposed"
#'
#' return(X)
#' }
#'
#' pif.confidence(X, theta, rr, thetavar, cft)
#'
#' #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)
#'
#' #Create variance of theta
#' almostvar <- matrix(runif(6^2), ncol = 6)
#'
#' thetavar <- t(almostvar) %*% almostvar
#'
#' 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)
#' }
#'
#' #Counterfactual of reducing BMI
#' cft <- function(X){
#' excess_bmi <- which(X[,"BMI"] > 25)
#' X[excess_bmi,"BMI"] <- 25
#' return(X)
#' }
#'
#' pif.confidence(X, thetahat, rr, thetavar, cft)
#' }
#' @export
pif.confidence <- function(X, thetahat, rr, thetavar,
cft = NA,
method = "empirical",
confidence_method = "bootstrap",
confidence = 95,
nsim = 1000,
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_cft = TRUE, check_rr = TRUE,
check_xvar = TRUE, check_integrals = TRUE, check_thetas = TRUE,
is_paf = FALSE){
#Choose method
method <- method[1]
confidence_method <- confidence_method[1]
switch (method,
"kernel" = {
pif.confidence.bootstrap(X = X, thetahat = thetahat, thetavar = thetavar, rr = rr, cft = cft, weights = weights,
method = "kernel", nboost = nsim, n=n, adjust = adjust, confidence = confidence,
ktype = ktype, bw = bw, check_exposure = check_exposure, check_rr = check_rr,
check_integrals = check_integrals, check_thetas = check_thetas, is_paf = is_paf)
},
"approximate" = {
switch(confidence_method,
"linear" = {
pif.confidence.approximate(Xmean = X, Xvar = Xvar, thetahat = thetahat, thetavar = thetavar, rr = rr,
cft = cft, check_thetas = check_thetas, check_cft = check_cft,
check_xvar = check_xvar, check_rr = check_rr, check_integrals = check_integrals,
check_exposure = check_exposure, deriv.method.args = deriv.method.args,
deriv.method = deriv.method, nsim = nsim, confidence = confidence,
is_paf = is_paf)
},
{
pif.confidence.approximate.loglinear(Xmean = X, Xvar = Xvar, thetahat = thetahat, thetavar = thetavar, rr = rr,
cft = cft, deriv.method.args = deriv.method.args, deriv.method = deriv.method,
check_exposure = check_exposure, check_rr = check_rr, check_integrals = check_integrals,
nsim = nsim, confidence = confidence, check_thetas = check_thetas,
is_paf = is_paf)
}
)
},
{
switch (confidence_method,
"linear" = {
pif.confidence.linear(X = X, thetahat = thetahat, rr = rr, thetavar = thetavar, cft = cft, weights = weights,
confidence = confidence, nsim=nsim, check_thetas = check_thetas,
check_exposure = check_exposure, check_rr = check_rr,
check_integrals = check_integrals, is_paf = is_paf)
},
"loglinear" = {
pif.confidence.loglinear(X = X, thetahat = thetahat, thetavar = thetavar, rr = rr, cft = cft, weights = weights,
nsim = nsim, confidence=confidence, check_thetas = check_thetas,
check_exposure = check_exposure,
check_cft = check_cft, is_paf = is_paf)
},
{
pif.confidence.bootstrap(X = X, thetahat = thetahat, thetavar = thetavar, rr = rr, cft = cft, weights = weights,
method = "empirical", nboost = nsim, confidence = confidence,
check_exposure = check_exposure, check_rr = check_rr,
check_integrals = check_integrals, check_thetas = check_thetas,
is_paf = is_paf)
}
)
}
)
}
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