/
pifpaffunctions.R
259 lines (245 loc) · 9.94 KB
/
pifpaffunctions.R
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library(MASS)
library(devtools)
devtools::install_github("colleenchan/pifpaf", force = TRUE)
library(pifpaf)
#' Returns closed-form PAF given a parametric distribution
#'
#' @param beta beta coefficient in exponential relative risk
#' @param p0 proportion of zeroes
#' @param exp assumed parametric distribution of exposure
#' @param param1 parameter 1 of parametric distribution
#' @param param2 parameter 2 of parametric distribution
#' @param trunc.val upper truncation bound
#'
#' @return A list of the true PAF value, mean and variance of the exposure
#'
true.paf <- function(beta, p0, exp, param1, param2, trunc.val){
if (exp == "weibull"){
int <- tryCatch({
integrate(function(x) {dweibull(x, param1, param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dweibull(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
meanx <- param2 * gamma(1 + 1/param1)
varx <- param2^2 * (gamma(1 + 2/param1) - (gamma(1 + 1/param1))^2)
} else if (exp == "lognormal"){
int <- tryCatch({
integrate(function(x) {dlnorm(x, param1, param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dlnorm(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
meanx <- exp(param1 - param2^2)
varx <- (exp(param2^2) - 1) * exp(2 * param1 + param2^2)
} else if (exp == "gamma"){
int <- tryCatch({
integrate(function(x) {dgamma(x, shape = param1, scale = param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dgamma(x, shape = param1, scale = param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
meanx <- param1 * param2
varx <- param1 * param2^2
} else if (exp == "normal"){
int <- tryCatch({
integrate(function(x) {dnorm(x, param1, param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dnorm(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
meanx <- param1
varx <- param2^2
}
else{
stop("exp must be either lognormal, normal, gamma, or weibull")
}
# E[X] = p(0) + (1-p)E[Xnonzero]
meanx <- meanx * (1 - p0)
# Var(X) = E[X^2] - [EX]^2 where
# E[X^2] = p(0^2) * (1-p)E[Xnonzero^2] where
# E[Xnonzero^2] = Var(Xnonzero) + E[Xnonzero]^2
varx <- (varx + meanx^2) * (1-p0) - meanx^2
return(list(paf = 1 - 1/(p0 + (1-p0)*int), mean = meanx, var = varx))
}
#' Returns closed-form PIF of form g(x) = b * x given a parametric distribution
#'
#' @param beta beta coefficient in exponential relative risk
#' @param p0 proportion of zeroes
#' @param exp parametric distribution
#' @param param1 parameter 1 of parametric distribution
#' @param param2 parameter 2 of parametric distribution
#' @param trunc.val upper truncation bound
#' @param b slope of linear counterfactual exposure function
#'
#' @return A list of the true PAF value, mean and variance of the exposure
#'
true.pif <- function(beta,
p0,
exp,
param1,
param2,
trunc.val,
b = 0){
if (exp == "weibull"){
int <- tryCatch({
integrate(function(x) {dweibull(x, param1, param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dweibull(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
intgx <- tryCatch({
integrate(function(x) {dweibull(x, param1, param2) * exp(beta*b*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dweibull(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
} else if (exp == "lognormal"){
int <- tryCatch({
integrate(function(x) {dlnorm(x, param1, param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dlnorm(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
intgx <- tryCatch({
integrate(function(x) {dlnorm(x, param1, param2) * exp(beta*b*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dlnorm(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
} else if (exp == "gamma"){
int <- tryCatch({
integrate(function(x) {dgamma(x, shape = param1, scale = param2) *
exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dgamma(x, shape = param1, scale = param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
intgx <- tryCatch({
integrate(function(x) {dgamma(x, shape = param1, scale = param2) *
exp(beta*b*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dgamma(x, shape = param1, scale = param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
} else if (exp == "normal"){
int <- tryCatch({
integrate(function(x) {dnorm(x, param1, param2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dnorm(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
intgx <- tryCatch({
integrate(function(x) {dnorm(x, param1, param2) * exp(beta*b*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dnorm(x, param1, param2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ return(Inf) })
}
else{
stop("exp must be either lognormal, normal, gamma, or weibull")
}
return(pif = (int - intgx) / int)
}
#' Standard approach to estimating the PAF.
#' Matches mean and variance using method of moments
#'
#' @param meanx mean of the exposure data
#' @param varx variance of the exposure data
#' @param exposure parametric distribution
#' @param beta beta coefficient in exponential relative risk
#'
#' @return A list of the PAF, mean and variance of the exposure
paf.std <- function(meanx, varx, exposure, beta){
if (exposure == "gamma"){
par1 <- meanx^2 / varx # shape k
par2 <- varx / meanx # scale theta
int <- tryCatch({
integrate(function(x) {dgamma(x, shape = par1, scale = par2) * exp(beta*x)},
lower = 0, upper = Inf)$value},
error = function(e){ return(Inf) })
}
if (exposure == "lognormal"){
par1 <- log(meanx^2 / sqrt(varx + meanx^2)) # log mu
par2 <- log(sqrt((varx / meanx^2) + 1)) # log sigma
int <- tryCatch({
integrate(function(x) {dlnorm(x, par1, par2) * exp(beta*x)},
lower = 0, upper = Inf, reltol = 1e-20)$value},
error = function(e){ return(Inf) })
}
if (exposure == "normal"){
par1 <- meanx
par2 <- sqrt(varx)
int <- tryCatch({
integrate(function(x) {dnorm(x, par1, par2) * exp(beta*x)},
lower = 0, upper = Inf)$value /
integrate(function(x) {dnorm(x, par1, par2)},
lower = 0, upper = Inf)$value},
error = function(e){ return(Inf) })
print(int)
}
if (exposure == "weibull"){
mcf <- function(k, x.bar, sd.x) {
t1 <- sqrt((gamma((k + 2)/k)/(gamma((k + 1)/k)^2)) - 1)
((sd.x/x.bar) - t1)^2
}
par1 <- nlminb(start = 1, objective = mcf, lower = .Machine$double.eps,
x.bar = meanx, sd.x = sqrt(varx))$par # shape k
par2 <- meanx / gamma((par1 + 1)/par1) # scale lambda
int <- tryCatch({
integrate(function(x) {dweibull(x, par1, par2) * exp(beta*x)},
lower = 0, upper = Inf)$value},
error = function(e){ return(Inf) })
}
paf <- 1 - 1/int
return(list(paf = paf, param1 = par1, param2 = par2))
}
# Kehoe mixture method
#'
#' @param x vector of exposure values
#' @param exposure assumed parametric distribution of exposure
#' @param beta beta coefficient in exponential relative risk
#' @param trunc.val upper truncation bound
#'
#' @return PAF and mean and variance of exposure
paf.kehoe <- function(x, exposure, beta, trunc.val = Inf){
p0 <- mean(x == 0)
x <- x[x != 0]
mod <- suppressWarnings(as.numeric(fitdistr(x, exposure)$estimate))
par1 <- mod[1]
par2 <- mod[2]
if (exposure == "gamma"){
int <- tryCatch(
{integrate(function(x) {dgamma(x, shape = par1, scale = par2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dgamma(x, par1, par2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ Inf })
}
if (exposure == "lognormal"){
int <- tryCatch(
{integrate(function(x) {dlnorm(x, par1, par2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dlnorm(x, par1, par2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ Inf })
}
if (exposure == "normal"){
int <- tryCatch(
{integrate(function(x) {dnorm(x, par1, par2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dnorm(x, par1, par2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ Inf })
}
if (exposure == "weibull"){
int <- tryCatch(
{integrate(function(x) {dweibull(x, par1, par2) * exp(beta*x)},
lower = 0, upper = trunc.val)$value /
integrate(function(x) {dweibull(x, par1, par2)},
lower = 0, upper = trunc.val)$value},
error = function(e){ Inf })
}
paf <- 1 - 1/(p0 + (1 - p0) * int)
return(c(paf = paf, param1 = par1, param2 = par2))
}