Description Usage Arguments Details Value Note Author(s) References See Also Examples
Function for estimating the Potential Impact Fraction pif
from a cross-sectional sample of the exposure X
with known Relative
Risk function rr
with parameter theta
, where the Potential
Impact Fraction is given by:
PIF = (mean(rr(X; theta)) - mean(rr(cft(X);theta)))/mean(rr(X; theta)) .
1 2 3 4 5 | pif(X, thetahat, rr, cft = NA, 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_integrals = TRUE, check_rr = TRUE, is_paf = FALSE)
|
X |
Random sample ( |
thetahat |
Asymptotically consistent or Fisher consistent
estimator ( |
rr |
**Optional** |
cft |
Function |
method |
Either |
weights |
Normalized survey |
Xvar |
Variance of exposure levels (for |
deriv.method.args |
|
deriv.method |
|
adjust |
Adjust bandwith parameter (for |
n |
Number of equally spaced points at which the density (for
|
ktype |
|
bw |
Smoothing bandwith parameter (for
|
check_exposure |
Check exposure |
check_integrals |
Check that counterfactual of theoretical minimum risk exposure and relative risk's expected values are well defined for this scenario. |
check_rr |
Check that Relative Risk function |
is_paf |
Boolean forcing evaluation of |
The "empirical"
method estimates the pif
by
PIF = 1 - weighted.mean(rr(cft(X), theta), weights)/ weighted.mean(rr(cft(X), theta), weights).
The "kernel"
method approximates the density
of
the exposure X
and estimates its expected value from that
approximation:
PIF = 1 - integrate(rr(cft(X), theta)*f(x))/integrate(rr(X, theta)*f(x)).
The "approximate"
method conducts a Laplace approximation of the pif
.
Additional information on the methods is dicussed in the package's vignette:
browseVignettes("pifpaf")
.
In practice "approximate"
method should be the last choice.
Simulations have shown that "empirical"
's convergence is faster than
"kernel"
for most functions. In addition, the scope of
"kernel"
is limited as it does not work with multivariate exposure
data X
.
pif Estimate of Potential Impact Fraction.
For more information on kernels see density
.
Do not use the $
operator when using "approximate"
method
.
Rodrigo Zepeda-Tello rzepeda17@gmail.com
Dalia Camacho-Garc<c3><ad>a-Forment<c3><ad> daliaf172@gmail.com
Vander Hoorn, S., Ezzati, M., Rodgers, A., Lopez, A. D., & Murray, C. J. (2004). 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.
See pif.confidence
for confidence interval estimation,
and paf
for Population Attributable Fraction estimation.
Sensitivity analysis plots can be done with pif.plot
,
pif.sensitivity
, and pif.heatmap
.
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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 | #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)}
#Without specifying counterfactual pif matches paf
pif(X, thetahat, rr)
paf(X, thetahat, rr)
#Same example with kernel method
pif(X, thetahat, rr, method = "kernel")
#Same example with approximate method
Xmean <- data.frame(Exposure = mean(X[,"Exposure"]))
Xvar <- var(X[,"Exposure"])
pif(Xmean, thetahat, rr, method = "approximate", Xvar = Xvar)
#Same example considering counterfactual of halving exposure
cft <- function(X){ 0.5*X }
pif(X, thetahat, rr, cft, method = "empirical")
#Example 2: Linear Relative Risk
#--------------------------------------------
set.seed(18427)
X <- data.frame(Exposure = rbeta(100,3,1))
thetahat <- 0.12
rr <- function(X, theta){theta*X + 1}
cft <- function(X){ 0.5*X }
weights <- runif(100)
normalized_weights <- weights/sum(weights)
pif(X, thetahat, rr, 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(X, thetahat, rr, cft, weights = normalized_weights)
#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 and counterfactuals avoid using $ 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"])
}
#Creating a counterfactual.
cft <- function(X){
Y <- X
Y[,"Exposure"] <- 0.5*X[,"Exposure"]
Y[,"Covariate"] <- 1.1*X[,"Covariate"] + 1
return(Y)
}
pif(X, thetahat, rr_better, cft)
#Same multivariate example for approximate method calculating
#mean and variance
Xmean <- data.frame(Exposure = mean(X$Exposure),
Covariate = mean(X$Covariate))
Xvar <- var(X)
pif(Xmean, thetahat, rr_better, method = "approximate", Xvar = Xvar)
## Not run:
#The one with $ operators doesn't work:
pif(Xmean, thetahat, rr_not, method = "approximate", Xvar = Xvar)
## End(Not run)
## Not run:
#Warning: Multivariate cases cannot be evaluated with kernel method
pif(X, thetahat, rr_better, method = "kernel")
## End(Not run)
#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)
}
pif(X, thetahat, rr, check_rr = FALSE)
#Counterfactual of reducing all obesity to normality
cft <- function(X){
X[which(X[,"Exposure"] == "Obese"),] <- "Normal"
return(X)
}
pif(X, thetahat, rr, 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 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)
}
#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(BMI_adjusted, thetahat, rr, 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)
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(X, theta, rr, 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)
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(X, thetahat, rr, cft)
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