Attributable fraction for cross-sectional sampling designs.

Description

AF.cs estimates the model-based adjusted attributable fraction for data from cross-sectional sampling designs.

Usage

AF.cs(formula, data, exposure, clusterid)

Arguments

Details

Af.cs estimates the attributable fraction for a binary outcome Y under the hypothetical scenario where a binary exposure X is eliminated from the population. The estimate is adjusted for confounders Z by logistic regression (glm). Let the AF be defined as

AF = 1 - Pr(Y0 = 1) / Pr(Y = 1)

where Pr(Y0 = 1) denotes the counterfactual probability of the outcome if the exposure would have been eliminated from the population and Pr(Y = 1) denotes the factual probability of the outcome. If Z is sufficient for confounding control, then Pr(Y0 = 1) can be expressed as E_z{Pr(Y = 1 |X = 0,Z)}. The function uses logistic regression to estimate Pr(Y=1|X=0,Z), and the marginal sample distribution of Z to approximate the outer expectation (Sj<c3><83><c2><b6>lander and Vansteelandt, 2012). If clusterid is supplied, then a clustered sandwich formula is used in all variance calculations.

Value

Author(s)

Elisabeth Dahlqwist, Arvid Sj<c3><83><c2><b6>lander

References

Greenland, S. and Drescher, K. (1993). Maximum Likelihood Estimation of the Attributable Fraction from logistic Models. Biometrics 49, 865-872.

Sj<c3><83><c2><b6>lander, A. and Vansteelandt, S. (2011). Doubly robust estimation of attributable fractions. Biostatistics 12, 112-121.

See Also

glm used for fitting the logistic regression model.

Examples

# Simulate a cross-sectional sample
expit <- function(x) 1 / (1 + exp( - x))
n <- 1000
Z <- rnorm(n = n)
X <- rbinom(n = n, size = 1, prob = expit(Z))
Y <- rbinom(n = n, size = 1, prob = expit(Z + X))

# Example 1: non clustered data from a cross-sectional sampling design
data <- data.frame(Y, X, Z)
AF.est.cs <- AF.cs(formula = Y ~ X + Z + X * Z, data = data, exposure = "X")
summary(AF.est.cs)

# Example 2: clustered data from a cross-sectional sampling design
# Duplicate observations in order to create clustered data
id <- rep(1:n, 2)
data <- data.frame(id = id, Y = c(Y, Y), X = c(X, X), Z = c(Z, Z))
AF.est.cs.clust <- AF.cs(formula = Y ~ X + Z + X * Z, data = data,
                         exposure = "X", clusterid = "id")
summary(AF.est.cs.clust)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
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Type 'q()' to quit R.

> library(AF)
Loading required package: survival
Loading required package: drgee
Loading required package: nleqslv
Loading required package: Rcpp
Loading required package: data.table
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/AF/AF.cs.Rd_%03d_medium.png", width=480, height=480)
> ### Name: AF.cs
> ### Title: Attributable fraction for cross-sectional sampling designs.
> ### Aliases: AF.cs
> 
> ### ** Examples
> 
> # Simulate a cross-sectional sample
> expit <- function(x) 1 / (1 + exp( - x))
> n <- 1000
> Z <- rnorm(n = n)
> X <- rbinom(n = n, size = 1, prob = expit(Z))
> Y <- rbinom(n = n, size = 1, prob = expit(Z + X))
> 
> # Example 1: non clustered data from a cross-sectional sampling design
> data <- data.frame(Y, X, Z)
> AF.est.cs <- AF.cs(formula = Y ~ X + Z + X * Z, data = data, exposure = "X")
> summary(AF.est.cs)
Call:  
AF.cs(formula = Y ~ X + Z + X * Z, data = data, exposure = "X")

Estimated attributable fraction (AF) and untransformed 95% Wald CI: 

        AF  Std.Error  z value     Pr(>|z|) Lower limit Upper limit
 0.1258242 0.02635683 4.773876 1.807137e-06  0.07416579   0.1774826

Exposure : X 
Outcome  : Y 

 Observations Cases
         1000   588

Method for confounder adjustment:  Logistic regression 

Formula:  Y ~ X + Z + X * Z 
> 
> # Example 2: clustered data from a cross-sectional sampling design
> # Duplicate observations in order to create clustered data
> id <- rep(1:n, 2)
> data <- data.frame(id = id, Y = c(Y, Y), X = c(X, X), Z = c(Z, Z))
> AF.est.cs.clust <- AF.cs(formula = Y ~ X + Z + X * Z, data = data,
+                          exposure = "X", clusterid = "id")
> summary(AF.est.cs.clust)
Call:  
AF.cs(formula = Y ~ X + Z + X * Z, data = data, exposure = "X", 
    clusterid = "id")

Estimated attributable fraction (AF) and untransformed 95% Wald CI: 

        AF  Robust SE  z value     Pr(>|z|) Lower limit Upper limit
 0.1258242 0.02635683 4.773876 1.807137e-06  0.07416579   0.1774826

Exposure : X 
Outcome  : Y 

 Observations Cases Clusters
         2000  1176     1000

Method for confounder adjustment:  Logistic regression 

Formula:  Y ~ X + Z + X * Z 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>