AF.cs {AF} | R Documentation |
Attributable fraction for cross-sectional sampling designs. NOTE! Deprecated function. Use AFglm
.
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
formula |
an object of class " |
data |
an optional data frame, list or environment (or object coercible by |
exposure |
the name of the exposure variable as a string. The exposure must be binary (0/1) where unexposed is coded as 0. |
clusterid |
the name of the cluster identifier variable as a string, if data are clustered. |
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
where denotes the counterfactual probability of the outcome if
the exposure would have been eliminated from the population and
denotes the factual probability of the outcome.
If
Z
is sufficient for confounding control, then can be expressed as
The function uses logistic regression to estimate
, and the marginal sample distribution of
Z
to approximate the outer expectation (Sjölander and Vansteelandt, 2012).
If clusterid
is supplied, then a clustered sandwich formula is used in all variance calculations.
Value
AF.est |
estimated attributable fraction. |
AF.var |
estimated variance of |
P.est |
estimated factual proportion of cases; |
P.var |
estimated variance of |
P0.est |
estimated counterfactual proportion of cases if exposure would be eliminated; |
P0.var |
estimated variance of |
object |
the fitted model. Fitted using logistic regression, |
Author(s)
Elisabeth Dahlqwist, Arvid Sjölander
References
Greenland, S. and Drescher, K. (1993). Maximum Likelihood Estimation of the Attributable Fraction from logistic Models. Biometrics 49, 865-872.
Sjölander, A. and Vansteelandt, S. (2011). Doubly robust estimation of attributable fractions. Biostatistics 12, 112-121.
See Also
The new and more general version of the function: AFglm
.
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)
# Estimation of the attributable fraction
AF.cs_est <- AF.cs(formula = Y ~ X + Z + X * Z, data = data, exposure = "X")
summary(AF.cs_est)
# 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))
# Estimation of the attributable fraction
AF.cs_clust <- AF.cs(formula = Y ~ X + Z + X * Z, data = data,
exposure = "X", clusterid = "id")
summary(AF.cs_clust)