AF.ch {AF} | R Documentation |
Attributable fraction function for cohort sampling designs with time-to-event outcomes. NOTE! Deprecated function. Use AFcoxph
.
Description
AF.ch
estimates the model-based adjusted attributable fraction function for data from cohort sampling designs with time-to-event outcomes.
Usage
AF.ch(formula, data, exposure, ties = "breslow", times, clusterid)
Arguments
formula |
a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the |
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. |
ties |
a character string specifying the method for tie handling. If there are no tied death times all the methods are equivalent. Uses the Breslow method by default. |
times |
a scalar or vector of time points specified by the user for which the attributable fraction function is estimated. If not specified the observed death times will be used. |
clusterid |
the name of the cluster identifier variable as a string, if data are clustered. |
Details
Af.ch
estimates the attributable fraction for a time-to-event outcome
under the hypothetical scenario where a binary exposure X
is eliminated from the population. The estimate is adjusted for confounders Z
by the Cox proportional hazards model (coxph
). Let the AF function be defined as
where denotes the counterfactual survival function for the event if
the exposure would have been eliminated from the population at baseline and
denotes the factual survival function.
If
Z
is sufficient for confounding control, then can be expressed as
.
The function uses Cox proportional hazards regression to estimate
, and the marginal sample distribution of
Z
to approximate the outer expectation (Sjölander and Vansteelandt, 2014). If clusterid
is supplied, then a clustered sandwich formula is used in all variance calculations.
Value
AF.est |
estimated attributable fraction function for every time point specified by |
AF.var |
estimated variance of |
S.est |
estimated factual survival function; |
S.var |
estimated variance of |
S0.est |
estimated counterfactual survival function if exposure would be eliminated; |
S0.var |
estimated variance of |
object |
the fitted model. Fitted using Cox proportional hazard, |
Author(s)
Elisabeth Dahlqwist, Arvid Sjölander
References
Chen, L., Lin, D. Y., and Zeng, D. (2010). Attributable fraction functions for censored event times. Biometrika 97, 713-726.
Sjölander, A. and Vansteelandt, S. (2014). Doubly robust estimation of attributable fractions in survival analysis. Statistical Methods in Medical Research. doi: 10.1177/0962280214564003.
See Also
The new and more general version of the function: AFcoxph
. coxph
and Surv
used for fitting the Cox proportional hazards model.
Examples
# Simulate a sample from a cohort sampling design with time-to-event outcome
expit <- function(x) 1 / (1 + exp( - x))
n <- 500
time <- c(seq(from = 0.2, to = 1, by = 0.2))
Z <- rnorm(n = n)
X <- rbinom(n = n, size = 1, prob = expit(Z))
Tim <- rexp(n = n, rate = exp(X + Z))
C <- rexp(n = n, rate = exp(X + Z))
Tobs <- pmin(Tim, C)
D <- as.numeric(Tobs < C)
#Ties created by rounding
Tobs <- round(Tobs, digits = 2)
# Example 1: non clustered data from a cohort sampling design with time-to-event outcomes
data <- data.frame(Tobs, D, X, Z)
# Estimation of the attributable fraction
AF.ch_est <- AF.ch(formula = Surv(Tobs, D) ~ X + Z + X * Z, data = data,
exposure = "X", times = time)
summary(AF.ch_est)
# Example 2: clustered data from a cohort sampling design with time-to-event outcomes
# Duplicate observations in order to create clustered data
id <- rep(1:n, 2)
data <- data.frame(Tobs = c(Tobs, Tobs), D = c(D, D), X = c(X, X), Z = c(Z, Z), id = id)
# Estimation of the attributable fraction
AF.ch_clust <- AF.ch(formula = Surv(Tobs, D) ~ X + Z + X * Z, data = data,
exposure = "X", times = time, clusterid = "id")
summary(AF.ch_clust)
plot(AF.ch_clust, CI = TRUE)