Description Usage Arguments Details Value Author(s) References See Also Examples
AFcoxph
estimates the model-based adjusted attributable fraction function from a Cox Proportional Hazard regression model in form of a coxph
object. This model is commonly used for data from cohort sampling designs with time-to-event outcomes.
1 |
object |
a fitted Cox Proportional Hazard regression model 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. |
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 event times will be used. |
clusterid |
the name of the cluster identifier variable as a string, if data are clustered. Cluster robust standard errors will be calculated. |
AFcoxph
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
AF = 1 - {1 - S0(t)} / {1 - S(t)}
where S0(t) denotes the counterfactual survival function for the event if
the exposure would have been eliminated from the population at baseline and S(t) denotes the factual survival function.
If Z
is sufficient for confounding control, then S0(t) can be expressed as E_z{S(t|X=0,Z)}.
The function uses a fitted Cox proportional hazards regression to estimate S(t|X=0,Z), and the marginal sample distribution of Z
to approximate the outer expectation (Sj<c3><b6>lander and Vansteelandt, 2014). If clusterid
is supplied, then a clustered sandwich formula is used in all variance calculations.
AF.est |
estimated attributable fraction function for every time point specified by |
AF.var |
estimated variance of |
S.est |
estimated factual survival function; S(t). |
S.var |
estimated variance of |
S0.est |
estimated counterfactual survival function if exposure would be eliminated; S0(t). |
S0.var |
estimated variance of |
Elisabeth Dahlqwist, Arvid Sj<c3><b6>lander
Chen, L., Lin, D. Y., and Zeng, D. (2010). Attributable fraction functions for censored event times. Biometrika 97, 713-726.
Sj<c3><b6>lander, A. and Vansteelandt, S. (2014). Doubly robust estimation of attributable fractions in survival analysis. Statistical Methods in Medical Research. doi: 10.1177/0962280214564003.
coxph
and Surv
used for fitting the Cox proportional hazards model.
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 | # 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)
# Fit a Cox PH regression model
fit <- coxph(formula = Surv(Tobs, D) ~ X + Z + X * Z, data = data, ties="breslow")
# Estimate the attributable fraction from the fitted Cox PH regression model
AFcoxph_est <- AFcoxph(fit, data=data, exposure ="X", times = time)
summary(AFcoxph_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)
# Fit a Cox PH regression model
fit <- coxph(formula = Surv(Tobs, D) ~ X + Z + X * Z, data = data, ties="breslow")
# Estimate the attributable fraction from the fitted Cox PH regression model
AFcoxph_clust <- AFcoxph(object = fit, data = data,
exposure = "X", times = time, clusterid = "id")
summary(AFcoxph_clust)
plot(AFcoxph_clust, CI = TRUE)
# Estimate the attributable fraction from the fitted Cox PH regression model, time unspecified
AFcoxph_clust_no_time <- AFcoxph(object = fit, data = data,
exposure = "X", clusterid = "id")
summary(AFcoxph_clust_no_time)
plot(AFcoxph_clust, CI = TRUE)
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