AFparfrailty {AF} | R Documentation |

`parfrailty`

object (commonly used for cohort sampling family designs with time-to-event outcomes).`AFparfrailty`

estimates the model-based adjusted attributable fraction function from a shared Weibull gamma-frailty model in form of a `parfrailty`

object. This model is commonly used for data from cohort sampling familty designs with time-to-event outcomes.

```
AFparfrailty(object, data, exposure, times, clusterid)
```

`object` |
a fitted Weibull gamma-parfrailty 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 death times will be used. |

`clusterid` |
the name of the cluster identifier variable as a string, if data are clustered. |

`AFparfrailty`

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 shared frailty model (`parfrailty`

).
The baseline hazard is assumed to follow a Weibull distribution and the unobserved shared frailty effects `U`

are assumed to be gamma distributed.
Let the AF function be defined as

`AF=1-\frac{\{1-S_0(t)\}}{\{1-S(t)\}}`

where `S_0(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`

and `U`

are sufficient for confounding control, then `S_0(t)`

can be expressed as `E_Z\{S(t\mid{X=0,Z })\}`

.
The function uses a fitted Weibull gamma-frailty model to estimate `S(t\mid{X=0,Z})`

, and the marginal sample distribution of `Z`

to approximate the outer expectation. 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.var` |
estimated variance of |

`S0.est` |
estimated counterfactual survival function if exposure would be eliminated; |

`S0.var` |
estimated variance of |

Elisabeth Dahlqwist, Arvid Sjölander

`parfrailty`

used for fitting the Weibull gamma-frailty and `stdParfrailty`

used for standardization of a `parfrailty`

object.

```
# Example 1: clustered data with frailty U
expit <- function(x) 1 / (1 + exp( - x))
n <- 100
m <- 2
alpha <- 1.5
eta <- 1
phi <- 0.5
beta <- 1
id <- rep(1:n,each=m)
U <- rep(rgamma(n, shape = 1 / phi, scale = phi), each = m)
Z <- rnorm(n * m)
X <- rbinom(n * m, size = 1, prob = expit(Z))
# Reparametrize scale as in rweibull function
weibull.scale <- alpha / (U * exp(beta * X)) ^ (1 / eta)
t <- rweibull(n * m, shape = eta, scale = weibull.scale)
# Right censoring
c <- runif(n * m, 0, 10)
delta <- as.numeric(t < c)
t <- pmin(t, c)
data <- data.frame(t, delta, X, Z, id)
# Fit a parfrailty object
library(stdReg)
fit <- parfrailty(formula = Surv(t, delta) ~ X + Z + X * Z, data = data, clusterid = "id")
summary(fit)
# Estimate the attributable fraction from the fitted frailty model
time <- c(seq(from = 0.2, to = 1, by = 0.2))
AFparfrailty_est <- AFparfrailty(object = fit, data = data, exposure = "X",
times = time, clusterid = "id")
summary(AFparfrailty_est)
plot(AFparfrailty_est, CI = TRUE, ylim=c(0.1,0.7))
```

[Package *AF* version 0.1.5 Index]