AFcoxph {AF} | R Documentation |

## Attributable fraction function based on a Cox Proportional Hazard regression model as a `coxph`

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

### Description

`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.

### Usage

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

### Arguments

`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. |

### Details

`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-\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`

is 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 Cox proportional hazards regression to estimate `S(t\mid{X=0,Z})`

, 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 |

### 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

`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)
# 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)
```

*AF*version 0.1.5 Index]