AF.cs {AF} | R Documentation |

`AFglm`

.`AF.cs`

estimates the model-based adjusted attributable fraction for data from cross-sectional sampling designs.

```
AF.cs(formula, data, exposure, clusterid)
```

`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. |

`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

`AF=1-\frac{Pr(Y_0=1)}{Pr(Y=1)}`

where `Pr(Y_0=1)`

denotes the counterfactual probability of the outcome if
the exposure would have been eliminated from the population and `Pr(Y = 1)`

denotes the factual probability of the outcome.
If `Z`

is sufficient for confounding control, then `Pr(Y_0=1)`

can be expressed as
`E_Z\{Pr(Y=1\mid{X=0,Z})\}.`

The function uses logistic regression to estimate `Pr(Y=1\mid{X=0,Z})`

, 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.

`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, |

Elisabeth Dahlqwist, Arvid Sjölander

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.

The new and more general version of the function: `AFglm`

.

```
# 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)
```

[Package *AF* version 0.1.5 Index]