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 - Pr(Y0 = 1) / Pr(Y = 1)*

where *Pr(Y0 = 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(Y0 = 1)* can be expressed as
*E_z{Pr(Y = 1 |X = 0,Z)}.*
The function uses logistic regression to estimate *Pr(Y=1|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]