# Adjustment Criterion

### Description

Test whether a set fulfills the adjustment criterion, that means, it removes all confounding bias when estimating a *total* effect. This is an extension of Pearl's Back-door criterion (Shpitser et al, 2010; van der Zander et al, 2014; Perkovic et al, 2015) which is complete in the sense that either a set fulfills this criterion, or it does not remove all confounding bias.

### Usage

1 | ```
isAdjustmentSet(x, Z, exposure = NULL, outcome = NULL)
``` |

### Arguments

`x` |
the input graph, a DAG, MAG, PDAG, or PAG. |

`Z` |
vector of variable names. |

`exposure` |
name(s) of the exposure variable(s). If not given (default), then the exposure variables are supposed to be defined in the graph itself. |

`outcome` |
name(s) of the outcome variable(s), also taken from the graph if not given. |

### Details

If the input graph is a MAG or PAG, then it must not contain any undirected edges (=hidden selection variables).

### References

E. Perkovic, J. Textor, M. Kalisch and M. H. Maathuis (2015), A
Complete Generalized Adjustment Criterion. In *Proceedings of UAI
2015.*

I. Shpitser, T. VanderWeele and J. M. Robins (2010), On the
validity of covariate adjustment for estimating causal effects. In
*Proceedings of UAI 2010.*