2023-04-12 (updated: 2023-08-31)

Lucy D’Agostino McGowan

Wake Forest University

We have measured variables, what should we adjust for?

exposure |
outcome |
covariate |
---|---|---|

0.49 | 1.71 | 2.24 |

0.07 | 0.68 | 0.92 |

0.40 | -1.60 | -0.10 |

. | . | . |

. | . | . |

. | . | . |

0.55 | -1.73 | -2.34 |

`quartets`

package`exposure`

and `covariate`

: `causal_collider`

, `causal_confounding`

, `causal_mediator`

, `causal_m_bias`

`exposure`

and `outcome`

`exposure`

and the `outcome`

`10:00`

Data generating mechanism | Correct causal model | Correct causal effect |
---|---|---|

(1) Collider | Y ~ X | 1.0 |

(2) Confounder | Y ~ X ; Z | 0.5 |

(3) Mediator | Direct effect: Y ~ X ; Z Total Effect: Y ~ X | Direct effect: 0.0 Total effect: 1.0 |

(4) M-Bias | Y ~ X | 1.0 |

D’Agostino McGowan L, Gerke T, Barrett M (2023). Causal inference is not a statistical problem. Preprint arXiv:2304.02683v1.

Data generating mechanism | ATE not adjusting for Z | ATE adjusting for Z | Correlation of X and Z |
---|---|---|---|

(1) Collider | 1.00 | 0.55 | 0.70 |

(2) Confounder | 1.00 | 0.50 | 0.70 |

(3) Mediator | 1.00 | 0.00 | 0.70 |

(4) M-Bias | 1.00 | 0.88 | 0.70 |

```
# A tibble: 100 × 6
exposure_baseline outcome_baseline covariate_baseline
<dbl> <dbl> <dbl>
1 -1.43 0.287 -0.0963
2 0.0593 -0.978 -1.11
3 0.370 0.348 0.647
4 0.00471 0.851 0.755
5 0.340 1.94 1.19
6 -3.61 -0.235 -0.588
7 1.44 -0.827 -1.13
8 1.02 -0.0410 0.689
9 -2.43 -2.10 -1.49
10 -1.26 -2.41 -2.78
# ℹ 90 more rows
# ℹ 3 more variables: exposure_followup <dbl>,
# outcome_followup <dbl>, covariate_followup <dbl>
```

*Time-varying data*

**True causal effect**: 1 **Estimated causal effect**: 0.55

**True causal effect**: 1 **Estimated causal effect**: 1

`outcome_followup ~ exposure_baseline + covariate_baseline`

Data generating mechanism | ATE not adjusting for pre-exposure Z | ATE adjusting for pre-exposure Z | Correct causal effect |
---|---|---|---|

(1) Collider | 1.00 | 1.00 | 1.00 |

(2) Confounder | 1.00 | 0.50 | 0.50 |

(3) Mediator | 1.00 | 1.00 | 1.00 |

(4) M-Bias | 1.00 | 0.88 | 1.00 |

- The relationship between Z and the unmeasured confounders needs to be really large (Liu et al 2012)
- “To obsess about the possibility of [M-bias] generates bad practical advice in all but the most unusual circumstances” (Rubin 2009)
- There are (almost) no true zeros (Gelman 2011)
- Asymptotic theory shows that induction of M-bias is quite sensitive to various deviations from the exact M-Structure (Ding and Miratrix 2014)

`outcome_followup`

and `exposure_baseline`

adjusting for `covariate_baseline`

: `causal_collider_time`

, `causal_confounding_time`

, `causal_mediator_time`

, `causal_m_bias_time`

`10:00`