Categories → Process , Causal Inference , Causal Effect
In causal inference, frontdoor and backdoor adjustments are two methods used to define how to estimate the causal effect of a treatment or exposure on an outcome variable.
The term "adjustment" refers to changing the set of variables included as covariates or features in a model. This is known as an adjustment set. Note we are using feature and covariate interchangeably here.
A sufficient adjustment set is a set of covariates such that adjustment, stratification or selection (e.g. by matching) with only these variables will minimize bias when estimating the causal effect of the exposure (or treatment) on the outcome (see the DAGitty manual, section 5.5).
For example, if you want to build a regression model which predicts the causal effect of a treatment on an outcome, you should include only the value of the treatment and the specific variables in the adjustment set. Do NOT include other variables.
However, if you want to build a purely predictive model of the outcome, you might still want to include ALL the variables (see this link and Julian Schuessler's answer for a worked explanation of why).
What's the difference between predictive models and causal models? A purely predictive model aims to give the most accurate predictions given all the information available, over all the available data. In contrast, a causal model aims to be accurate when predicting the outcome in response to changes in the treatment or exposure. The causal model should give better answers to counterfactual, or hypothetical conditions (input variable configurations) that may be out-of-domain or simply rare in the data. If you care about being able to predict the effect of interventions or hypotheticals, you want a causal model. If you only want to predict outcomes like the current data, an ordinary predictive model is fine.
Adjustment sets can be produced by analysis of a Directed Acyclic Graph (or Causal Diagram) to yield an Estimand for a quantity of interest (e.g. the effect of one variable on another). The adjustment set is defined in the Estimand.
It's important to produce adjustment sets in a principled and correct manner - simply conditioning on all variables produces all sorts of new problems, such as over-stratification and collider bias.
Methods to generate sufficient adjustment sets for causal inference include the Backdoor criterion, and the Frontdoor criterion, both used in Causal Wizard.
The backdoor criterion is a set of conditions that, when satisfied, allow for adjustment of confounding variables to estimate the causal effect. The backdoor adjustment method involves controlling for all variables that are causes of both the treatment and the outcome. This method essentially blocks the association between the treatment and the outcome through controlling for a common cause, or a confounding variable. Backdoor adjustment can be accomplished using techniques such as regression analysis, propensity score matching, or inverse probability weighting.
Using the backoor criterion there are many methods you can use to model the effect of treatment on outcome, including propensity score methods and regression.
The frontdoor criterion is used when the backdoor criterion is not satisfied or is infeasible. The frontdoor criterion identifies a mediator variable that lies on the causal pathway between the treatment and the outcome. Adjustment for the mediator variable allows for estimation of the direct effect of the treatment on the outcome, rather than the total effect. The frontdoor adjustment method is typically used in situations where the mediator is easier to measure or manipulate than the confounding variable, or where the confounding variable cannot be measured directly.
Note that to estimate the causal effect of treatment on outcome, you'll need at least two models; a model of the effect of the treatment on the mediator, and a model of the effect of the mediator on the outcome. For example, two stage regression.
Check out this video by Brady Neal to understand how the frontdoor criterion produces an adjustment set:
https://www.youtube.com/watch?v=-kWocwaXqlk
In some circumstances, you might have only an Instrumental Variables Estimand. For example, if you have an unobserved confounding variable which directly affects both the treatment and outcome.
In this case it is not correct to speak of an Adjustment Set; instead, you have one or more Instrumental Variables, which are displayed in the graph. You can use an Instrumental Variable method to create a model which uses these Instrumental Variables. The model will estimate (i.e. predict) the causal effect of Treatment on Outcome.
In summary, backdoor adjustment involves controlling for a confounding variable to estimate the causal effect, while frontdoor adjustment involves controlling for a mediator variable that lies on the causal pathway. An Adjustment Set is a set of variables which must be controlled for.