Propensity score

As explained in Causal AI

A propensity score is a function of observed covariates representing the probability or treatment-predictive summary associated with receiving a treatment.

A propensity score summarizes how likely a subject is to receive a treatment given observed confounders. Traditionally, it is the conditional treatment probability, often fitted with logistic regression. More broadly, a learned function can compress the confounders’ influence while making them conditionally independent of treatment. section 11.4.2

Figure 11.10 The propensity score is a compression of the causal influence of the common causes in the backdoor adjustment set.

The figure visualizes propensity scores as a compression of common causes in a backdoor adjustment set. section 11.4.2

Use the score to reduce adjustment over many confounders when estimating a backdoor causal effect:

• Stratification groups observations into propensity-score subsets and adjusts across the resulting strata. section 11.4.2
• Matching pairs individuals with similar propensity scores before comparing treatment outcomes. section 11.4.2
• Weighting applies inverse-probability weights to construct the causal comparison. section 11.4.2

Online gaming treatment model

For high Side-Quest Engagement, estimate each player’s propensity from Guild Membership, Time Spent Playing, and Player Skill Level. DoWhy can then estimate an ATE using propensity-score stratification, matching, or weighting. section 11.4.2 section 11.7

How Causal AI covers it

How deep it goes

Defines probability and function forms, explains dimensionality reduction, and names matching, stratification, and weighting methods.

Examples

Uses an online gaming example involving engagement, guild membership, play time, and player skill.

What it assumes

Assumes a causal model, a valid backdoor adjustment set, and identified causal estimands before estimation.

What you can do after

Apply it via DoWhy using propensity-score stratification, matching, or inverse-probability weighting for ATE estimation.

How it connects

Connects propensity scores to confounding, backdoor adjustment, causal effects, logistic regression, matching, stratification, and inverse probability weighting.

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Also explained in

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  Causal Inference for Data ScienceA propensity score is the conditional probability that a unit receives a treatment given its observed covariates.

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Related concepts

• positivity assumptionuses · The positivity assumption is the condition that every treatment has a nonzero and non-unit probability of being assigned at every confounder value that occurs in the population.
• average treatment effect estimationuses · Average treatment effect estimation quantifies the population-average difference in outcomes that would result from two alternative treatments or interventions.
• propensity score methodused by · A propensity-score method is a causal-inference technique that estimates treatment effects by matching, weighting, stratifying, or otherwise adjusting units according to their observed treatment probabilities.
• machine learninguses · Machine learning is a field of computational methods in which systems learn patterns or relationships from data to make predictions, decisions, or other outputs.
• causal adjustmentused by · Causal adjustment estimates a causal effect by conditioning on variables that block noncausal pathways and averaging over their target-population distribution.
• backdoor pathaddresses · A backdoor path is a path between a putative cause and an outcome that begins with an arrow into the cause and can create a noncausal association.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.