Dose–response with average potential outcomes (DoubleML APO)
@misc{doubleml,
title = {DoubleML},
author = {Bach and Chernozhukov and Kurz and Spindler},
howpublished = {\url{https://docs.doubleml.org/}},
note = {Software / documentation}
}Follow the analysis.
Select a node to explore the method
Declare the multi-valued treatment
Data preparation — shapes the raw inputs into what the estimator expects.
Set up DoubleMLData with the dose as the treatment.
dml_data = dml.DoubleMLData(df, y_col='y', d_cols='d', x_cols=X)
Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.
Questions to explore- Which assumption matters most here, and what evidence could challenge it?
- What would you check before passing this output to the next step?
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Peer discussion
- Bring your experience, a question, or a different perspective.
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Average potential outcome at each level
The core estimate — where the causal quantity itself is computed.
An orthogonal APO per dose level, cross-fitted with ML nuisances.
apo = dml.DoubleMLAPOS(dml_data, ml_g, ml_m, treatment_levels=levels).fit()
Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.
Questions to explore- Which assumption matters most here, and what evidence could challenge it?
- What would you check before passing this output to the next step?
Choose a question to start your comment.
Peer discussion
- Bring your experience, a question, or a different perspective.
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Contrasts between doses
Uncertainty quantification — standard errors, intervals, and aggregation.
Differences of APOs give causal effects of moving from one dose to another.
apo.causal_contrast(reference_levels=0)
Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.
Questions to explore- Which assumption matters most here, and what evidence could challenge it?
- What would you check before passing this output to the next step?
Choose a question to start your comment.
Peer discussion
- Bring your experience, a question, or a different perspective.
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Plot the dose–response curve
Reporting — turn the numbers into a figure or table a reader can act on.
E[Y(d)] across the treatment range, with confidence bands.
# dose on x, APO on y, with CIs
Before using this step, make its assumptions and its output explicit. A useful peer note explains what you would check, what could go wrong, or what would change your interpretation.
Questions to explore- Which assumption matters most here, and what evidence could challenge it?
- What would you check before passing this output to the next step?
Choose a question to start your comment.
Peer discussion
- Bring your experience, a question, or a different perspective.
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Inputs & data
Outcome Y, a multi-valued / continuous treatment D (the dose), and covariates X.
Show data format & exampleHide example
Format — one row per unit: outcome y, dose d, covariates X.
y d x1 x2
2.1 0 0.4 -1.1
3.4 2 -0.1 0.6
1.8 1 1.2 0.3
![Average potential outcome E[Y(d)] estimated at each treatment level.](/static/img/figure-cache/doubleml/examples_py_double_ml_apo_14_0.cdbf95247ff4.png)
Figures reproduced from DoubleML — Bach, Chernozhukov, Kurz & Spindler — unofficial community showcase; all credit to the original authors.
⚠️ Unofficial community showcase of a DoubleML example. Not affiliated with the authors; figures are from the public documentation. All credit to Bach, Chernozhukov, Kurz & Spindler.
For a multi-valued or continuous treatment: estimate E[Y(d)] at each dose and the contrasts between them, all cross-fitted.
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