GuidesEstimate an average effect

Estimate an average effect

Write down which variables confound a treatment and an outcome, then estimate the average effect with an interval. The example measures what smoking during pregnancy does to birthweight.

Run the program#

The bundled birthweight data is the extract of US natality records used by Cattaneo (2010): 4,642 singleton births in Pennsylvania, with the mother's smoking, the baby's weight in grams and 17 background variables.

from ergodic import dag, estimate_effect
from ergodic.datasets import load_birthweight

# 1. Load 4,642 births: the mother's smoking, the birthweight and 17 confounders.
births = load_birthweight()
smoking, weight = births.treatment, births.outcome
print(smoking, "->", weight, "with", len(births.confounders), "confounders")

# 2. Draw the graph: each confounder affects both smoking and birthweight.
edges = [f"{c} -> {smoking}" for c in births.confounders]
edges += [f"{c} -> {weight}" for c in births.confounders]
graph = dag([*edges, f"{smoking} -> {weight}"])

# 3. Compare the raw difference in mean birthweight.
rows = births.data.to_pandas()
means = rows.groupby(smoking, observed=True)[weight].mean()
print(f"raw difference: {means['smoker'] - means['nonsmoker']:.1f} g")

# 4. Estimate the average effect, adjusting for the confounders.
estimate = estimate_effect(
    graph, births.data, smoking, weight, treated=births.treated, random_state=0
)
print(estimate)
low, high = estimate.interval()
print(f"95% interval: {low:.0f} g to {high:.0f} g")

mbsmoke -> bweight with 17 confounders
raw difference: -275.3 g
EffectEstimate(aipw, analytic: ate=-222.3, se=25.8, 95% CI [-273, -172], n=4642)
95% interval: -273 g to -172 g

• Babies of smokers weigh 275 g less on average. Part of that gap comes from the confounders, not from smoking.
• Adjusted for the confounders, smoking lowers birthweight by about 222 g. The 95% interval runs from 273 g to 172 g lower. The Stata treatment-effects manual's doubly robust estimate on the same extract is −231 g (standard error 26 g), well inside that interval; births.target records it with its source.
• aipw is the augmented inverse-probability-weighted estimator. It combines an outcome model and a propensity model, and stays consistent if either one is right.

Draw the graph#

The graph is your assumption about the world. Each confounder points at both the treatment and the outcome:

edges = [f"{c} -> {smoking}" for c in births.confounders]
edges += [f"{c} -> {weight}" for c in births.confounders]
graph = dag([*edges, f"{smoking} -> {weight}"])

estimate_effect reads the adjustment set from this graph. You never pass the confounders to it directly.

Choose the treated level#

treated= names the level that counts as treatment. Here the mbsmoke column holds "smoker" and "nonsmoker", and births.treated is "smoker". The estimate is the mean outcome if everyone were treated minus the mean if no one were.

By default the propensity model is logistic regression. The outcome model is ordinary least squares for a continuous outcome, as here, and logistic regression for a binary one. Pass learner= (an alias, a learner, or a mapping from slot to learner) to use other models.

Next steps#