ACE estimations from real observational data

This notebook serves as a demonstration of the CausalEffectEstimation module for estimating causal effects on both generated and real datasets.

import pyagrum as gum
import pyagrum.lib.discretizer as disc
import pyagrum.lib.notebook as gnb
import pyagrum.explain as gexpl

import pyagrum.causal as csl
import pyagrum.causal.notebook as cslnb

import pandas as pd
import matplotlib.pyplot as plt

In this example, we show how to estimate the ACE (Average Causal Effect) using real data that does not adhere to RCT conditions.

Dataset

The dataset under consideration is the Census Adult Income dataset. The objective of this analysis is to determine whether possessing a graduate degree increases the likelihood of earning an income exceeding $50,000 per year.

df = pd.read_pickle("./res/df_causal_discovery.p")
df = df.rename(columns={"hours-per-week": "hoursPerWeek"})
df.describe()

	age	hoursPerWeek	hasGraduateDegree	inRelationship	isWhite	isFemale	greaterThan50k
count	29170.000000	29170.000000	29170.000000	29170.000000	29170.000000	29170.000000	29170.000000
mean	38.655674	40.447755	0.052348	0.406616	0.878334	0.331916	0.245835
std	13.722408	12.417203	0.222732	0.491211	0.326905	0.470909	0.430588
min	17.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	28.000000	40.000000	0.000000	0.000000	1.000000	0.000000	0.000000
50%	37.000000	40.000000	0.000000	0.000000	1.000000	0.000000	0.000000
75%	48.000000	45.000000	0.000000	1.000000	1.000000	1.000000	0.000000
max	90.000000	99.000000	1.000000	1.000000	1.000000	1.000000	1.000000

Setup

We begin by focusing exclusively on the age covariate to inform our estimations. We hypothesize that age is a causal factor influencing both the hasGraduateDegree variable and the greaterThan50k outcome.

discretizer = disc.Discretizer(defaultDiscretizationMethod="NoDiscretization", defaultNumberOfBins=None)
template = discretizer.discretizedTemplate(df[["age", "hasGraduateDegree", "greaterThan50k"]])
template.addArcs([("age", "hasGraduateDegree"), ("age", "greaterThan50k"), ("hasGraduateDegree", "greaterThan50k")])

causal_model = csl.CausalModel(template)

cslnb.showCausalModel(causal_model, size="50")

T = "hasGraduateDegree"
Y = "greaterThan50k"
X = "age"

cee = csl.CausalEffectEstimation(df, causal_model)

Causal Identification

cee.identifyAdjustmentSet(intervention=T, outcome=Y)

Backdoor adjustment found.

Supported estimators include:
- CausalModelEstimator
- SLearner
- TLearner
- XLearner
- PStratification
- IPW





'Backdoor'

Causal Estimation

cee.fitCausalBNEstimator()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.2332334047559898

cee.fitSLearner()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.29760513570330316

cee.fitIPW()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.29038491617382495

Incorporating covariates and Unknown Adjustment

Let’s examine whether incorporating all available covariates influences the estimation of the ACE. We will employ structure learning techniques to determine the DAG that the algorithm identifies from the data.

discretizer = disc.Discretizer(defaultNumberOfBins=5, defaultDiscretizationMethod="uniform")
template = discretizer.discretizedTemplate(df)

structure_learner = gum.BNLearner(df, template)
## we help the learning algorithm by giving it some causal constraints
structure_learner.setSliceOrder(
  [["isWhite", "isFemale"], ["age"], ["hasGraduateDegree", "inRelationship", "hoursPerWeek"]]
)
structure_learner.addNoParentNode("isWhite")
structure_learner.addNoParentNode("isFemale")
structure_learner.useNMLCorrection()
structure_learner.useSmoothingPrior(1e-6)

learned_bn = structure_learner.learnBN()

causal_model = csl.CausalModel(learned_bn)

gnb.sideBySide(gexpl.getInformation(learned_bn, size="50"))

cee = csl.CausalEffectEstimation(df, causal_model)

cee.identifyAdjustmentSet(intervention=T, outcome=Y)

Backdoor adjustment found.

Supported estimators include:
- CausalModelEstimator
- SLearner
- TLearner
- XLearner
- PStratification
- IPW





'Backdoor'

In this scenario, no adjustment set is available for causal inference:

• This is not a randomized controlled trial (RCT) due to the presence of a backdoor path from hasGraduateDegree to greaterThan50k, which traverses through age and inRelationship.
• The backdoor criterion is not met, as every node is a descendant of the intervention variable hasGraduateDegree.
• The (Generalized) Frontdoor criterion is not applicable due to the absence of mediator variables.
• There are no (Generalized) Instrumental Variables, as hasGraduateDegree lacks any ancestors in the causal graph.

Consequently, the causal effect can only be estimated using the CausalBNEstimator, provided that the causal effect of the intervention on the outcome is identifiable through do-calculus.

cee.fitCausalBNEstimator()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.24151595674049395

We observe a stronger Causal Effect within the previously defined causal structure.

User specified adjustment

Alternatively, it is possible to manually specify an adjustment set. However, it is important to note that this approach does not guarantee an asymptotically unbiased estimator.

cee.useBackdoorAdjustment(T, Y, {"age", "inRelationship"})

cee.fitSLearner()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.2860493646590411

cee.fitTLearner()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.2749304594008821

cee.fitIPW()
tau_hat = cee.estimateCausalEffect()

print(f"ACE = {tau_hat}")

ACE = 0.2713082028700332

We obtain more consistent results when specifying the backdoor adjustment using a selected subset of covariates.

CACE estimations

To estimate the Conditional Average Causal Effect (CACE) using CausalEffectEstimation, pandas query strings can be utilized to specify the relevant conditions. Additionally, the Individual Causal Effect (ICE) can be estimated by providing a pandas.DataFrame containing the features of the individual units.

cee.fitTLearner()
tau_hat0 = cee.estimateCausalEffect(conditional="inRelationship == 0")
tau_hat1 = cee.estimateCausalEffect(conditional="inRelationship == 1")

print(f"CACE (inRelationship == 0) = {tau_hat0}")
print(f"CACE (inRelationship == 1) = {tau_hat1}")

CACE (inRelationship == 0) = 0.22769492525672883
CACE (inRelationship == 1) = 0.34386224091181283

cee.fitTLearner()
tau_hat0 = cee.estimateCausalEffect(conditional="isFemale == 0")
tau_hat1 = cee.estimateCausalEffect(conditional="isFemale == 1")

print(f"CACE (isFemale == 0) = {tau_hat0}")
print(f"CACE (isFemale == 1) = {tau_hat1}")

CACE (isFemale == 0) = 0.2983895058122265
CACE (isFemale == 1) = 0.22771192020812456

cee.fitTLearner()
changes = sorted(df["age"].unique())
booking = list()

for i in changes:
  tau_hat = cee.estimateCausalEffect(conditional=f"age <= {i}")
  booking.append(tau_hat)

plt.plot(changes, booking)
plt.title("CACE with \n(age <= x) as Conditional")
plt.xlabel("age")
plt.ylabel("CACE")
plt.show()

cee.fitTLearner()
changes = sorted(df["hoursPerWeek"].unique())
booking = list()

for i in changes:
  tau_hat = cee.estimateCausalEffect(conditional=f"hoursPerWeek <= {i}")
  booking.append(tau_hat)

plt.plot(changes, booking)
plt.title("CACE with \n(hoursPerWeek <= x) as Conditional")
plt.xlabel("hoursPerWeek")
plt.ylabel("CACE")
plt.show()