Local Distribution Estimators

This page documents local distribution treatment effect estimators that compute treatment effects weighted by treatment propensity within each stratum. These estimators are particularly useful for handling treatment assignment heterogeneity across strata.

SimpleLocalDistributionEstimator

class dte_adj.SimpleLocalDistributionEstimator[source]

Bases: SimpleStratifiedDistributionEstimator

A class for computing Local Distribution Treatment Effects (LDTE) and Local Probability Treatment Effects (LPTE) using simple empirical estimation.

This estimator computes treatment effects that are weighted by treatment propensity within each stratum, providing estimates that are locally robust to treatment assignment heterogeneity across strata. It uses empirical methods without ML adjustment.

fit(covariates: ndarray, treatment_arms: ndarray, treatment_indicator: ndarray, outcomes: ndarray, strata: ndarray) → SimpleLocalDistributionEstimator[source]

Train the SimpleLocalDistributionEstimator.

Parameters:

  • covariates (np.ndarray) – Pre-treatment covariates.

  • treatment_arms (np.ndarray) – Treatment assignment variable (Z).

  • treatment_indicator (np.ndarray) – Treatment indicator variable (D).

  • outcomes (np.ndarray) – Scalar-valued observed outcome.

  • strata (np.ndarray) – Stratum indicators.

Returns:

The fitted estimator.

Return type:

SimpleLocalDistributionEstimator

predict_ldte(target_treatment_arm: int, control_treatment_arm: int, locations: ndarray, alpha: float = 0.05) → Tuple[ndarray, ndarray, ndarray][source]

Compute Local Distribution Treatment Effects (LDTE).

LDTE measures the difference in cumulative distribution functions between treatment groups weighted by treatment propensity within each stratum. This provides estimates that are locally robust to treatment assignment heterogeneity across strata.

Parameters:

  • target_treatment_arm (int) – The index of the treatment arm of the treatment group.

  • control_treatment_arm (int) – The index of the treatment arm of the control group.

  • locations (np.ndarray) – Scalar values to be used for computing the cumulative distribution.

  • alpha (float, optional) – Significance level of the confidence bound. Defaults to 0.05.

Returns:

A tuple containing:

  • Expected LDTEs (np.ndarray): Local treatment effect estimates at each location

  • Lower bounds (np.ndarray): Lower confidence interval bounds

  • Upper bounds (np.ndarray): Upper confidence interval bounds

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

Example

import numpy as np
from sklearn.linear_model import LogisticRegression
from dte_adj import AdjustedLocalDistributionEstimator

# Generate sample data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)  # Binary strata
D = np.random.binomial(1, 0.3 + 0.4 * strata, 1000)  # Treatment depends on strata
Y = X[:, 0] + 2 * D + strata + np.random.randn(1000)

# Fit local estimator
base_model = LogisticRegression()
estimator = AdjustedLocalDistributionEstimator(base_model)
estimator.fit(X, D, D, Y, strata)  # treatment_arms = treatment_indicator for binary case

# Compute LDTE
locations = np.linspace(Y.min(), Y.max(), 20)
ldte, lower, upper = estimator.predict_ldte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"LDTE shape: {ldte.shape}")  # Should match locations.shape
print(f"Average LDTE: {ldte.mean():.3f}")
predict_lpte(target_treatment_arm: int, control_treatment_arm: int, locations: ndarray, alpha: float = 0.05) → Tuple[ndarray, ndarray, ndarray][source]

Compute Local Probability Treatment Effects (LPTE).

LPTE measures the difference in probability mass between treatment groups for intervals defined by consecutive location pairs, weighted by treatment propensity within each stratum. This provides locally robust estimates of treatment effects on interval probabilities.

Parameters:

  • target_treatment_arm (int) – The index of the treatment arm of the treatment group.

  • control_treatment_arm (int) – The index of the treatment arm of the control group.

  • locations (np.ndarray) – Scalar values defining interval boundaries for probability computation. For each interval (locations[i], locations[i+1]], the LPTE is computed.

  • alpha (float, optional) – Significance level of the confidence bound. Defaults to 0.05.

Returns:

A tuple containing:

  • Expected LPTEs (np.ndarray): Local treatment effect estimates for each interval, shape (len(locations)-1,)

  • Lower bounds (np.ndarray): Lower confidence interval bounds

  • Upper bounds (np.ndarray): Upper confidence interval bounds

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

Example

import numpy as np
from dte_adj import SimpleLocalDistributionEstimator

# Generate sample data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)  # Binary strata
Z = np.random.binomial(1, 0.5, 1000)  # Treatment assignment
D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)  # Treatment receipt
Y = X[:, 0] + 2 * D + strata + np.random.randn(1000)

# Fit local estimator
estimator = SimpleLocalDistributionEstimator()
estimator.fit(X, Z, D, Y, strata)

# Define interval boundaries
locations = np.array([-2, -1, 0, 1, 2])  # Creates intervals: (-2,-1], (-1,0], (0,1], (1,2]

# Compute LPTE
lpte, lower, upper = estimator.predict_lpte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"LPTE shape: {lpte.shape}")  # Should be (4,) for 4 intervals
print(f"Interval effects: {lpte}")

AdjustedLocalDistributionEstimator

class dte_adj.AdjustedLocalDistributionEstimator(base_model: Any, folds=3, is_multi_task=False)[source]

Bases: AdjustedStratifiedDistributionEstimator

A class for computing Local Distribution Treatment Effects (LDTE) and Local Probability Treatment Effects (LPTE) using machine learning adjustment.

This estimator combines the benefits of ML adjustment with local treatment effect estimation, providing precise estimates of treatment effects that are weighted by treatment propensity within each stratum. It uses cross-fitting to avoid overfitting issues.

fit(covariates: ndarray, treatment_arms: ndarray, treatment_indicator: ndarray, outcomes: ndarray, strata: ndarray) → AdjustedLocalDistributionEstimator[source]

Train the AdjustedLocalDistributionEstimator.

Parameters:

  • covariates (np.ndarray) – Pre-treatment covariates.

  • treatment_arms (np.ndarray) – Treatment assignment variable (Z).

  • treatment_indicator (np.ndarray) – Treatment indicator variable (D).

  • outcomes (np.ndarray) – Scalar-valued observed outcome.

  • strata (np.ndarray) – Stratum indicators.

Returns:

The fitted estimator.

Return type:

AdjustedLocalDistributionEstimator

predict_ldte(target_treatment_arm: int, control_treatment_arm: int, locations: ndarray, alpha: float = 0.05) → Tuple[ndarray, ndarray, ndarray][source]

Compute Local Distribution Treatment Effects (LDTE) using ML adjustment.

This method combines machine learning adjustment with local treatment effect estimation to provide precise, locally robust estimates of distributional treatment effects.

Parameters:

  • target_treatment_arm (int) – The index of the treatment arm of the treatment group.

  • control_treatment_arm (int) – The index of the treatment arm of the control group.

  • locations (np.ndarray) – Scalar values to be used for computing the cumulative distribution.

  • alpha (float, optional) – Significance level of the confidence bound. Defaults to 0.05.

Returns:

A tuple containing:

  • Expected LDTEs (np.ndarray): Local treatment effect estimates at each location

  • Lower bounds (np.ndarray): Lower confidence interval bounds

  • Upper bounds (np.ndarray): Upper confidence interval bounds

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

Example

import numpy as np
from sklearn.ensemble import RandomForestClassifier
from dte_adj import AdjustedLocalDistributionEstimator

# Generate confounded data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)
# Treatment assignment depends on covariates
Z_prob = 1 / (1 + np.exp(-(X[:, 0] + X[:, 1] + strata)))
Z = np.random.binomial(1, Z_prob, 1000)
D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)
Y = X.sum(axis=1) + 2 * D + strata + np.random.randn(1000)

# Fit adjusted local estimator
base_model = RandomForestClassifier(n_estimators=100)
estimator = AdjustedLocalDistributionEstimator(base_model, folds=3)
estimator.fit(X, Z, D, Y, strata)

# Compute LDTE with ML adjustment
locations = np.linspace(Y.min(), Y.max(), 20)
ldte, lower, upper = estimator.predict_ldte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"Adjusted LDTE: {ldte.mean():.3f}")
predict_lpte(target_treatment_arm: int, control_treatment_arm: int, locations: ndarray, alpha: float = 0.05) → Tuple[ndarray, ndarray, ndarray][source]

Compute Local Probability Treatment Effects (LPTE) using ML adjustment.

This method combines machine learning adjustment with local treatment effect estimation to provide precise estimates of treatment effects on interval probabilities.

Parameters:

  • target_treatment_arm (int) – The index of the treatment arm of the treatment group.

  • control_treatment_arm (int) – The index of the treatment arm of the control group.

  • locations (np.ndarray) – Scalar values defining interval boundaries for probability computation. For each interval (locations[i], locations[i+1]], the LPTE is computed.

  • alpha (float, optional) – Significance level of the confidence bound. Defaults to 0.05.

Returns:

A tuple containing:

  • Expected LPTEs (np.ndarray): Local treatment effect estimates for each interval, shape (len(locations)-1,)

  • Lower bounds (np.ndarray): Lower confidence interval bounds

  • Upper bounds (np.ndarray): Upper confidence interval bounds

Return type:

Tuple[np.ndarray, np.ndarray, np.ndarray]

Example

import numpy as np
from sklearn.linear_model import LogisticRegression
from dte_adj import AdjustedLocalDistributionEstimator

# Generate confounded data with strata
np.random.seed(42)
X = np.random.randn(1000, 5)
strata = np.random.choice([0, 1], size=1000)
# Treatment assignment depends on covariates
Z_prob = 1 / (1 + np.exp(-(X[:, 0] + strata)))
Z = np.random.binomial(1, Z_prob, 1000)
D = np.random.binomial(1, 0.3 + 0.4 * Z, 1000)
Y = X.sum(axis=1) + 2 * D + strata + np.random.randn(1000)

# Fit adjusted local estimator
base_model = LogisticRegression()
estimator = AdjustedLocalDistributionEstimator(base_model, folds=3)
estimator.fit(X, Z, D, Y, strata)

# Define interval boundaries
locations = np.array([-2, -1, 0, 1, 2])

# Compute LPTE with ML adjustment
lpte, lower, upper = estimator.predict_lpte(
    target_treatment_arm=1,
    control_treatment_arm=0,
    locations=locations
)

print(f"Adjusted LPTE: {lpte}")