From 26b5af5ffb918bb9c1637be1bd5c42ad8facec65 Mon Sep 17 00:00:00 2001 From: okiner-3 Date: Tue, 14 Oct 2025 16:51:33 +0900 Subject: [PATCH 1/3] add a tutlial for oregon health insurance experiment --- docs/source/_static/oregon_dte.png | Bin 0 -> 66312 bytes docs/source/_static/oregon_dte_control.png | Bin 0 -> 32400 bytes docs/source/_static/oregon_dte_strata.png | Bin 0 -> 209356 bytes docs/source/_static/oregon_dte_visits.png | Bin 0 -> 32781 bytes docs/source/_static/oregon_pte.png | Bin 0 -> 41287 bytes docs/source/_static/oregon_pte_control.png | Bin 0 -> 25389 bytes docs/source/_static/oregon_pte_visits.png | Bin 0 -> 19175 bytes docs/source/tutorials.rst | 1 + docs/source/tutorials/oregon.rst | 562 +++++++++++++++++++++ 9 files changed, 563 insertions(+) create mode 100644 docs/source/_static/oregon_dte.png create mode 100644 docs/source/_static/oregon_dte_control.png create mode 100644 docs/source/_static/oregon_dte_strata.png create mode 100644 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of the ``dte_adj`` library using real-world datasets from famous randomized experiments. Each tutorial provides complete code examples, visualizations, and interpretations of distributional treatment effects. diff --git a/docs/source/tutorials/oregon.rst b/docs/source/tutorials/oregon.rst new file mode 100644 index 0000000..b162020 --- /dev/null +++ b/docs/source/tutorials/oregon.rst @@ -0,0 +1,562 @@ +Oregon Health Insurance Experiment +==================================== + +The Oregon Health Insurance Experiment is a landmark randomized controlled trial conducted in 2008, where approximately 24,000 low-income adults were randomly assigned to either receive the opportunity to enroll in Medicaid (treatment group) or remain uninsured (control group). This unique natural experiment allows us to examine how public health insurance affects healthcare utilization and costs across the entire distribution. + +**Background**: Due to budget constraints, Oregon decided to expand its Medicaid program through a lottery system, randomly selecting eligible individuals for enrollment opportunities. This created a rare natural experiment that enables rigorous causal evaluation of Medicaid's effects on healthcare utilization and outcomes. + +**Research Question**: How does Medicaid enrollment affect healthcare utilization (emergency department visits and costs), and how do these effects vary across the entire distribution of healthcare outcomes? + +Data Setup and Loading +~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + import numpy as np + import pandas as pd + import matplotlib.pyplot as plt + import os + from sklearn.linear_model import LinearRegression + from sklearn.preprocessing import LabelEncoder + import dte_adj + from dte_adj.plot import plot + + # Load the Oregon Health Insurance Experiment dataset + base_path = "OHIE_Public_Use_Files/OHIE_Data" + df_descriptive = pd.read_stata(os.path.join(base_path, "oregonhie_descriptive_vars.dta")) + df_ed = pd.read_stata(os.path.join(base_path, "oregonhie_ed_vars.dta")) + df_inp = pd.read_stata(os.path.join(base_path, "oregonhie_inperson_vars.dta")) + df_state = pd.read_stata(os.path.join(base_path, "oregonhie_stateprograms_vars.dta")) + + # Merge all datasets + df = ( + df_descriptive + .merge(df_ed, on='person_id', how='inner') + .merge(df_inp, on='person_id', how='left') + .merge(df_state, on='person_id', how='inner') + ) + + print(f"Dataset shape: {df.shape}") + print(f"Average num_visit_cens_ed by enrollment:\n{df.groupby('ohp_all_ever_inperson')['num_visit_cens_ed'].mean()}") + print(f"Average ed_charg_tot_ed by enrollment:\n{df.groupby('ohp_all_ever_inperson')['ed_charg_tot_ed'].mean()}") + + # Prepare the data for dte_adj analysis + # Create treatment indicator: 0=Not enrolled, 1=Enrolled + treatment_mapping = {'NOT enrolled': 0, 'Enrolled': 1} + df['D'] = df['ohp_all_ever_inperson'].map(treatment_mapping).astype(float).fillna(-1).astype(int) + + # Use emergency department costs and visits as outcome variables + df['Y_ED_CHARG_TOT_ED'] = df['ed_charg_tot_ed'].fillna(0) + df['Y_NUM_VISIT_CENS_ED'] = df['num_visit_cens_ed'].fillna(0) + + # Create feature mappings for categorical variables + covariate_mapping = {'Not selected': 0, 'Selected': 1} + gender_mapping = {'Male': 0, 'Female': 1, 'Transgender F to M': 2, 'Transgender M to F': 3} + health_last12_mapping = {'1: Very poor': 1, '2: Poor': 2, '3: Fair': 3, '4: Good': 4, '5: Very good': 5, '6: Excellent': 6} + edu_mapping = {'HS diploma or GED': 0, 'Post HS, not 4-year': 1, 'Less than HS': 2, '4 year degree or more': 3} + + # Create control variables + df['W'] = df['treatment'].map(covariate_mapping).astype(float).fillna(-1).astype(int) + df['age'] = 2008 - df['birthyear_list'] + df['gender_inp'] = df['gender_inp'].map(gender_mapping).astype(float).fillna(-1).astype(int) + df['health_last12_inp'] = df['health_last12_inp'].map(health_last12_mapping).astype(float).fillna(-1).astype(int) + df['edu_inp'] = df['edu_inp'].map(edu_mapping).astype(float).fillna(-1).astype(int) + + # Select control variables: pre-randomization ED utilization variables + ctrl_cols = [col for col in df_ed.columns if 'pre' in col and 'num' in col] + ctrl_cols.append('charg_tot_pre_ed') + selected_cols = ['person_id', 'numhh_list', 'Y_NUM_VISIT_CENS_ED', 'Y_ED_CHARG_TOT_ED', 'D', 'W'] + ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp'] + df = df[selected_cols] + df = df[df.isna().any(axis=1) == False] + + # Create feature matrix + features = pd.DataFrame(df[['W'] + ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp']]) + X = features.values + + D = df['D'].values + Y_ED_CHARG_TOT_ED = df['Y_ED_CHARG_TOT_ED'].values + Y_NUM_VISIT_CENS_ED = df['Y_NUM_VISIT_CENS_ED'].values + + print(f"\nDataset size: {len(D):,} people") + print(f"Control group (Not enrolled): {(D==0).sum():,} ({(D==0).mean():.1%})") + print(f"Treatment group (Enrolled): {(D==1).sum():,} ({(D==1).mean():.1%})") + print("Average Outcome by Treatment:") + print(f"Not enrolled: {Y_NUM_VISIT_CENS_ED[D==0].mean():.2f} visits, ${Y_ED_CHARG_TOT_ED[D==0].mean():.2f} in ED costs") + print(f"Enrolled: {Y_NUM_VISIT_CENS_ED[D==1].mean():.2f} visits, ${Y_ED_CHARG_TOT_ED[D==1].mean():.2f} in ED costs") + +Emergency Department Cost Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + # Initialize estimators + simple_estimator = dte_adj.SimpleDistributionEstimator() + ml_estimator = dte_adj.AdjustedDistributionEstimator( + LinearRegression(), + folds=5 + ) + + # Fit estimators on the full dataset + simple_estimator.fit(X, D, Y_ED_CHARG_TOT_ED) + ml_estimator.fit(X, D, Y_ED_CHARG_TOT_ED) + + # Define evaluation points for emergency department costs + outcome_ed_costs_locations = np.linspace(Y_ED_CHARG_TOT_ED.min(), Y_ED_CHARG_TOT_ED.max(), 100) + +Distribution Treatment Effects: Medicaid Enrollment vs Control +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +First, let's examine how Medicaid enrollment affects the distribution of emergency department costs: + +.. code-block:: python + + # Compute DTE: Enrolled vs Not enrolled + dte_ctrl, lower_ctrl, upper_ctrl = simple_estimator.predict_dte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=outcome_ed_costs_locations, + variance_type="moment" + ) + + # Visualize Enrolled vs Control using dte_adj's plot function + plot(outcome_ed_costs_locations, dte_ctrl, lower_ctrl, upper_ctrl, + title="Medicaid Enrollment vs Control (Emergency Department Costs)", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect") + +.. image:: ../_static/oregon_dte_control.png + :alt: Oregon Health Insurance Experiment vs Control Analysis + :width: 500px + :align: center + +Probability Treatment Effects: Cost Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Let's also examine how Medicaid enrollment affects the probability of incurring specific ranges of emergency department costs using Probability Treatment Effects (PTE): + +.. code-block:: python + + # Compute PTE: Enrolled vs Not enrolled + pte_ctrl, pte_lower_ctrl, pte_upper_ctrl = simple_estimator.predict_pte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=[-1] + outcome_ed_costs_locations, + variance_type="moment" + ) + + fig, ax = plt.subplots(figsize=(10, 6)) + + # Visualize PTE results using dte_adj's plot function with bar charts + plot(outcome_ed_costs_locations[1:], pte_ctrl, pte_lower_ctrl, pte_upper_ctrl, + chart_type="bar", + title="Medicaid Enrollment vs Control", + xlabel="Emergency Department Costs ($)", ylabel="Probability Treatment Effect", + ax=ax) + + plt.tight_layout() + plt.show() + +.. image:: ../_static/oregon_pte_control.png + :alt: Oregon Health Insurance Experiment vs Control PTE Analysis + :width: 800px + :align: center + +Estimator Comparison: Simple vs ML-Adjusted +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Let's compare the results from both simple and machine learning-adjusted estimators to examine the robustness of our findings: + +.. code-block:: python + + # Compute DTE with both estimators + dte_simple, lower_simple, upper_simple = simple_estimator.predict_dte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=outcome_ed_costs_locations, + variance_type="moment" + ) + + dte_ml, lower_ml, upper_ml = ml_estimator.predict_dte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=outcome_ed_costs_locations, + variance_type="moment" + ) + + # Visualize the distribution treatment effects using dte_adj's built-in plot function + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) + + # Simple estimator + plot(outcome_ed_costs_locations, dte_simple, lower_simple, upper_simple, + title="Medicaid Enrollment vs Control (Simple Estimator)", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", + color="purple", + ax=ax1) + + # ML-adjusted estimator + plot(outcome_ed_costs_locations, dte_ml, lower_ml, upper_ml, + title="Medicaid Enrollment vs Control (ML-Adjusted Estimator)", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", + ax=ax2) + + plt.tight_layout() + plt.show() + +The analysis produces the following distribution treatment effects visualization: + +.. image:: ../_static/oregon_dte.png + :alt: Oregon Health Insurance Experiment DTE Analysis + :width: 800px + :align: center + +**DTE Interpretation**: The positive DTE values indicate that Medicaid enrollment increases the cumulative probability of individuals having emergency department costs at or below each threshold compared to those not enrolled. This suggests that while Medicaid increases overall ED utilization, it may also help contain costs for some individuals. + +**Statistical Significance**: Both simple and ML-adjusted estimators show similar patterns, providing robust evidence that Medicaid enrollment has significant distributional effects on emergency department costs. The confidence intervals indicate that these effects are statistically significant across most cost levels. + +**Healthcare Access Implications**: The DTE analysis reveals that Medicaid enrollment affects the entire distribution of emergency department costs, not just the average. This provides insights into how public health insurance impacts healthcare utilization patterns across different cost categories. + +Cost Analysis with PTE +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + # Compute Probability Treatment Effects + pte_simple, pte_lower_simple, pte_upper_simple = simple_estimator.predict_pte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=[-1] + outcome_ed_costs_locations, + variance_type="moment" + ) + + pte_ml, pte_lower_ml, pte_upper_ml = ml_estimator.predict_pte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=[-1] + outcome_ed_costs_locations, + variance_type="moment" + ) + + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) + + # Simple estimator + plot(outcome_ed_costs_locations[1:], pte_simple, pte_lower_simple, pte_upper_simple, + chart_type="bar", + title="Effects of Emergency Department Costs (Simple Estimator)", + xlabel="Emergency Department Costs ($)", ylabel="Probability Treatment Effect", color="purple", + ax=ax1) + + # ML-adjusted estimator + plot(outcome_ed_costs_locations[1:], pte_ml, pte_lower_ml, pte_upper_ml, + chart_type="bar", + title="Effects of Emergency Department Costs (ML-Adjusted Estimator)", + xlabel="Emergency Department Costs ($)", ylabel="Probability Treatment Effect", + ax=ax2) + plt.tight_layout() + plt.show() + +The Probability Treatment Effects analysis produces the following visualization: + +.. image:: ../_static/oregon_pte.png + :alt: Oregon Health Insurance Experiment PTE Analysis + :width: 800px + :align: center + +The side-by-side bar charts show probability treatment effects across different emergency department cost intervals, revealing how Medicaid enrollment affects healthcare utilization patterns: + +**Cost Distribution Effects**: The PTE analysis shows how Medicaid enrollment changes the probability of individuals incurring emergency department costs in specific ranges. Positive bars indicate cost intervals where Medicaid enrollment increases the likelihood of incurring costs in that range, while negative bars show intervals where it decreases the probability. + +**Healthcare Utilization Patterns**: Both simple and ML-adjusted estimators reveal consistent patterns in how Medicaid enrollment affects emergency department utilization across different cost categories. The analysis shows that Medicaid enrollment has heterogeneous effects, increasing utilization in some cost ranges while potentially reducing it in others. + +**Access vs. Utilization Trade-offs**: The probability treatment effects reveal the complex relationship between health insurance coverage and emergency department use. While Medicaid provides access to care, the distributional effects suggest that it may help some individuals avoid very high-cost emergency situations while increasing utilization for routine or preventive care. + +**Methodological Robustness**: Both simple and ML-adjusted estimators confirm similar patterns, providing robust evidence for the distributional effects of Medicaid enrollment on emergency department costs. The ML-adjusted analysis provides more precise estimates that account for confounding factors. + +**Policy Implications**: Understanding these distributional effects is crucial for healthcare policy. The analysis reveals that Medicaid's impact varies across the cost distribution, which has important implications for healthcare budgeting and understanding the true effects of public health insurance programs. + +**Conclusion**: Using the real Oregon Health Insurance Experiment dataset with 24,000 participants, the distributional analysis reveals nuanced patterns in how Medicaid enrollment affects healthcare utilization. The analysis goes beyond simple average comparisons to show how treatment effects vary across the entire emergency department cost distribution, providing insights into how public health insurance impacts different segments of the population. This demonstrates the power of distribution treatment effect analysis for understanding heterogeneous responses in healthcare policy interventions. + +Emergency Department Visits Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Now let's examine how Medicaid enrollment affects the distribution of emergency department visits (rather than costs): + +.. code-block:: python + + # Initialize estimators for visits analysis + simple_estimator_visits = dte_adj.SimpleDistributionEstimator() + ml_estimator_visits = dte_adj.AdjustedDistributionEstimator( + LinearRegression(), + folds=5 + ) + + # Fit estimators on the full dataset for visits + simple_estimator_visits.fit(X, D, Y_NUM_VISIT_CENS_ED) + ml_estimator_visits.fit(X, D, Y_NUM_VISIT_CENS_ED) + + # Define evaluation points for emergency department visits + outcome_ed_visits_locations = np.linspace(Y_NUM_VISIT_CENS_ED.min(), Y_NUM_VISIT_CENS_ED.max(), 20) + +Distribution Treatment Effects: Visits Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + # Compute DTE for visits: Enrolled vs Not enrolled + dte_visits_simple, lower_visits_simple, upper_visits_simple = simple_estimator_visits.predict_dte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=outcome_ed_visits_locations, + variance_type="moment" + ) + + dte_visits_ml, lower_visits_ml, upper_visits_ml = ml_estimator_visits.predict_dte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=outcome_ed_visits_locations, + variance_type="moment" + ) + + # Visualize the visits distribution treatment effects + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) + + # Simple estimator for visits + plot(outcome_ed_visits_locations, dte_visits_simple, lower_visits_simple, upper_visits_simple, + title="Medicaid Enrollment vs Control - Visits (Simple Estimator)", + xlabel="Emergency Department Visits", ylabel="Distribution Treatment Effect", + color="purple", + ax=ax1) + + # ML-adjusted estimator for visits + plot(outcome_ed_visits_locations, dte_visits_ml, lower_visits_ml, upper_visits_ml, + title="Medicaid Enrollment vs Control - Visits (ML-Adjusted Estimator)", + xlabel="Emergency Department Visits", ylabel="Distribution Treatment Effect", + ax=ax2) + + plt.tight_layout() + plt.show() + +.. image:: ../_static/oregon_dte_visits.png + :alt: Oregon Health Insurance Experiment DTE Visits Analysis + :width: 800px + :align: center + +Probability Treatment Effects: Visits Category Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + # Compute PTE for visits + pte_visits_simple, pte_lower_visits_simple, pte_upper_visits_simple = simple_estimator_visits.predict_pte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=[-1] + outcome_ed_visits_locations, + variance_type="moment" + ) + + pte_visits_ml, pte_lower_visits_ml, pte_upper_visits_ml = ml_estimator_visits.predict_pte( + target_treatment_arm=1, # Enrolled + control_treatment_arm=0, # Not enrolled + locations=[-1] + outcome_ed_visits_locations, + variance_type="moment" + ) + + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) + + # Simple estimator for visits PTE + plot(outcome_ed_visits_locations[1:], pte_visits_simple, pte_lower_visits_simple, pte_upper_visits_simple, + chart_type="bar", + title="Effects of Emergency Department Visits (Simple Estimator)", + xlabel="Emergency Department Visits", ylabel="Probability Treatment Effect", color="purple", + ax=ax1) + + # ML-adjusted estimator for visits PTE + plot(outcome_ed_visits_locations[1:], pte_visits_ml, pte_lower_visits_ml, pte_upper_visits_ml, + chart_type="bar", + title="Effects of Emergency Department Visits (ML-Adjusted Estimator)", + xlabel="Emergency Department Visits", ylabel="Probability Treatment Effect", + ax=ax2) + plt.tight_layout() + plt.show() + +.. image:: ../_static/oregon_pte_visits.png + :alt: Oregon Health Insurance Experiment PTE Visits Analysis + :width: 800px + :align: center + + +**Key Insights from Visits Analysis**: + +The emergency department visits analysis reveals complementary patterns to the cost analysis: + +**Visit Frequency Effects**: Medicaid enrollment shows distinct effects on the probability of different visit frequencies. The PTE analysis reveals which visit count categories are most affected by Medicaid enrollment. + +**Utilization Patterns**: The distributional analysis of visits provides insights into how health insurance affects the frequency of emergency department use, separate from the cost per visit. This helps distinguish between intensive margin effects (cost per visit) and extensive margin effects (frequency of visits). + +**Policy Understanding**: By analyzing both costs and visits separately, we gain a more complete picture of how Medicaid affects emergency department utilization. This dual analysis is crucial for understanding the full impact of health insurance policy on healthcare delivery. + + +Stratified Analysis by Household Registration +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The Oregon experiment allows us to examine how treatment effects vary across different household registration patterns. This stratified analysis helps identify heterogeneous treatment effects and provides insights into which populations benefit most from Medicaid enrollment. + +.. code-block:: python + + # Stratified Analysis by household registration type + strata_consolidated = df['numhh_list'].copy() + strata_consolidated = strata_consolidated.replace({ + 'signed self up + 1 additional person': 'signed self up + others', + 'signed self up + 2 additional people': 'signed self up + others' + }) + + strata_consolidated_values = strata_consolidated.values + unique_consolidated_strata = np.unique(strata_consolidated_values) + + # Store results for each stratum + individual_results = {} + + for stratum in unique_consolidated_strata: + print(f"\nAnalyzing stratum: {stratum}") + + # Filter data for this stratum + stratum_mask = strata_consolidated_values == stratum + X_stratum = X[stratum_mask] + D_stratum = D[stratum_mask] + Y_stratum = Y_ED_CHARG_TOT_ED[stratum_mask] + + print(f" Sample size: {len(D_stratum):,}") + print(f" Treatment group: {(D_stratum == 1).sum():,}") + print(f" Control group: {(D_stratum == 0).sum():,}") + + # Initialize estimators for this stratum + simple_stratum_estimator = dte_adj.SimpleDistributionEstimator() + ml_stratum_estimator = dte_adj.AdjustedDistributionEstimator( + LinearRegression(), + folds=3 # Reduced folds due to smaller sample size + ) + + # Fit estimators on stratum data + simple_stratum_estimator.fit(X_stratum, D_stratum, Y_stratum) + ml_stratum_estimator.fit(X_stratum, D_stratum, Y_stratum) + + # Compute DTE for this stratum + dte_simple_stratum, lower_simple_stratum, upper_simple_stratum = simple_stratum_estimator.predict_dte( + target_treatment_arm=1, + control_treatment_arm=0, + locations=outcome_ed_costs_locations, + variance_type="moment" + ) + + dte_ml_stratum, lower_ml_stratum, upper_ml_stratum = ml_stratum_estimator.predict_dte( + target_treatment_arm=1, + control_treatment_arm=0, + locations=outcome_ed_costs_locations, + variance_type="moment" + ) + + # Store results for visualization + individual_results[stratum] = { + 'simple': { + 'dte': dte_simple_stratum, + 'lower': lower_simple_stratum, + 'upper': upper_simple_stratum + }, + 'ml': { + 'dte': dte_ml_stratum, + 'lower': lower_ml_stratum, + 'upper': upper_ml_stratum + }, + 'sample_size': len(D_stratum), + 'treatment_size': (D_stratum == 1).sum(), + 'control_size': (D_stratum == 0).sum() + } + +Visualization: Comparing Overall Population vs Stratified Results +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + # Comparison: Overall vs Individual Strata + fig, axes = plt.subplots(2, 3, figsize=(24, 12)) + + # Row 1: Simple estimators + # Overall (all data) + plot(outcome_ed_costs_locations, dte_simple, lower_simple, upper_simple, + title="Overall Population\n(Simple Estimator)", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", + color="black", ax=axes[0, 0]) + + # Individual strata + col_idx = 1 + for stratum, results in individual_results.items(): + if results is None or col_idx > 2: + continue + + plot(outcome_ed_costs_locations, results['simple']['dte'], + results['simple']['lower'], results['simple']['upper'], + title=f"{stratum}\n(Simple Estimator, n={results['sample_size']:,})", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", + color="blue" if col_idx == 1 else "green", ax=axes[0, col_idx]) + col_idx += 1 + + # Row 2: ML-Adjusted estimators + # Overall (all data) + plot(outcome_ed_costs_locations, dte_ml, lower_ml, upper_ml, + title="Overall Population\n(ML-Adjusted Estimator)", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", + color="black", ax=axes[1, 0]) + + # Individual strata + col_idx = 1 + for stratum, results in individual_results.items(): + if results is None or col_idx > 2: + continue + + plot(outcome_ed_costs_locations, results['ml']['dte'], + results['ml']['lower'], results['ml']['upper'], + title=f"{stratum}\n(ML-Adjusted Estimator, n={results['sample_size']:,})", + xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", + color="red" if col_idx == 1 else "purple", ax=axes[1, col_idx]) + col_idx += 1 + + plt.suptitle("Comparison: Overall Population vs Individual Household Registration Strata", fontsize=16) + plt.tight_layout() + plt.show() + +.. image:: ../_static/oregon_dte_strata.png + :alt: Oregon Health Insurance Experiment DTE Strata Analysis + :width: 800px + :align: center + +**Key Insights from Stratified Analysis**: + +The stratified analysis by household registration type reveals important heterogeneity in how Medicaid enrollment affects different populations: + +**Heterogeneous Treatment Effects**: The comparison between overall population effects and individual strata shows that treatment effects vary significantly across different household registration patterns. This heterogeneity suggests that "one-size-fits-all" policy evaluations may miss important subgroup differences. + +**Sample Size Considerations**: Different strata have varying sample sizes, which affects the precision of estimates. Larger strata (like "signed self up") provide more precise estimates, while smaller strata show wider confidence intervals but may reveal important effect heterogeneity. + +**Policy Targeting Implications**: Understanding which household types respond most strongly to Medicaid enrollment can inform more targeted policy interventions and help identify populations that would benefit most from expanded coverage. + +**Methodological Consistency**: Both simple and ML-adjusted estimators show similar patterns within each stratum, providing confidence in the robustness of the stratified findings across different analytical approaches. + +Conclusion +~~~~~~~~~~ + +The Oregon Health Insurance Experiment provides a unique opportunity to study the distributional effects of Medicaid enrollment using the `dte_adj` library. This analysis demonstrates several key capabilities: + +**Distributional vs. Average Effects**: While traditional analyses focus on average treatment effects, the distributional approach reveals how Medicaid affects the entire distribution of healthcare utilization and costs, providing a more complete picture of policy impacts. + +**Multiple Outcome Analysis**: By analyzing both emergency department costs and visits separately, we gain insights into different dimensions of healthcare utilization - the intensive margin (cost per visit) and extensive margin (frequency of visits). + +**Heterogeneity Analysis**: The stratified analysis by household registration type reveals important treatment effect heterogeneity, showing that different populations respond differently to Medicaid enrollment. + +**Methodological Robustness**: Comparing simple and ML-adjusted estimators provides confidence in our findings and demonstrates the robustness of the distributional treatment effect methodology. + +**Policy Implications**: The distributional effects have important implications for healthcare policy, revealing that public health insurance affects different segments of the population in different ways, which is crucial for policy design and evaluation. + +Next Steps +~~~~~~~~~~ + +- Try with your own randomized experiment data +- Experiment with different ML models (XGBoost, Neural Networks) for adjustment +- Explore stratified estimators for covariate-adaptive randomization designs +- Use multi-task learning (``is_multi_task=True``) for computational efficiency with many locations From 39b2acd6135ee98663551100a6722fd27b43c8ca Mon Sep 17 00:00:00 2001 From: okiner-3 Date: Sun, 19 Oct 2025 17:00:06 +0900 Subject: [PATCH 2/3] replace functions from predict_{dte, pte} to predict_{ldte, lpte} due to Non-Compliance --- docs/source/_static/oregon_dte.png | Bin 66312 -> 0 bytes docs/source/_static/oregon_dte_control.png | Bin 32400 -> 0 bytes docs/source/_static/oregon_dte_strata.png | 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a/docs/source/tutorials/oregon.rst b/docs/source/tutorials/oregon.rst index b162020..24b284e 100644 --- a/docs/source/tutorials/oregon.rst +++ b/docs/source/tutorials/oregon.rst @@ -3,13 +3,26 @@ Oregon Health Insurance Experiment The Oregon Health Insurance Experiment is a landmark randomized controlled trial conducted in 2008, where approximately 24,000 low-income adults were randomly assigned to either receive the opportunity to enroll in Medicaid (treatment group) or remain uninsured (control group). This unique natural experiment allows us to examine how public health insurance affects healthcare utilization and costs across the entire distribution. -**Background**: Due to budget constraints, Oregon decided to expand its Medicaid program through a lottery system, randomly selecting eligible individuals for enrollment opportunities. This created a rare natural experiment that enables rigorous causal evaluation of Medicaid's effects on healthcare utilization and outcomes. +**Background**: Due to budget constraints, Oregon decided to expand its Medicaid program through a lottery system, randomly selecting eligible individuals for enrollment opportunities. This created a rare natural experiment with non-compliance (not all selected individuals enrolled) that enables rigorous causal evaluation using Local Distribution Treatment Effects (LDTE) methodology. -**Research Question**: How does Medicaid enrollment affect healthcare utilization (emergency department visits and costs), and how do these effects vary across the entire distribution of healthcare outcomes? +**Research Question**: How does Medicaid assignment (and enrollment) affect healthcare utilization (emergency department visits and costs), accounting for non-compliance, and how do these effects vary across the entire distribution of healthcare outcomes? Data Setup and Loading ~~~~~~~~~~~~~~~~~~~~~~~ +**Data Source**: The Oregon Health Insurance Experiment data used in this tutorial is publicly available through the National Bureau of Economic Research (NBER). You can download the dataset from the official NBER Public Use Data Archive at: https://www.nber.org/research/data/oregon-health-insurance-experiment-data + +The dataset includes multiple files containing information about participants in the experiment: + +- ``oregonhie_descriptive_vars.dta``: Demographic and baseline characteristics +- ``oregonhie_ed_vars.dta``: Emergency department utilization data +- ``oregonhie_inperson_vars.dta``: In-person survey responses +- ``oregonhie_stateprograms_vars.dta``: State program participation data + +This data supports research on how health insurance affects healthcare utilization and is maintained by researchers Amy Finkelstein and Katherine Baicker. Please ensure you comply with the data use agreements when downloading and using this dataset. + +**Important**: When using this dataset for research or publications, appropriate citation is required as specified in the NBER data use agreement. + .. code-block:: python import numpy as np @@ -41,7 +54,11 @@ Data Setup and Loading print(f"Average ed_charg_tot_ed by enrollment:\n{df.groupby('ohp_all_ever_inperson')['ed_charg_tot_ed'].mean()}") # Prepare the data for dte_adj analysis - # Create treatment indicator: 0=Not enrolled, 1=Enrolled + # Create treatment assignment (instrumental variable): 0=Not selected, 1=Selected + treatment_assignment_mapping = {'Not selected': 0, 'Selected': 1} + df['Z'] = df['treatment'].map(treatment_assignment_mapping).astype(float).fillna(-1).astype(int) + + # Create actual treatment indicator: 0=Not enrolled, 1=Enrolled, -1=Missing treatment_mapping = {'NOT enrolled': 0, 'Enrolled': 1} df['D'] = df['ohp_all_ever_inperson'].map(treatment_mapping).astype(float).fillna(-1).astype(int) @@ -49,14 +66,14 @@ Data Setup and Loading df['Y_ED_CHARG_TOT_ED'] = df['ed_charg_tot_ed'].fillna(0) df['Y_NUM_VISIT_CENS_ED'] = df['num_visit_cens_ed'].fillna(0) + # Create strata based on household size + df['strata'] = df['numhh_list'] + # Create feature mappings for categorical variables - covariate_mapping = {'Not selected': 0, 'Selected': 1} gender_mapping = {'Male': 0, 'Female': 1, 'Transgender F to M': 2, 'Transgender M to F': 3} health_last12_mapping = {'1: Very poor': 1, '2: Poor': 2, '3: Fair': 3, '4: Good': 4, '5: Very good': 5, '6: Excellent': 6} edu_mapping = {'HS diploma or GED': 0, 'Post HS, not 4-year': 1, 'Less than HS': 2, '4 year degree or more': 3} - # Create control variables - df['W'] = df['treatment'].map(covariate_mapping).astype(float).fillna(-1).astype(int) df['age'] = 2008 - df['birthyear_list'] df['gender_inp'] = df['gender_inp'].map(gender_mapping).astype(float).fillna(-1).astype(int) df['health_last12_inp'] = df['health_last12_inp'].map(health_last12_mapping).astype(float).fillna(-1).astype(int) @@ -65,213 +82,215 @@ Data Setup and Loading # Select control variables: pre-randomization ED utilization variables ctrl_cols = [col for col in df_ed.columns if 'pre' in col and 'num' in col] ctrl_cols.append('charg_tot_pre_ed') - selected_cols = ['person_id', 'numhh_list', 'Y_NUM_VISIT_CENS_ED', 'Y_ED_CHARG_TOT_ED', 'D', 'W'] + ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp'] + selected_cols = ['person_id', 'strata', 'Y_NUM_VISIT_CENS_ED', 'Y_ED_CHARG_TOT_ED', 'Z', 'D'] + ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp'] df = df[selected_cols] df = df[df.isna().any(axis=1) == False] - # Create feature matrix - features = pd.DataFrame(df[['W'] + ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp']]) + # Create feature matrix (excluding treatment variables) + features = pd.DataFrame(df[ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp']]) X = features.values - D = df['D'].values + Z = df['Z'].values # Treatment assignment (instrumental variable) + D = df['D'].values # Actual treatment (endogenous variable) + strata = df['strata'].values # Stratification variable Y_ED_CHARG_TOT_ED = df['Y_ED_CHARG_TOT_ED'].values Y_NUM_VISIT_CENS_ED = df['Y_NUM_VISIT_CENS_ED'].values print(f"\nDataset size: {len(D):,} people") - print(f"Control group (Not enrolled): {(D==0).sum():,} ({(D==0).mean():.1%})") - print(f"Treatment group (Enrolled): {(D==1).sum():,} ({(D==1).mean():.1%})") - print("Average Outcome by Treatment:") - print(f"Not enrolled: {Y_NUM_VISIT_CENS_ED[D==0].mean():.2f} visits, ${Y_ED_CHARG_TOT_ED[D==0].mean():.2f} in ED costs") - print(f"Enrolled: {Y_NUM_VISIT_CENS_ED[D==1].mean():.2f} visits, ${Y_ED_CHARG_TOT_ED[D==1].mean():.2f} in ED costs") + print(f"Treatment assignment (Z) - Not selected: {(Z==0).sum():,} ({(Z==0).mean():.1%})") + print(f"Treatment assignment (Z) - Selected: {(Z==1).sum():,} ({(Z==1).mean():.1%})") + print(f"Actual treatment (D) - Not enrolled: {(D==0).sum():,} ({(D==0).mean():.1%})") + print(f"Actual treatment (D) - Enrolled: {(D==1).sum():,} ({(D==1).mean():.1%})") + print("\nCompliance rate (among those assigned to treatment):") + print(f"Compliance rate: {(D[Z==1]==1).mean():.1%}") + print("\nAverage Outcome by Actual Treatment (D):") + print(f"Not enrolled (D=0): {Y_NUM_VISIT_CENS_ED[D==0].mean():.2f} visits, ${Y_ED_CHARG_TOT_ED[D==0].mean():.2f} in ED costs") + print(f"Enrolled (D=1): {Y_NUM_VISIT_CENS_ED[D==1].mean():.2f} visits, ${Y_ED_CHARG_TOT_ED[D==1].mean():.2f} in ED costs") Emergency Department Cost Analysis ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: python - # Initialize estimators - simple_estimator = dte_adj.SimpleDistributionEstimator() - ml_estimator = dte_adj.AdjustedDistributionEstimator( + # Initialize LOCAL estimators for non-compliance scenario + simple_local_estimator = dte_adj.SimpleLocalDistributionEstimator() + ml_local_estimator = dte_adj.AdjustedLocalDistributionEstimator( LinearRegression(), folds=5 ) - # Fit estimators on the full dataset - simple_estimator.fit(X, D, Y_ED_CHARG_TOT_ED) - ml_estimator.fit(X, D, Y_ED_CHARG_TOT_ED) + # Fit estimators: fit(covariates, treatment_arms, treatment_indicator, outcomes, strata) + # treatment_arms = Z (Treatment assignment), treatment_indicator = D (Actual treatment) + simple_local_estimator.fit(X, Z, D, Y_ED_CHARG_TOT_ED, strata) + ml_local_estimator.fit(X, Z, D, Y_ED_CHARG_TOT_ED, strata) # Define evaluation points for emergency department costs outcome_ed_costs_locations = np.linspace(Y_ED_CHARG_TOT_ED.min(), Y_ED_CHARG_TOT_ED.max(), 100) -Distribution Treatment Effects: Medicaid Enrollment vs Control -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Local Distribution Treatment Effects: Medicaid Assignment vs Control +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -First, let's examine how Medicaid enrollment affects the distribution of emergency department costs: +First, let's examine how Medicaid assignment (accounting for non-compliance) affects the distribution of emergency department costs: .. code-block:: python - # Compute DTE: Enrolled vs Not enrolled - dte_ctrl, lower_ctrl, upper_ctrl = simple_estimator.predict_dte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=outcome_ed_costs_locations, - variance_type="moment" + # Compute Local Distribution Treatment Effects (LDTE) + ldte_ctrl, ldte_lower_ctrl, ldte_upper_ctrl = simple_local_estimator.predict_ldte( + target_treatment_arm=1, # Z=1 (assigned to treatment) + control_treatment_arm=0, # Z=0 (assigned to control) + locations=outcome_ed_costs_locations ) - # Visualize Enrolled vs Control using dte_adj's plot function - plot(outcome_ed_costs_locations, dte_ctrl, lower_ctrl, upper_ctrl, - title="Medicaid Enrollment vs Control (Emergency Department Costs)", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect") + # Visualize Treatment vs Control using dte_adj's plot function + plot(outcome_ed_costs_locations, ldte_ctrl, ldte_lower_ctrl, ldte_upper_ctrl, + title="Treatment vs Control", + xlabel="Emergency Department Costs ($)", ylabel="Local Distribution Treatment Effect") -.. image:: ../_static/oregon_dte_control.png +.. image:: ../_static/oregon_ldte_control.png :alt: Oregon Health Insurance Experiment vs Control Analysis :width: 500px :align: center -Probability Treatment Effects: Cost Analysis -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Local Probability Treatment Effects: Cost Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Let's also examine how Medicaid enrollment affects the probability of incurring specific ranges of emergency department costs using Probability Treatment Effects (PTE): +Let's also examine how Medicaid assignment affects the probability of incurring specific ranges of emergency department costs using Local Probability Treatment Effects (LPTE): .. code-block:: python - # Compute PTE: Enrolled vs Not enrolled - pte_ctrl, pte_lower_ctrl, pte_upper_ctrl = simple_estimator.predict_pte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=[-1] + outcome_ed_costs_locations, - variance_type="moment" + # Compute Local Probability Treatment Effects (LPTE) + lpte_ctrl, lpte_lower_ctrl, lpte_upper_ctrl = simple_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 (assigned to treatment) + control_treatment_arm=0, # Z=0 (assigned to control) + locations=[-1] + outcome_ed_costs_locations ) fig, ax = plt.subplots(figsize=(10, 6)) - # Visualize PTE results using dte_adj's plot function with bar charts - plot(outcome_ed_costs_locations[1:], pte_ctrl, pte_lower_ctrl, pte_upper_ctrl, + # Visualize LPTE results using dte_adj's plot function with bar charts + # Treatment vs Control LPTE + plot(outcome_ed_costs_locations[1:], lpte_ctrl, lpte_lower_ctrl, lpte_upper_ctrl, chart_type="bar", - title="Medicaid Enrollment vs Control", - xlabel="Emergency Department Costs ($)", ylabel="Probability Treatment Effect", + title="Treatment vs Control", + xlabel="Emergency Department Costs ($)", ylabel="Local Probability Treatment Effect", ax=ax) plt.tight_layout() plt.show() -.. image:: ../_static/oregon_pte_control.png - :alt: Oregon Health Insurance Experiment vs Control PTE Analysis +.. image:: ../_static/oregon_lpte_control.png + :alt: Oregon Health Insurance Experiment vs Control LPTE Analysis :width: 800px :align: center -Estimator Comparison: Simple vs ML-Adjusted -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Local Estimator Comparison: Simple vs ML-Adjusted (Costs) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Let's compare the results from both simple and machine learning-adjusted estimators to examine the robustness of our findings: +Let's compare the results from both simple and machine learning-adjusted local estimators to examine the robustness of our findings: .. code-block:: python - # Compute DTE with both estimators - dte_simple, lower_simple, upper_simple = simple_estimator.predict_dte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=outcome_ed_costs_locations, - variance_type="moment" + # Compute LDTE: Treatment vs Control + ldte_simple, lower_simple, upper_simple = simple_local_estimator.predict_ldte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=outcome_ed_costs_locations ) - dte_ml, lower_ml, upper_ml = ml_estimator.predict_dte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=outcome_ed_costs_locations, - variance_type="moment" + ldte_ml, lower_ml, upper_ml = ml_local_estimator.predict_ldte( + target_treatment_arm=1, # Selected for treatment (Enrolled) + control_treatment_arm=0, # Not selected for treatment (Not enrolled) + locations=outcome_ed_costs_locations ) # Visualize the distribution treatment effects using dte_adj's built-in plot function fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) - # Simple estimator - plot(outcome_ed_costs_locations, dte_simple, lower_simple, upper_simple, - title="Medicaid Enrollment vs Control (Simple Estimator)", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", - color="purple", - ax=ax1) + # Visualize Treatment vs Control using dte_adj's plot function + plot(outcome_ed_costs_locations, ldte_simple, lower_simple, upper_simple, + title="Treatment vs Control (Simple Local Estimator)", + xlabel="Emergency Department Costs", ylabel="Local Distribution Treatment Effect", + color="purple", + ax=ax1) - # ML-adjusted estimator - plot(outcome_ed_costs_locations, dte_ml, lower_ml, upper_ml, - title="Medicaid Enrollment vs Control (ML-Adjusted Estimator)", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", - ax=ax2) + plot(outcome_ed_costs_locations, ldte_ml, lower_ml, upper_ml, + title="Treatment vs Control (ML-Adjusted Local Estimator)", + xlabel="Emergency Department Costs", ylabel="Local Distribution Treatment Effect", + ax=ax2) plt.tight_layout() plt.show() -The analysis produces the following distribution treatment effects visualization: +The analysis produces the following local distribution treatment effects visualization: -.. image:: ../_static/oregon_dte.png - :alt: Oregon Health Insurance Experiment DTE Analysis +.. image:: ../_static/oregon_ldte_costs_comparison.png + :alt: Oregon Health Insurance Experiment LDTE Analysis :width: 800px :align: center -**DTE Interpretation**: The positive DTE values indicate that Medicaid enrollment increases the cumulative probability of individuals having emergency department costs at or below each threshold compared to those not enrolled. This suggests that while Medicaid increases overall ED utilization, it may also help contain costs for some individuals. +**LDTE Interpretation**: The positive LDTE values indicate that Medicaid assignment increases the cumulative probability of individuals having emergency department costs at or below each threshold among compliers (those who enroll when selected). This suggests that while Medicaid increases overall ED utilization, it may also help contain costs for some individuals who actually enroll. -**Statistical Significance**: Both simple and ML-adjusted estimators show similar patterns, providing robust evidence that Medicaid enrollment has significant distributional effects on emergency department costs. The confidence intervals indicate that these effects are statistically significant across most cost levels. +**Statistical Significance**: Both simple and ML-adjusted local estimators show similar patterns, providing robust evidence that Medicaid assignment has significant distributional effects on emergency department costs for compliers. The confidence intervals indicate that these effects are statistically significant across most cost levels. -**Healthcare Access Implications**: The DTE analysis reveals that Medicaid enrollment affects the entire distribution of emergency department costs, not just the average. This provides insights into how public health insurance impacts healthcare utilization patterns across different cost categories. +**Non-Compliance Considerations**: The LDTE analysis accounts for the fact that not all individuals assigned to treatment actually enrolled in Medicaid, providing a more accurate estimate of the effects for those who actually receive treatment when assigned. -Cost Analysis with PTE -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Cost Analysis with Local PTE +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: python - # Compute Probability Treatment Effects - pte_simple, pte_lower_simple, pte_upper_simple = simple_estimator.predict_pte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=[-1] + outcome_ed_costs_locations, - variance_type="moment" + # Compute Local Probability Treatment Effects + lpte_simple, lpte_lower_simple, lpte_upper_simple = simple_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_costs_locations ) - pte_ml, pte_lower_ml, pte_upper_ml = ml_estimator.predict_pte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=[-1] + outcome_ed_costs_locations, - variance_type="moment" + lpte_ml, lpte_lower_ml, lpte_upper_ml = ml_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_costs_locations ) fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) - # Simple estimator - plot(outcome_ed_costs_locations[1:], pte_simple, pte_lower_simple, pte_upper_simple, + # Simple local estimator + plot(outcome_ed_costs_locations[1:], lpte_simple, lpte_lower_simple, lpte_upper_simple, chart_type="bar", - title="Effects of Emergency Department Costs (Simple Estimator)", - xlabel="Emergency Department Costs ($)", ylabel="Probability Treatment Effect", color="purple", + title="Effects of Emergency Department Costs (Simple Local Estimator)", + xlabel="Emergency Department Costs", ylabel="Local Probability Treatment Effect", + color="purple", ax=ax1) - # ML-adjusted estimator - plot(outcome_ed_costs_locations[1:], pte_ml, pte_lower_ml, pte_upper_ml, + # ML-adjusted local estimator + plot(outcome_ed_costs_locations[1:], lpte_ml, lpte_lower_ml, lpte_upper_ml, chart_type="bar", - title="Effects of Emergency Department Costs (ML-Adjusted Estimator)", - xlabel="Emergency Department Costs ($)", ylabel="Probability Treatment Effect", + title="Effects of Emergency Department Costs (ML-Adjusted Local Estimator)", + xlabel="Emergency Department Costs", ylabel="Local Probability Treatment Effect", ax=ax2) plt.tight_layout() plt.show() -The Probability Treatment Effects analysis produces the following visualization: +The Local Probability Treatment Effects analysis produces the following visualization: -.. image:: ../_static/oregon_pte.png - :alt: Oregon Health Insurance Experiment PTE Analysis +.. image:: ../_static/oregon_lpte_costs_comparison.png + :alt: Oregon Health Insurance Experiment LPTE Analysis :width: 800px :align: center The side-by-side bar charts show probability treatment effects across different emergency department cost intervals, revealing how Medicaid enrollment affects healthcare utilization patterns: -**Cost Distribution Effects**: The PTE analysis shows how Medicaid enrollment changes the probability of individuals incurring emergency department costs in specific ranges. Positive bars indicate cost intervals where Medicaid enrollment increases the likelihood of incurring costs in that range, while negative bars show intervals where it decreases the probability. +**Cost Distribution Effects**: The LPTE analysis shows how Medicaid assignment changes the probability of compliers incurring emergency department costs in specific ranges. Positive bars indicate cost intervals where Medicaid assignment increases the likelihood of incurring costs in that range, while negative bars show intervals where it decreases the probability. -**Healthcare Utilization Patterns**: Both simple and ML-adjusted estimators reveal consistent patterns in how Medicaid enrollment affects emergency department utilization across different cost categories. The analysis shows that Medicaid enrollment has heterogeneous effects, increasing utilization in some cost ranges while potentially reducing it in others. +**Healthcare Utilization Patterns**: Both simple and ML-adjusted local estimators reveal consistent patterns in how Medicaid assignment affects emergency department utilization across different cost categories for compliers. The analysis shows that Medicaid assignment has heterogeneous effects, increasing utilization in some cost ranges while potentially reducing it in others. **Access vs. Utilization Trade-offs**: The probability treatment effects reveal the complex relationship between health insurance coverage and emergency department use. While Medicaid provides access to care, the distributional effects suggest that it may help some individuals avoid very high-cost emergency situations while increasing utilization for routine or preventive care. -**Methodological Robustness**: Both simple and ML-adjusted estimators confirm similar patterns, providing robust evidence for the distributional effects of Medicaid enrollment on emergency department costs. The ML-adjusted analysis provides more precise estimates that account for confounding factors. +**Methodological Robustness**: Both simple and ML-adjusted local estimators confirm similar patterns, providing robust evidence for the distributional effects of Medicaid assignment on emergency department costs for compliers. The ML-adjusted analysis provides more precise estimates that account for confounding factors while handling non-compliance. -**Policy Implications**: Understanding these distributional effects is crucial for healthcare policy. The analysis reveals that Medicaid's impact varies across the cost distribution, which has important implications for healthcare budgeting and understanding the true effects of public health insurance programs. +**Policy Implications**: Understanding these distributional effects is crucial for healthcare policy. The local analysis reveals that Medicaid's impact varies across the cost distribution for those who actually enroll when assigned, which has important implications for healthcare budgeting and understanding the true effects of public health insurance programs on compliers. -**Conclusion**: Using the real Oregon Health Insurance Experiment dataset with 24,000 participants, the distributional analysis reveals nuanced patterns in how Medicaid enrollment affects healthcare utilization. The analysis goes beyond simple average comparisons to show how treatment effects vary across the entire emergency department cost distribution, providing insights into how public health insurance impacts different segments of the population. This demonstrates the power of distribution treatment effect analysis for understanding heterogeneous responses in healthcare policy interventions. +**Conclusion**: Using the real Oregon Health Insurance Experiment dataset with 24,000 participants, the local distributional analysis reveals nuanced patterns in how Medicaid assignment affects healthcare utilization among compliers. The analysis accounts for non-compliance and goes beyond simple average comparisons to show how treatment effects vary across the entire emergency department cost distribution, providing insights into how public health insurance impacts different segments of the population who actually enroll. This demonstrates the power of local distribution treatment effect analysis for understanding heterogeneous responses in healthcare policy interventions with non-compliance. Emergency Department Visits Analysis ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -280,16 +299,17 @@ Now let's examine how Medicaid enrollment affects the distribution of emergency .. code-block:: python - # Initialize estimators for visits analysis - simple_estimator_visits = dte_adj.SimpleDistributionEstimator() - ml_estimator_visits = dte_adj.AdjustedDistributionEstimator( + # Initialize local estimators for visits analysis + simple_local_estimator = dte_adj.SimpleLocalDistributionEstimator() + ml_local_estimator = dte_adj.AdjustedLocalDistributionEstimator( LinearRegression(), folds=5 ) - # Fit estimators on the full dataset for visits - simple_estimator_visits.fit(X, D, Y_NUM_VISIT_CENS_ED) - ml_estimator_visits.fit(X, D, Y_NUM_VISIT_CENS_ED) + # Fit local estimators on the full dataset + # Parameters: X, treatment_arms, treatment_indicator, outcomes, strata + simple_local_estimator.fit(X, Z, D, Y_NUM_VISIT_CENS_ED, strata) + ml_local_estimator.fit(X, Z, D, Y_NUM_VISIT_CENS_ED, strata) # Define evaluation points for emergency department visits outcome_ed_visits_locations = np.linspace(Y_NUM_VISIT_CENS_ED.min(), Y_NUM_VISIT_CENS_ED.max(), 20) @@ -299,98 +319,197 @@ Distribution Treatment Effects: Visits Analysis .. code-block:: python - # Compute DTE for visits: Enrolled vs Not enrolled - dte_visits_simple, lower_visits_simple, upper_visits_simple = simple_estimator_visits.predict_dte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=outcome_ed_visits_locations, - variance_type="moment" + # Compute LDTE: Treatment vs Control + ldte_ctrl, lower_ctrl, upper_ctrl = simple_local_estimator.predict_ldte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=outcome_ed_visits_locations ) - dte_visits_ml, lower_visits_ml, upper_visits_ml = ml_estimator_visits.predict_dte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=outcome_ed_visits_locations, - variance_type="moment" + # LDTE: Treatment vs Control + ldte_simple, lower_simple, upper_simple = simple_local_estimator.predict_ldte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=outcome_ed_visits_locations ) - # Visualize the visits distribution treatment effects + ldte_ml, lower_ml, upper_ml = ml_local_estimator.predict_ldte( + target_treatment_arm=1, # Selected for treatment (Enrolled) + control_treatment_arm=0, # Not selected for treatment (Not enrolled) + locations=outcome_ed_visits_locations + ) + + # Visualize the local distribution treatment effects using dte_adj's built-in plot function fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) - # Simple estimator for visits - plot(outcome_ed_visits_locations, dte_visits_simple, lower_visits_simple, upper_visits_simple, - title="Medicaid Enrollment vs Control - Visits (Simple Estimator)", - xlabel="Emergency Department Visits", ylabel="Distribution Treatment Effect", + # Visualize Treatment vs Control using dte_adj's plot function + plot(outcome_ed_visits_locations, ldte_simple, lower_simple, upper_simple, + title="Treatment vs Control (Simple Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Distribution Treatment Effect", + color="purple", + ax=ax1) + + plot(outcome_ed_visits_locations, ldte_ml, lower_ml, upper_ml, + title="Treatment vs Control (ML-Adjusted Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Distribution Treatment Effect", + ax=ax2) + + plt.tight_layout() + plt.show() + +.. image:: ../_static/oregon_ldte_visits.png + :alt: Oregon Health Insurance Experiment LDTE Visits Analysis + :width: 800px + :align: center + +Probability Treatment Effects: Visits Analysis +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. code-block:: python + + # Compute LPTE: Treatment vs Control + lpte_ctrl, lpte_lower_ctrl, lpte_upper_ctrl = simple_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_visits_locations + ) + + # Compute Local Probability Treatment Effects + lpte_simple, lpte_lower_simple, lpte_upper_simple = simple_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_visits_locations + ) + + lpte_ml, lpte_lower_ml, lpte_upper_ml = ml_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_visits_locations + ) + + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) + + # Simple local estimator + plot(outcome_ed_visits_locations[1:], lpte_simple, lpte_lower_simple, lpte_upper_simple, + chart_type="bar", + title="Effects of Emergency Department Visits (Simple Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Probability Treatment Effect", color="purple", ax=ax1) - # ML-adjusted estimator for visits - plot(outcome_ed_visits_locations, dte_visits_ml, lower_visits_ml, upper_visits_ml, - title="Medicaid Enrollment vs Control - Visits (ML-Adjusted Estimator)", - xlabel="Emergency Department Visits", ylabel="Distribution Treatment Effect", + # ML-adjusted local estimator + plot(outcome_ed_visits_locations[1:], lpte_ml, lpte_lower_ml, lpte_upper_ml, + chart_type="bar", + title="Effects of Emergency Department Visits (ML-Adjusted Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Probability Treatment Effect", ax=ax2) plt.tight_layout() plt.show() -.. image:: ../_static/oregon_dte_visits.png - :alt: Oregon Health Insurance Experiment DTE Visits Analysis +.. image:: ../_static/oregon_lpte_visits.png + :alt: Oregon Health Insurance Experiment LPTE Visits Analysis :width: 800px :align: center -Probability Treatment Effects: Visits Category Analysis -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Local Estimator Comparison: Simple vs ML-Adjusted (Visits) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Let's compare the results from both simple and machine learning-adjusted local estimators for visits analysis: + +.. code-block:: python + + # Compute LDTE: Treatment vs Control + ldte_simple, lower_simple, upper_simple = simple_local_estimator.predict_ldte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=outcome_ed_visits_locations + ) + + ldte_ml, lower_ml, upper_ml = ml_local_estimator.predict_ldte( + target_treatment_arm=1, # Selected for treatment (Enrolled) + control_treatment_arm=0, # Not selected for treatment (Not enrolled) + locations=outcome_ed_visits_locations + ) + + # Visualize the local distribution treatment effects using dte_adj's built-in plot function + fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) + + # Visualize Treatment vs Control using dte_adj's plot function + plot(outcome_ed_visits_locations, ldte_simple, lower_simple, upper_simple, + title="Treatment vs Control (Simple Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Distribution Treatment Effect", + color="purple", + ax=ax1) + + plot(outcome_ed_visits_locations, ldte_ml, lower_ml, upper_ml, + title="Treatment vs Control (ML-Adjusted Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Distribution Treatment Effect", + ax=ax2) + + plt.tight_layout() + plt.show() + +.. image:: ../_static/oregon_ldte_visits_comparison.png + :alt: Oregon Health Insurance Experiment LDTE Visits Analysis + :width: 800px + :align: center + +Visits Analysis with Local PTE +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: python - # Compute PTE for visits - pte_visits_simple, pte_lower_visits_simple, pte_upper_visits_simple = simple_estimator_visits.predict_pte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=[-1] + outcome_ed_visits_locations, - variance_type="moment" + # Compute Local Probability Treatment Effects + lpte_simple, lpte_lower_simple, lpte_upper_simple = simple_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_visits_locations ) - pte_visits_ml, pte_lower_visits_ml, pte_upper_visits_ml = ml_estimator_visits.predict_pte( - target_treatment_arm=1, # Enrolled - control_treatment_arm=0, # Not enrolled - locations=[-1] + outcome_ed_visits_locations, - variance_type="moment" + lpte_ml, lpte_lower_ml, lpte_upper_ml = ml_local_estimator.predict_lpte( + target_treatment_arm=1, # Z=1 Selected for treatment (Enrolled) + control_treatment_arm=0, # Z=0 Not selected for treatment (Not enrolled) + locations=[-1] + outcome_ed_visits_locations ) fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6)) - # Simple estimator for visits PTE - plot(outcome_ed_visits_locations[1:], pte_visits_simple, pte_lower_visits_simple, pte_upper_visits_simple, + # Simple local estimator + plot(outcome_ed_visits_locations[1:], lpte_simple, lpte_lower_simple, lpte_upper_simple, chart_type="bar", - title="Effects of Emergency Department Visits (Simple Estimator)", - xlabel="Emergency Department Visits", ylabel="Probability Treatment Effect", color="purple", + title="Effects of Emergency Department Visits (Simple Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Probability Treatment Effect", + color="purple", ax=ax1) - # ML-adjusted estimator for visits PTE - plot(outcome_ed_visits_locations[1:], pte_visits_ml, pte_lower_visits_ml, pte_upper_visits_ml, + # ML-adjusted local estimator + plot(outcome_ed_visits_locations[1:], lpte_ml, lpte_lower_ml, lpte_upper_ml, chart_type="bar", - title="Effects of Emergency Department Visits (ML-Adjusted Estimator)", - xlabel="Emergency Department Visits", ylabel="Probability Treatment Effect", + title="Effects of Emergency Department Visits (ML-Adjusted Local Estimator)", + xlabel="Emergency Department Visits", ylabel="Local Probability Treatment Effect", ax=ax2) + plt.tight_layout() plt.show() -.. image:: ../_static/oregon_pte_visits.png - :alt: Oregon Health Insurance Experiment PTE Visits Analysis +.. image:: ../_static/oregon_lpte_visits_comparison.png + :alt: Oregon Health Insurance Experiment LPTE Visits Analysis :width: 800px :align: center - **Key Insights from Visits Analysis**: The emergency department visits analysis reveals complementary patterns to the cost analysis: -**Visit Frequency Effects**: Medicaid enrollment shows distinct effects on the probability of different visit frequencies. The PTE analysis reveals which visit count categories are most affected by Medicaid enrollment. +**Visit Frequency Effects**: Medicaid assignment shows distinct effects on the probability of different visit frequencies for compliers. The LPTE analysis reveals which visit count categories are most affected by Medicaid assignment among those who actually enroll. -**Utilization Patterns**: The distributional analysis of visits provides insights into how health insurance affects the frequency of emergency department use, separate from the cost per visit. This helps distinguish between intensive margin effects (cost per visit) and extensive margin effects (frequency of visits). +**Utilization Patterns**: The local distributional analysis of visits provides insights into how health insurance assignment affects the frequency of emergency department use for compliers, separate from the cost per visit. This helps distinguish between intensive margin effects (cost per visit) and extensive margin effects (frequency of visits) for the complier population. -**Policy Understanding**: By analyzing both costs and visits separately, we gain a more complete picture of how Medicaid affects emergency department utilization. This dual analysis is crucial for understanding the full impact of health insurance policy on healthcare delivery. +**Policy Understanding**: By analyzing both costs and visits separately using local estimators, we gain a more complete picture of how Medicaid assignment affects emergency department utilization for those who actually enroll when selected. This dual analysis is crucial for understanding the full impact of health insurance policy on healthcare delivery in non-compliance scenarios. + +**Methodological Robustness**: Both simple and ML-adjusted local estimators show similar patterns for visits analysis, providing confidence in the robustness of the findings while properly accounting for non-compliance in the experimental design. Stratified Analysis by Household Registration @@ -400,8 +519,11 @@ The Oregon experiment allows us to examine how treatment effects vary across dif .. code-block:: python - # Stratified Analysis by household registration type - strata_consolidated = df['numhh_list'].copy() + # Individual Stratum Analysis with Local Estimators + print("\n=== Individual Stratum Analysis (Local Estimators) ===") + + # Consolidated stratification for practical analysis + strata_consolidated = df['strata'].copy() strata_consolidated = strata_consolidated.replace({ 'signed self up + 1 additional person': 'signed self up + others', 'signed self up + 2 additional people': 'signed self up + others' @@ -410,7 +532,7 @@ The Oregon experiment allows us to examine how treatment effects vary across dif strata_consolidated_values = strata_consolidated.values unique_consolidated_strata = np.unique(strata_consolidated_values) - # Store results for each stratum + # Individual estimations for each stratum individual_results = {} for stratum in unique_consolidated_strata: @@ -419,54 +541,56 @@ The Oregon experiment allows us to examine how treatment effects vary across dif # Filter data for this stratum stratum_mask = strata_consolidated_values == stratum X_stratum = X[stratum_mask] - D_stratum = D[stratum_mask] + treatment_arms_stratum = Z[stratum_mask] + treatment_indicator_stratum = D[stratum_mask] Y_stratum = Y_ED_CHARG_TOT_ED[stratum_mask] - print(f" Sample size: {len(D_stratum):,}") - print(f" Treatment group: {(D_stratum == 1).sum():,}") - print(f" Control group: {(D_stratum == 0).sum():,}") + # Create uniform strata for this subset (all observations in same stratum) + strata_stratum = np.zeros(len(X_stratum), dtype=int) - # Initialize estimators for this stratum - simple_stratum_estimator = dte_adj.SimpleDistributionEstimator() - ml_stratum_estimator = dte_adj.AdjustedDistributionEstimator( + print(f" Sample size: {len(treatment_indicator_stratum):,}") + print(f" Treatment assignment (Selected): {(treatment_arms_stratum == 1).sum():,}") + print(f" Treatment indicator (Enrolled): {(treatment_indicator_stratum == 1).sum():,}") + + # Initialize local estimators for this stratum + simple_stratum_estimator = dte_adj.SimpleLocalDistributionEstimator() + ml_stratum_estimator = dte_adj.AdjustedLocalDistributionEstimator( LinearRegression(), folds=3 # Reduced folds due to smaller sample size ) # Fit estimators on stratum data - simple_stratum_estimator.fit(X_stratum, D_stratum, Y_stratum) - ml_stratum_estimator.fit(X_stratum, D_stratum, Y_stratum) + simple_stratum_estimator.fit(X_stratum, treatment_arms_stratum, treatment_indicator_stratum, Y_stratum, strata_stratum) + ml_stratum_estimator.fit(X_stratum, treatment_arms_stratum, treatment_indicator_stratum, Y_stratum, strata_stratum) - # Compute DTE for this stratum - dte_simple_stratum, lower_simple_stratum, upper_simple_stratum = simple_stratum_estimator.predict_dte( + # Compute LDTE for this stratum + ldte_simple_stratum, lower_simple_stratum, upper_simple_stratum = simple_stratum_estimator.predict_ldte( target_treatment_arm=1, control_treatment_arm=0, - locations=outcome_ed_costs_locations, - variance_type="moment" + locations=outcome_ed_costs_locations ) - dte_ml_stratum, lower_ml_stratum, upper_ml_stratum = ml_stratum_estimator.predict_dte( + ldte_ml_stratum, lower_ml_stratum, upper_ml_stratum = ml_stratum_estimator.predict_ldte( target_treatment_arm=1, control_treatment_arm=0, - locations=outcome_ed_costs_locations, - variance_type="moment" + locations=outcome_ed_costs_locations ) - # Store results for visualization + # Store results individual_results[stratum] = { 'simple': { - 'dte': dte_simple_stratum, + 'ldte': ldte_simple_stratum, 'lower': lower_simple_stratum, 'upper': upper_simple_stratum }, 'ml': { - 'dte': dte_ml_stratum, + 'ldte': ldte_ml_stratum, 'lower': lower_ml_stratum, 'upper': upper_ml_stratum }, - 'sample_size': len(D_stratum), - 'treatment_size': (D_stratum == 1).sum(), - 'control_size': (D_stratum == 0).sum() + 'sample_size': len(treatment_indicator_stratum), + 'treatment_assignment_size': (treatment_arms_stratum == 1).sum(), + 'treatment_indicator_size': (treatment_indicator_stratum == 1).sum() } Visualization: Comparing Overall Population vs Stratified Results @@ -474,15 +598,15 @@ Visualization: Comparing Overall Population vs Stratified Results .. code-block:: python - # Comparison: Overall vs Individual Strata + # Comparison: Overall vs Individual Strata (Local Estimators) fig, axes = plt.subplots(2, 3, figsize=(24, 12)) - # Row 1: Simple estimators + # Row 1: Simple local estimators # Overall (all data) - plot(outcome_ed_costs_locations, dte_simple, lower_simple, upper_simple, - title="Overall Population\n(Simple Estimator)", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", - color="black", ax=axes[0, 0]) + plot(outcome_ed_costs_locations, ldte_simple, lower_simple, upper_simple, + title="Overall Population\n(Simple Local Estimator)", + xlabel="Emergency Department Costs", ylabel="Local Distribution Treatment Effect", + color="black", ax=axes[0, 0]) # Individual strata col_idx = 1 @@ -490,19 +614,19 @@ Visualization: Comparing Overall Population vs Stratified Results if results is None or col_idx > 2: continue - plot(outcome_ed_costs_locations, results['simple']['dte'], - results['simple']['lower'], results['simple']['upper'], - title=f"{stratum}\n(Simple Estimator, n={results['sample_size']:,})", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", - color="blue" if col_idx == 1 else "green", ax=axes[0, col_idx]) + plot(outcome_ed_costs_locations, results['simple']['ldte'], + results['simple']['lower'], results['simple']['upper'], + title=f"{stratum}\n(Simple Local Estimator, n={results['sample_size']:,})", + xlabel="Emergency Department Costs", ylabel="Local Distribution Treatment Effect", + color="blue" if col_idx == 1 else "green", ax=axes[0, col_idx]) col_idx += 1 - # Row 2: ML-Adjusted estimators + # Row 2: ML-Adjusted local estimators # Overall (all data) - plot(outcome_ed_costs_locations, dte_ml, lower_ml, upper_ml, - title="Overall Population\n(ML-Adjusted Estimator)", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", - color="black", ax=axes[1, 0]) + plot(outcome_ed_costs_locations, ldte_ml, lower_ml, upper_ml, + title="Overall Population\n(ML-Adjusted Local Estimator)", + xlabel="Emergency Department Costs", ylabel="Local Distribution Treatment Effect", + color="black", ax=axes[1, 0]) # Individual strata col_idx = 1 @@ -510,48 +634,50 @@ Visualization: Comparing Overall Population vs Stratified Results if results is None or col_idx > 2: continue - plot(outcome_ed_costs_locations, results['ml']['dte'], - results['ml']['lower'], results['ml']['upper'], - title=f"{stratum}\n(ML-Adjusted Estimator, n={results['sample_size']:,})", - xlabel="Emergency Department Costs ($)", ylabel="Distribution Treatment Effect", - color="red" if col_idx == 1 else "purple", ax=axes[1, col_idx]) + plot(outcome_ed_costs_locations, results['ml']['ldte'], + results['ml']['lower'], results['ml']['upper'], + title=f"{stratum}\n(ML-Adjusted Local Estimator, n={results['sample_size']:,})", + xlabel="Emergency Department Costs", ylabel="Local Distribution Treatment Effect", + color="red" if col_idx == 1 else "purple", ax=axes[1, col_idx]) col_idx += 1 - plt.suptitle("Comparison: Overall Population vs Individual Household Registration Strata", fontsize=16) + plt.suptitle("Comparison: Overall Population vs Individual Household Registration Strata (Local Estimators)", fontsize=16) plt.tight_layout() plt.show() -.. image:: ../_static/oregon_dte_strata.png +.. image:: ../_static/oregon_ldte_strata.png :alt: Oregon Health Insurance Experiment DTE Strata Analysis :width: 800px :align: center **Key Insights from Stratified Analysis**: -The stratified analysis by household registration type reveals important heterogeneity in how Medicaid enrollment affects different populations: +The stratified analysis by household registration type reveals important heterogeneity in how Medicaid assignment affects different populations: -**Heterogeneous Treatment Effects**: The comparison between overall population effects and individual strata shows that treatment effects vary significantly across different household registration patterns. This heterogeneity suggests that "one-size-fits-all" policy evaluations may miss important subgroup differences. +**Heterogeneous Local Treatment Effects**: The comparison between overall population effects and individual strata shows that local treatment effects vary significantly across different household registration patterns. This heterogeneity suggests that "one-size-fits-all" policy evaluations may miss important subgroup differences in complier populations. -**Sample Size Considerations**: Different strata have varying sample sizes, which affects the precision of estimates. Larger strata (like "signed self up") provide more precise estimates, while smaller strata show wider confidence intervals but may reveal important effect heterogeneity. +**Sample Size Considerations**: Different strata have varying sample sizes, which affects the precision of estimates. Larger strata (like "signed self up") provide more precise estimates, while smaller strata show wider confidence intervals but may reveal important effect heterogeneity among compliers. -**Policy Targeting Implications**: Understanding which household types respond most strongly to Medicaid enrollment can inform more targeted policy interventions and help identify populations that would benefit most from expanded coverage. +**Policy Targeting Implications**: Understanding which household types respond most strongly to Medicaid assignment can inform more targeted policy interventions and help identify populations that would benefit most from expanded coverage when they actually enroll. -**Methodological Consistency**: Both simple and ML-adjusted estimators show similar patterns within each stratum, providing confidence in the robustness of the stratified findings across different analytical approaches. +**Methodological Consistency**: Both simple and ML-adjusted local estimators show similar patterns within each stratum, providing confidence in the robustness of the stratified findings across different analytical approaches while accounting for non-compliance. Conclusion ~~~~~~~~~~ -The Oregon Health Insurance Experiment provides a unique opportunity to study the distributional effects of Medicaid enrollment using the `dte_adj` library. This analysis demonstrates several key capabilities: +The Oregon Health Insurance Experiment provides a unique opportunity to study the local distributional effects of Medicaid assignment using the `dte_adj` library while accounting for non-compliance. This analysis demonstrates several key capabilities: + +**Local Distributional vs. Average Effects**: While traditional analyses focus on average treatment effects, the local distributional approach reveals how Medicaid assignment affects the entire distribution of healthcare utilization and costs for compliers (those who enroll when selected), providing a more accurate picture of policy impacts on the treated population. -**Distributional vs. Average Effects**: While traditional analyses focus on average treatment effects, the distributional approach reveals how Medicaid affects the entire distribution of healthcare utilization and costs, providing a more complete picture of policy impacts. +**Non-Compliance Handling**: By using Local Distribution Treatment Effects (LDTE) and Local Probability Treatment Effects (LPTE), we properly account for the fact that not all individuals assigned to treatment actually enrolled, providing estimates that are valid for the complier population. -**Multiple Outcome Analysis**: By analyzing both emergency department costs and visits separately, we gain insights into different dimensions of healthcare utilization - the intensive margin (cost per visit) and extensive margin (frequency of visits). +**Multiple Outcome Analysis**: By analyzing both emergency department costs and visits separately using local estimators, we gain insights into different dimensions of healthcare utilization for compliers - the intensive margin (cost per visit) and extensive margin (frequency of visits). -**Heterogeneity Analysis**: The stratified analysis by household registration type reveals important treatment effect heterogeneity, showing that different populations respond differently to Medicaid enrollment. +**Heterogeneity Analysis**: The stratified analysis by household registration type reveals important local treatment effect heterogeneity, showing that different populations respond differently to Medicaid assignment when they actually enroll. -**Methodological Robustness**: Comparing simple and ML-adjusted estimators provides confidence in our findings and demonstrates the robustness of the distributional treatment effect methodology. +**Methodological Robustness**: Comparing simple and ML-adjusted local estimators provides confidence in our findings and demonstrates the robustness of the local distributional treatment effect methodology for handling non-compliance scenarios. -**Policy Implications**: The distributional effects have important implications for healthcare policy, revealing that public health insurance affects different segments of the population in different ways, which is crucial for policy design and evaluation. +**Policy Implications**: The local distributional effects have important implications for healthcare policy, revealing that public health insurance affects different segments of the complier population in different ways, which is crucial for policy design and evaluation when considering real-world implementation challenges. Next Steps ~~~~~~~~~~ From 68f80097ed24d7b365235473f3422ebfc3d182e4 Mon Sep 17 00:00:00 2001 From: okiner-3 Date: Sun, 30 Nov 2025 16:18:59 +0900 Subject: [PATCH 3/3] fix preprocessing --- docs/source/tutorials/oregon.rst | 36 +++++++++++++++----------------- 1 file changed, 17 insertions(+), 19 deletions(-) diff --git a/docs/source/tutorials/oregon.rst b/docs/source/tutorials/oregon.rst index 24b284e..6a4eede 100644 --- a/docs/source/tutorials/oregon.rst +++ b/docs/source/tutorials/oregon.rst @@ -21,8 +21,6 @@ The dataset includes multiple files containing information about participants in This data supports research on how health insurance affects healthcare utilization and is maintained by researchers Amy Finkelstein and Katherine Baicker. Please ensure you comply with the data use agreements when downloading and using this dataset. -**Important**: When using this dataset for research or publications, appropriate citation is required as specified in the NBER data use agreement. - .. code-block:: python import numpy as np @@ -56,18 +54,18 @@ This data supports research on how health insurance affects healthcare utilizati # Prepare the data for dte_adj analysis # Create treatment assignment (instrumental variable): 0=Not selected, 1=Selected treatment_assignment_mapping = {'Not selected': 0, 'Selected': 1} - df['Z'] = df['treatment'].map(treatment_assignment_mapping).astype(float).fillna(-1).astype(int) + df['Z'] = df['treatment'].map(treatment_assignment_mapping) # Create actual treatment indicator: 0=Not enrolled, 1=Enrolled, -1=Missing treatment_mapping = {'NOT enrolled': 0, 'Enrolled': 1} - df['D'] = df['ohp_all_ever_inperson'].map(treatment_mapping).astype(float).fillna(-1).astype(int) - - # Use emergency department costs and visits as outcome variables - df['Y_ED_CHARG_TOT_ED'] = df['ed_charg_tot_ed'].fillna(0) - df['Y_NUM_VISIT_CENS_ED'] = df['num_visit_cens_ed'].fillna(0) + df['D'] = df['ohp_all_ever_inperson'].map(treatment_mapping) # Create strata based on household size - df['strata'] = df['numhh_list'] + df.rename(columns={'numhh_list': 'strata'}, inplace=True) + df['strata'] = df['strata'].replace({ + 'signed self up + 1 additional person': 'signed self up + others', + 'signed self up + 2 additional people': 'signed self up + others' + }) # Create feature mappings for categorical variables gender_mapping = {'Male': 0, 'Female': 1, 'Transgender F to M': 2, 'Transgender M to F': 3} @@ -80,21 +78,21 @@ This data supports research on how health insurance affects healthcare utilizati df['edu_inp'] = df['edu_inp'].map(edu_mapping).astype(float).fillna(-1).astype(int) # Select control variables: pre-randomization ED utilization variables - ctrl_cols = [col for col in df_ed.columns if 'pre' in col and 'num' in col] - ctrl_cols.append('charg_tot_pre_ed') - selected_cols = ['person_id', 'strata', 'Y_NUM_VISIT_CENS_ED', 'Y_ED_CHARG_TOT_ED', 'Z', 'D'] + ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp'] + ctrl_cols = [col for col in df_ed.columns if 'pre' in col and 'num' in col] + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp', 'charg_tot_pre_ed'] + selected_cols = ['person_id', 'strata', 'ed_charg_tot_ed', 'num_visit_cens_ed', 'Z', 'D'] + ctrl_cols df = df[selected_cols] - df = df[df.isna().any(axis=1) == False] + df = df.dropna().reset_index(drop=True) # Create feature matrix (excluding treatment variables) - features = pd.DataFrame(df[ctrl_cols + ['gender_inp', 'age', 'health_last12_inp', 'edu_inp']]) - X = features.values + X = df[ctrl_cols].values - Z = df['Z'].values # Treatment assignment (instrumental variable) - D = df['D'].values # Actual treatment (endogenous variable) + Z = df['Z'].astype(int).values # Treatment assignment (instrumental variable) + D = df['D'].astype(int).values # Actual treatment (endogenous variable) strata = df['strata'].values # Stratification variable - Y_ED_CHARG_TOT_ED = df['Y_ED_CHARG_TOT_ED'].values - Y_NUM_VISIT_CENS_ED = df['Y_NUM_VISIT_CENS_ED'].values + + # Use num_visit_cens_ed and ed_charg_tot_ed as outcome variables + Y_ED_CHARG_TOT_ED = df['ed_charg_tot_ed'].values + Y_NUM_VISIT_CENS_ED = df['num_visit_cens_ed'].values print(f"\nDataset size: {len(D):,} people") print(f"Treatment assignment (Z) - Not selected: {(Z==0).sum():,} ({(Z==0).mean():.1%})")