Estimating Heterogeneous Treatment Effects Using Both Weak Instruments and Observational Data

Core Concepts

This paper proposes a novel two-stage framework for estimating conditional average treatment effects (CATEs) by combining observational data and instrumental variable (IV) data, effectively addressing the limitations of each approach when used in isolation, particularly in scenarios with weak instruments or low compliance.

Abstract

Oprescu, M., & Kallus, N. (2024). Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data. Advances in Neural Information Processing Systems, 38.

This research paper aims to develop a robust method for estimating conditional average treatment effects (CATEs) in settings where observational data suffers from unobserved confounding and instrumental variable (IV) data exhibits low compliance, including situations where some subgroups have zero compliance.

Key Insights Distilled From

Estimating Heterogeneous Treatment Effects by Combining Weak Instruments and Observational Data

by Miruna Opres... at arxiv.org 11-05-2024

https://arxiv.org/pdf/2406.06452.pdf

Deeper Inquiries

How can this framework be extended to handle time-varying treatments and confounders, which are common in longitudinal studies?

Extending this framework to accommodate time-varying treatments and confounders in longitudinal studies presents a significant challenge but also a promising research direction. Here's a breakdown of the key considerations and potential approaches:
Challenges:

Temporal Dependencies: Longitudinal data inherently involve temporal dependencies between treatments, confounders, and outcomes at different time points. Standard IV assumptions, like unconfounded compliance, need to be carefully adapted to this dynamic setting.
Time-Varying Confounding: Confounders themselves might evolve over time, influenced by past treatments and outcomes. This necessitates more sophisticated methods for disentangling the causal effects from the complex interplay of time-varying factors.
High Dimensionality: Longitudinal data often result in high-dimensional datasets, especially when considering multiple time points. This can exacerbate the curse of dimensionality and pose challenges for both estimation and inference.
Potential Extensions:

Marginal Structural Models (MSMs): MSMs offer a powerful framework for handling time-varying treatments and confounders. The core idea is to model the relationship between the treatment history and the outcome, adjusting for time-varying confounding through weighting or stratification based on the estimated propensity of treatment at each time point. Combining MSMs with the proposed two-stage framework could involve:

Stage 1: Estimate biased CATEs at each time point from observational data using methods like inverse probability weighting (IPW) or g-estimation within the MSM framework.
Stage 2: Leverage IV data to learn and correct for time-varying bias in the estimated CATEs, potentially using a similar weighting scheme based on compliance over time.

Structural Nested Mean Models (SNMMs): SNMMs provide an alternative approach for estimating the causal effects of time-varying treatments. They focus on modeling the effect of a treatment at a given time point, conditional on past treatment and covariate history. Integrating SNMMs with the proposed framework could involve:

Stage 1: Estimate biased CATEs at each time point from observational data using g-estimation or other SNMM-based methods.
Stage 2: Utilize IV data to debias the SNMM estimates, potentially by incorporating compliance information into the estimating equations.

Recurrent Neural Networks (RNNs): RNNs are well-suited for modeling sequential data and could be adapted to handle time-varying treatments and confounders. One potential approach is to use RNNs within the shared representation learning framework:

Stage 1: Train an RNN on observational data to learn a joint representation of the treatment and outcome history, capturing temporal dependencies and potential confounding.
Stage 2: Use IV data to adjust the RNN's predictions, potentially by incorporating compliance information into the loss function or by training a separate module to predict and correct for bias.

Additional Considerations:

Assumptions: Carefully revisit and adapt the IV assumptions to the longitudinal setting, paying close attention to potential violations and their implications for bias.
Data Requirements: Longitudinal studies with IVs and rich observational data are relatively rare. Consider alternative quasi-experimental designs or leverage external data sources when feasible.
Computational Complexity: Estimating CATEs with time-varying treatments and confounders is computationally demanding. Explore efficient algorithms and computational resources to handle the increased complexity.

Could the reliance on parametric assumptions for the bias function or shared representation be relaxed while maintaining the desirable properties of the estimator?

Relaxing the parametric assumptions for the bias function or shared representation while preserving the estimator's desirable properties is an active area of research in causal inference and machine learning. Here are some promising directions:
1. Nonparametric Methods:

Kernel-Based Methods: Instead of assuming a parametric form, kernel-based methods can estimate the bias function nonparametrically. This approach involves weighting data points based on their proximity in the covariate space, allowing for more flexible bias correction. However, kernel methods can suffer from the curse of dimensionality and require careful bandwidth selection.
Gaussian Processes (GPs): GPs offer a powerful Bayesian nonparametric framework for function approximation. They can be used to model the bias function, allowing for flexible and data-driven estimation. However, GPs can be computationally demanding for large datasets.
2. Semiparametric Methods:

Single-Index Models: These models relax the linearity assumption by assuming that the bias function depends on a linear combination of covariates, but the functional form of this dependence is left unspecified. This provides more flexibility while retaining some of the advantages of parametric models.
Additive Models: Additive models assume that the bias function can be decomposed into a sum of smooth functions of individual covariates. This allows for nonlinear relationships between covariates and the bias while maintaining interpretability.
3. Flexible Representation Learning:

Deep Neural Networks (DNNs): DNNs with appropriate regularization can learn highly flexible representations without explicit parametric assumptions. However, careful architecture design and regularization are crucial to prevent overfitting and ensure generalization.
Variational Autoencoders (VAEs): VAEs can learn latent representations that capture complex relationships in the data. These representations can be used to model the bias function in a more flexible manner.
4. Doubly Robust Estimation:

Augmented Inverse Probability Weighting (AIPW): AIPW combines regression-based and weighting-based estimators to achieve double robustness. This means that the estimator remains consistent if either the bias function or the propensity score model is correctly specified.
Challenges and Considerations:

Bias-Variance Trade-off: Relaxing parametric assumptions introduces more flexibility but can also increase variance. Carefully balance bias reduction with variance control through regularization or model selection techniques.
Computational Complexity: Nonparametric and semiparametric methods can be computationally more demanding than parametric approaches.
Interpretability: Nonparametric models can be more challenging to interpret than parametric models. Consider the trade-off between flexibility and interpretability based on the application.

What are the ethical implications of using machine learning techniques to combine observational and experimental data for causal inference, particularly in sensitive domains like healthcare?

Combining observational and experimental data using machine learning for causal inference in healthcare presents significant ethical implications that demand careful consideration:
1. Fairness and Bias Amplification:

Data Biases: Both observational and experimental data can inherit biases present in healthcare systems, such as disparities in access to care or representation of certain demographics. Machine learning models trained on such data can perpetuate and even amplify these biases, leading to unfair or discriminatory treatment recommendations.
Algorithmic Transparency: The complexity of some machine learning models can make it challenging to understand how they arrive at specific treatment recommendations. This lack of transparency can exacerbate concerns about fairness and make it difficult to identify and mitigate potential biases.
2. Privacy and Data Security:

Data Linkage: Combining observational and experimental data often requires linking individual records from different sources, raising privacy concerns, especially if data contain sensitive health information.
Data Security: Aggregated datasets containing both observational and experimental data can be attractive targets for data breaches. Robust data security measures are essential to protect patient privacy and prevent unauthorized access.
3. Informed Consent and Patient Autonomy:

Transparency in Data Use: Patients participating in experimental studies might not be aware that their data could be combined with observational data for further analysis. Informed consent processes should clearly explain the potential uses of data, including data linkage and machine learning applications.
Patient Choice: Patients should have a say in how their data are used. Consider mechanisms for patients to opt out of data linkage or specific analyses, especially those involving sensitive health information.
4. Responsibility and Accountability:

Algorithmic Accountability: When machine learning algorithms inform treatment decisions, it's crucial to establish clear lines of responsibility and accountability for potential errors or biases.
Human Oversight: Maintain human oversight in the decision-making process. Machine learning models should be used as tools to assist healthcare professionals, not replace their judgment or expertise.
Mitigating Ethical Risks:

Diverse and Representative Data: Strive for diverse and representative datasets to minimize bias and ensure equitable treatment recommendations.
Fairness-Aware Machine Learning: Employ fairness-aware machine learning techniques that explicitly address and mitigate potential biases in the data and models.
Explainable AI (XAI): Utilize XAI methods to enhance the transparency and interpretability of machine learning models, making it easier to understand and scrutinize their recommendations.
Robust Privacy and Security Measures: Implement strong data de-identification techniques, secure data storage, and access controls to safeguard patient privacy.
Ethical Review Boards: Engage ethical review boards to assess the potential risks and benefits of combining observational and experimental data using machine learning, particularly in sensitive healthcare applications.
By proactively addressing these ethical implications, we can harness the power of machine learning to improve healthcare outcomes while upholding fairness, privacy, and patient autonomy.