Estimating Treatment Effects with Unmeasured Confounders Using a Joint Modeling Approach in Longitudinal Data

Core Concepts

This paper proposes a novel joint mixed-effects modeling approach to estimate treatment effects in longitudinal studies while addressing the challenge of unmeasured confounders.

Abstract

• Bibliographic Information: Lee, N., & Ma, S. (2024). A joint modeling approach to treatment effects estimation with unmeasured confounders. arXiv preprint arXiv:2411.10980v1.
• Research Objective: This paper aims to develop a new method for estimating treatment effects in longitudinal studies when unmeasured confounders are present.
• Methodology: The authors propose a joint mixed-effects modeling approach that incorporates both outcome regression (OR) and propensity score (PS) functions. The OR model allows for interactions between treatment assignments and both observed and unobserved confounding factors. The PS model is a logistic mixed-effects model. A new Laplacian-variant EM algorithm is developed to estimate the model parameters.
• Key Findings: The proposed method allows for the estimation of average treatment effects (ATE) and heterogeneous treatment effects (HTE) in the presence of unmeasured confounders. Simulation studies demonstrate the accuracy of the proposed method in estimating model parameters. The application of the method to the CitieS-Health Barcelona Panel Study suggests a significant impact of unmeasured confounders on the causal relationship between air pollution and cognitive health.
• Main Conclusions: The joint mixed-effects modeling approach provides a robust framework for estimating treatment effects when unmeasured confounders are a concern. The Laplacian-variant EM algorithm offers an effective way to estimate model parameters. The findings highlight the importance of accounting for unmeasured confounding in causal inference, particularly in air pollution and health research.
• Significance: This research contributes to the field of causal inference by providing a new method for addressing unmeasured confounding in longitudinal data. The findings have implications for environmental policy and public health interventions aimed at mitigating the negative effects of air pollution.
• Limitations and Future Research: The study acknowledges the limitations of observational studies in establishing causality definitively. Future research could explore the application of the proposed method to other health outcomes and environmental exposures. Additionally, investigating the impact of different assumptions about the distribution of unmeasured confounders on treatment effect estimates would be valuable.

Stats

The dataset comprises 3,333 observations from 286 distinct participants.
The annual average standard for PM2.5 levels is 12 µg/m3.

Quotes

"Estimating treatment effects using observation data often relies on the assumption of no unmeasured confounders. However, unmeasured confounding variables may exist in many real-world problems."
"In this paper, we propose a new mixed-effect joint modeling approach to identifying and estimating the outcome regression (OR) function and propensity score (PS) function in the presence of unmeasured confounders in longitudinal studies."

Key Insights Distilled From

A joint modeling approach to treatment effects estimation with unmeasured confounders

by Namhwa Lee, ... at arxiv.org 11-19-2024

https://arxiv.org/pdf/2411.10980.pdf

Deeper Inquiries

How might this joint modeling approach be adapted to handle time-varying treatments in addition to unmeasured confounders?

Adapting this joint modeling approach to handle time-varying treatments while accounting for unmeasured confounders presents a significant challenge in causal inference. Here's a breakdown of potential adaptations and the complexities involved:
1. Model Reformulation:

Outcome Regression (OR) Model: The OR model (3) needs to incorporate the time-varying nature of the treatment. One approach is to include past treatment history as covariates. For instance, we could include D_{i,j-1}, D_{i,j-2}, etc., to capture the lagged effects of treatment. Alternatively, we could model the treatment effect as a function of cumulative exposure or time since the last treatment.
Propensity Score (PS) Model: The PS model (4) also needs modification. Instead of a single propensity score, we would need to estimate a sequence of propensity scores for each time point, conditional on past treatment history, observed covariates, and the unmeasured confounder (bi). This could involve a series of linked logistic regressions or a more complex model like a dynamic discrete choice model.
2. Estimation Challenges:

Increased Complexity: The inclusion of time-varying treatments significantly increases the complexity of both the OR and PS models. This can lead to computational challenges, especially with the Laplace approximation used in the E-step.
Assumptions: The "conditional ignorability" assumption (A1) becomes more stringent with time-varying treatments. We need to assume that the treatment decision at each time point is independent of future potential outcomes, conditional on past treatment history, observed covariates, and the unmeasured confounder. This assumption is often difficult to justify in practice.
3. Alternative Approaches:

Marginal Structural Models (MSMs): MSMs offer a powerful framework for handling time-varying treatments. They involve weighting each individual's contribution to the analysis based on their estimated treatment history weights (inverse probability of treatment weights). These weights are derived from the sequence of propensity scores estimated in the PS model.
G-estimation: This semi-parametric method is particularly useful when there are concerns about model misspecification in the OR model. It focuses on estimating the parameters of a causal effect model directly, without explicitly modeling the outcome.
4. Considerations:

Data Requirements: Handling time-varying treatments requires detailed longitudinal data with frequent measurements of both the treatment and outcome variables.
Causal Interpretation: Careful consideration is needed when interpreting causal effects with time-varying treatments. The estimated effects represent the impact of a specific treatment strategy (e.g., always treated, never treated, or a dynamic treatment rule) rather than the effect of a single treatment episode.

Could the reliance on model assumptions regarding the unmeasured confounders be mitigated through alternative approaches like instrumental variables or sensitivity analysis?

Yes, the reliance on model assumptions regarding unmeasured confounders can be mitigated through alternative approaches like instrumental variables (IVs) or sensitivity analysis. Here's how:
1. Instrumental Variables (IVs):

Concept: IVs are variables that are:

Correlated with the treatment: They influence the likelihood of receiving the treatment.
Not directly related to the outcome: Their only impact on the outcome is through their effect on the treatment.
Not associated with unmeasured confounders: They are not influenced by the same factors that confound the relationship between the treatment and outcome.

Mitigation: IV methods leverage these properties to isolate the causal effect of the treatment, even in the presence of unmeasured confounding. By focusing on the variation in the treatment that is driven by the instrument, we can obtain unbiased estimates of the treatment effect.
Example: In a study on the effect of education (treatment) on earnings (outcome), distance to the nearest college could serve as an instrument. It likely influences educational attainment but is unlikely to directly affect earnings, except through its impact on education.
2. Sensitivity Analysis:

Concept: Sensitivity analysis explores how the estimated treatment effect changes under different assumptions about the strength and direction of the unmeasured confounding.
Mitigation: While we cannot directly observe or measure the unmeasured confounder, we can make plausible assumptions about its relationship with the treatment and outcome. By varying these assumptions systematically, we can assess the robustness of our findings to different levels of unmeasured confounding.
Example: In the air pollution study, we could perform a sensitivity analysis by assuming different strengths of association between the unmeasured confounder (e.g., socioeconomic status) and both air pollution exposure and cognitive health. This would allow us to see how the estimated effect of air pollution on cognitive health changes as we vary the assumed impact of the unmeasured confounder.
3. Comparison:

IVs: Offer a potentially more robust solution to unmeasured confounding but require finding a valid instrument, which can be challenging.
Sensitivity Analysis: More widely applicable but relies on assumptions about the unmeasured confounder, which cannot be fully verified with the observed data.
4. Conclusion:
Both IVs and sensitivity analysis provide valuable tools for addressing unmeasured confounding. The choice of approach depends on the specific context, data availability, and the plausibility of finding a valid instrument.

What are the broader ethical implications of using observational data and statistical modeling to infer causal relationships in health research, particularly when considering policy decisions?

Using observational data and statistical modeling to infer causal relationships in health research, especially for policy decisions, carries significant ethical implications:
1. Potential for Bias and Misinterpretation:

Unmeasured Confounding: As highlighted in the paper, observational studies are inherently vulnerable to unmeasured confounding. Failing to account for these confounders can lead to biased estimates of treatment effects, potentially resulting in misguided policies.
Model Dependence: Causal inferences drawn from statistical models are contingent on the validity of the model assumptions. If these assumptions are incorrect, the resulting causal interpretations may be misleading.
2. Implications for Resource Allocation and Intervention Strategies:

Misguided Policies: Policy decisions based on flawed causal inferences can lead to the misallocation of resources, potentially diverting funds from more effective interventions or even causing harm.
Health Disparities: If observational data is not carefully analyzed for biases related to socioeconomic factors, race, or access to healthcare, the resulting policies may exacerbate existing health disparities.
3. Transparency and Public Trust:

Clear Communication: Researchers have an ethical obligation to clearly communicate the limitations of observational studies and the potential for bias in causal inferences. This transparency is crucial for informed policymaking and maintaining public trust in health research.
Data Privacy: When using observational data, especially from large databases, researchers must prioritize data privacy and ensure that appropriate safeguards are in place to protect sensitive patient information.
4. Importance of Ethical Review and Oversight:

Independent Review: Ethical review boards (IRBs) play a vital role in scrutinizing research proposals that involve causal inference from observational data. They help ensure that potential biases are addressed, and appropriate methods are used.
Post-Publication Review: Continued scrutiny and critical evaluation of published studies are essential, especially when policy decisions are at stake.
5. Balancing Benefits and Risks:

Potential Benefits: Observational studies can provide valuable insights into complex health issues, especially when randomized controlled trials are infeasible or unethical.
Cautious Interpretation: However, it's crucial to interpret causal claims from observational data cautiously, acknowledging limitations and potential biases.
In conclusion, while observational data and statistical modeling offer powerful tools for health research, their use for causal inference, particularly in policy decisions, demands rigorous ethical considerations. Transparency, careful analysis, and a focus on mitigating bias are paramount to ensure that policies are based on sound evidence and promote equitable health outcomes.