Estimating Adverse Effects in Observational Studies with Truncation by Death Using a Bayesian Approach

Core Concepts

This paper proposes a novel Bayesian method for estimating the causal effects of interventions on adverse events in observational studies where death is a common occurrence, addressing the challenge of outcome truncation by death.

Abstract

Bibliographic Information:

Sisti, A., Zullo, A., & Gutman, R. (2016). A Bayesian Method for Adverse Effects Estimation in Observational Studies with Truncation by Death. Statistical Methods in Medical Research, XX(X), 2–31. https://doi.org/10.1177/ToBeAssigned

Research Objective:

This research paper aims to address the challenge of estimating the causal effects of interventions on adverse events in observational studies, particularly when death is a common outcome that can truncate the observation period.

Methodology:

The authors propose a Bayesian method that imputes unobserved mortality and adverse event outcomes for each participant under the intervention they did not receive. This imputation allows for the creation of a composite ordinal outcome combining death and adverse events on a scale of increasing severity. The method utilizes propensity score stratification and linear adjustments for covariates to model the conditional distributions of adverse events and death. Bayesian logistic regression models are employed to estimate the parameters, and posterior distributions of various causal estimands are obtained.

Key Findings:

The proposed Bayesian method provides statistically valid point and interval estimates for a range of causal estimands, including traditional measures like intention-to-treat effects and novel composite ordinal outcome estimands. The method demonstrates superior performance compared to traditional doubly robust estimators, particularly in capturing the nuanced interplay between adverse events and death.

Main Conclusions:

The paper concludes that the proposed Bayesian method offers a robust and flexible approach to estimating causal effects in observational studies with truncation by death. The composite ordinal outcome framework provides a more comprehensive understanding of treatment effects by considering the joint distribution of adverse events and mortality.

Significance:

This research significantly contributes to the field of causal inference by addressing a critical challenge in observational studies with high mortality rates. The proposed method enhances the accuracy and interpretability of treatment effect estimates, leading to more informed decision-making in healthcare and other fields.

Limitations and Future Research:

The study acknowledges the reliance on the strong ignorability assumption and proposes a sensitivity analysis to assess its validity. Future research could explore alternative approaches to sensitivity analysis and extend the method to handle time-to-event outcomes.

Stats

In 2023, about 1 in 10 individuals in the United States had diabetes, with approximately 90-95% of these cases classified as type 2 diabetes mellitus (T2DM).
The study included 1,064 new DPP4I users and 6,821 new SU users.
Propensity score matching yielded 1,008 patients initiating DPP4I and 1,008 initiating SU.

Quotes

Key Insights Distilled From

A Bayesian Method for Adverse Effects Estimation in Observational Studies with Truncation by Death

by Anthony Sist... at arxiv.org 10-08-2024

https://arxiv.org/pdf/2410.04561.pdf

Deeper Inquiries

How can this Bayesian method be adapted for use in situations where the assumption of no contamination of imputation across treatments is not plausible?

The assumption of "no contamination of imputation across treatments" essentially means assuming that the potential outcomes under one treatment assignment are independent of the potential outcomes under the other treatment assignment, conditional on the observed covariates. This assumption simplifies the imputation procedure but might not hold in some situations.
Here's how the Bayesian method can be adapted when this assumption is not plausible:

Joint Modeling of Potential Outcomes: Instead of modeling the outcomes under each treatment arm separately, a joint model for the potential outcomes (Y(1), Y(0)) can be specified. This joint model would explicitly account for the dependence between the potential outcomes, even after conditioning on observed covariates.

Shared Random Effects: One way to induce dependence in the joint model is by incorporating shared random effects. These random effects would capture unobserved factors that influence both potential outcomes. For instance, in the diabetes example, an unobserved individual frailty could make a person more susceptible to both heart failure and death, regardless of the treatment received.

Copula Models: Copula models provide a flexible framework for modeling the dependence structure between random variables. In this context, a copula could be used to link the marginal distributions of the potential outcomes (modeled separately), thereby accounting for their dependence.

Sensitivity Analysis: Even when using a joint model, it's crucial to conduct sensitivity analyses to assess the robustness of the findings to different assumptions about the dependence structure. This could involve varying the strength of the association in the joint model or exploring different copula functions.

By adopting these modifications, the Bayesian method can be extended to handle situations where the assumption of no contamination of imputation across treatments is not tenable, providing more reliable causal effect estimates.

Could a frequentist approach using multiple imputation and a composite ordinal outcome achieve comparable results to the proposed Bayesian method?

Yes, a frequentist approach using multiple imputation (MI) and a composite ordinal outcome could potentially achieve comparable results to the proposed Bayesian method. Here's how a frequentist approach could be structured:

Multiple Imputation: Similar to the Bayesian method, multiple imputation would be used to handle the missing potential outcomes. Instead of sampling from a posterior distribution, MI would involve:

Estimating parameters of an imputation model (e.g., logistic regression for the adverse event and death, potentially with interactions or shared random effects to account for dependence).
Imputing the missing potential outcomes multiple times by drawing from the predictive distribution of the fitted imputation model.

Composite Ordinal Outcome: The same composite ordinal outcome (combining death and adverse event severity) would be constructed within each imputed dataset.

Analysis of Ordinal Outcome: Within each imputed dataset, the causal effect of interest would be estimated using an appropriate method for ordinal outcomes. Common choices include:

The proportional odds model (if the proportional odds assumption holds).
The continuation ratio model.
The generalized estimating equations (GEE) approach for ordinal data.

Pooling Results: The estimates of the causal effect and their variances from each imputed dataset would be combined using Rubin's rules to obtain a single overall estimate, standard error, and confidence interval.

Comparison and Considerations:

Comparability: In large samples, the frequentist MI approach and the Bayesian method are expected to yield similar results, especially when using similar imputation models and prior distributions that are not overly informative.
Computational Burden: The computational burden of the frequentist MI approach might be lower than the Bayesian method, particularly when the Bayesian model involves complex structures or requires Markov Chain Monte Carlo (MCMC) sampling.
Uncertainty Quantification: The Bayesian method provides a more comprehensive characterization of uncertainty by directly yielding a posterior distribution for the causal effect. In contrast, the frequentist MI approach relies on asymptotic approximations for confidence interval construction.
In summary, both frequentist MI and Bayesian approaches can be used effectively with a composite ordinal outcome. The choice between them might depend on factors such as the complexity of the imputation model, computational resources, and the desired level of detail in uncertainty quantification.

How can the insights from this research be applied to improve the design and analysis of observational studies in other fields facing similar challenges with outcome truncation?

The insights from this research on handling outcome truncation using a composite ordinal outcome and multiple imputation have broad applicability across various fields facing similar challenges in observational studies. Here's how these insights can be applied:
Design:

Anticipate Truncation: Researchers should carefully consider the potential for outcome truncation during the study design phase. Identify outcomes where truncation by death or other competing events is likely.

Collect Rich Covariate Information: Gather comprehensive data on covariates that are potentially related to both the treatment assignment and the outcomes of interest. This rich covariate information is crucial for building flexible imputation models and reducing bias due to confounding.

Consider Composite Outcomes: When facing outcome truncation, explore the use of composite ordinal outcomes that combine the truncated outcome with the truncating event (e.g., death). This allows for a more complete picture of the treatment's effects.

Analysis:

Multiple Imputation: Employ multiple imputation techniques to handle missing potential outcomes due to truncation. Carefully consider the assumptions of the imputation model and explore potential dependencies between potential outcomes.

Ordinal Outcome Analysis: Utilize appropriate statistical methods for analyzing ordinal outcomes, such as the proportional odds model, continuation ratio model, or GEE for ordinal data.

Sensitivity Analysis: Conduct thorough sensitivity analyses to assess the robustness of the findings to different assumptions about the missing data mechanism, the imputation model, and the dependence structure between potential outcomes.

Fields of Application:
These insights can be applied to improve observational studies in fields such as:

Oncology: Studies evaluating cancer treatments often face truncation due to death from cancer or other causes.
Cardiovascular Disease: Studies of interventions for heart disease may encounter truncation due to death from cardiovascular events.
Critical Care Medicine: Research in intensive care units frequently deals with outcome truncation as death is a common occurrence.
Transplantation: Studies assessing the effectiveness of organ transplantation must account for truncation due to death while waiting for a transplant or post-transplant complications.
By incorporating these design and analysis strategies, researchers can enhance the validity and reliability of causal effect estimates in observational studies affected by outcome truncation, leading to more informed decision-making in various fields.