[Paper Review] A Bayesian Nonparametric Approach for Evaluating the Causal Effect of Treatment in Randomized Trials with Semi-Competing Risks

Yanxun Xu, Daniel O. Scharfstein+2 more|arXiv (Cornell University)|Mar 20, 2019

Advanced Causal Inference Techniques29 references4 citations

TL;DR

This paper proposes a Bayesian nonparametric approach to estimate the causal effect of treatment on nonterminal events in randomized trials with semi-competing risks, using principal stratification and a sensitivity parameter to handle identifiability. The method provides robust inference through flexible modeling of observed data distributions and demonstrates improved fit and credible causal estimates in a brain cancer trial, outperforming naive approaches in model fit and treatment effect estimation.

ABSTRACT

We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the idea of principal stratification, we define a novel estimand for the causal effect of treatment on the nonterminal event. We introduce identification assumptions, indexed by a sensitivity parameter, and show how to draw inference using our BNP approach. We conduct simulation studies and illustrate our methodology using data from a brain cancer trial.

Motivation & Objective

• To address the challenge of estimating causal effects on nonterminal outcomes when terminal events (e.g., death) may preclude observation of progression in randomized trials.
• To define a novel causal estimand based on principal stratification that quantifies the treatment effect on progression under semi-competing risks.
• To develop a flexible Bayesian nonparametric model that accommodates baseline covariates and handles the identification of the estimand through a sensitivity parameter.
• To evaluate the method’s performance through simulation and real data analysis in a phase II brain tumor trial.
• To provide a robust framework for causal inference that allows for uncertainty quantification and predictive inference under model misspecification.

Proposed method

• Proposes a time-varying relative risk-based causal estimand using principal stratification, focusing on the subgroup where progression would be observable under both treatment and control.
• Introduces identification assumptions indexed by a sensitivity parameter ρ, representing the correlation between survival under treatment and control, to address non-identifiability.
• Employs a dependent Dirichlet process (DDP) prior to flexibly model the joint distribution of observed failure times and baseline covariates, enabling nonparametric estimation of the data distribution.
• Uses posterior summarization to draw inference on the causal estimand, with the ability to incorporate prior distributions on ρ for integrated uncertainty quantification.
• Applies the method to a brain tumor trial with 219 patients, using posterior predictive checks and model fit via log-pseudo marginal likelihood (LPML).
• Performs sensitivity analysis across multiple values of ρ (0.2, 0.5, 0.8) to assess robustness of results to assumptions about unobserved dependence.

Experimental results

Research questions

• RQ1 How can we define a valid causal estimand for the effect of treatment on progression in the presence of semi-competing risks?
• RQ2 What identification assumptions are required to link the observable data distribution to the causal estimand, and how can they be parameterized?
• RQ3 How can Bayesian nonparametric methods be adapted to model the joint distribution of failure times and covariates in this context?
• RQ4 How does the proposed method compare to standard approaches in terms of model fit and causal effect estimation?
• RQ5 How sensitive are the causal effect estimates to the choice of the sensitivity parameter ρ?

Key findings

• The BNP approach produced a posterior estimated difference in survival at 365 days of 6.2% (95% CI: -1.2% to 13.3%), compared to 2.6% from Kaplan-Meier, indicating higher treatment-specific survival estimates.
• The Naive approach yielded a higher estimated treatment difference of 8.4% (95% CI: 0.2% to 17.9%), but produced lower survival estimates for the control group than Kaplan-Meier.
• LPML comparisons showed the BNP model had better fit than the Naive model, with LPML values of -144 (treatment) and -137 (control) versus -161 and -174, respectively.
• Posterior estimates of the causal estimand τ(u) showed lower risk of progression under treatment across all time points except near u=0, though with wide credible intervals indicating high uncertainty.
• The results were robust to different values of the sensitivity parameter ρ (0.2, 0.5, 0.8), with minimal differences in posterior estimates across ρ values.
• The BNP model demonstrated superior fit to both survival and progression data, with LPML of -227 (treatment) and -215 (control), compared to -232 and -214 for the Naive model.