[Paper Review] Bayesian Stacked Parametric Survival with Frailty Components and Interval Censored Failure Times

Matthew W. Wheeler, Joost Westerhout+2 more|arXiv (Cornell University)|Aug 29, 2019

Statistical Methods in Clinical Trials20 references4 citations

TL;DR

This paper proposes a Bayesian stacked parametric survival model with frailty components for interval-censored failure time data, using posterior predictive stacking to combine multiple parametric models and improve predictive accuracy. The method outperforms single-model approaches by reducing bias and better capturing uncertainty, especially in the tails of dose-to-failure distributions, as demonstrated in food allergy challenge studies with improved ED05 estimates for peanut and sesame allergens.

ABSTRACT

To better understand effects of exposure to food allergens, food challenge studies are designed to slowly increase the dose of an allergen delivered to allergic individuals until an objective reaction occurs. These dose-to-failure studies are used to determine acceptable intake levels and are analyzed using parametric failure time models. Though these models can provide estimates of the survival curve, their parametric form may misrepresent the survival function for doses of interest, and different models that describe the data similarly may produce different dose-to-failure estimates. Motivated by predictive inference, we developed a Bayesian approach to combine survival estimates based upon posterior predictive stacking, where the weights are formed to maximize posterior predictive accuracy. The approach allows for the inclusion of flexible models, and, in our case, allows us to include random effects to account for frailty components entering the model through study-to-study heterogeneity. The methodology is investigated in simulation, and is used to estimate allergic population eliciting doses for multiple food allergens.

Motivation & Objective

• To address the limitations of single parametric survival models in estimating dose-to-failure distributions for interval-censored data, particularly in the tails.
• To develop a robust, flexible framework that combines multiple parametric survival models using Bayesian stacking to enhance predictive accuracy.
• To incorporate random effects (frailty components) to account for study-to-study heterogeneity in multi-center food allergy challenge studies.
• To provide more reliable and conservative estimates of population-based eliciting doses (ED01, ED05) for food allergens.
• To extend model averaging techniques to interval-censored failure time data, a gap in current risk assessment methodologies.

Proposed method

• Uses posterior predictive stacking to combine multiple parametric survival models, assigning weights based on posterior predictive accuracy.
• Applies accelerated failure time (AFT) models as base learners, including flexible distributions such as Log-Laplace, Weibull, Log-Logistic, and Log-Gaussian.
• Incorporates random effects (frailty components) to model study-level variability and account for heterogeneity across clinical trials.
• Employs a Bayesian hierarchical framework to jointly estimate model weights and survival parameters, ensuring coherent uncertainty quantification.
• Utilizes Markov Chain Monte Carlo (MCMC) sampling to obtain posterior distributions for model parameters and predictions.
• Validates the method through simulation studies and applies it to real-world oral food challenge data from 17 peanut and 3 sesame allergy studies.

Experimental results

Research questions

• RQ1 Can Bayesian stacked parametric survival models with frailty components improve predictive accuracy for interval-censored failure time data compared to single-model approaches?
• RQ2 How do model stacking weights vary across different parametric distributions in the context of food allergy dose-to-failure estimation?
• RQ3 To what extent does the inclusion of frailty components reduce bias and improve uncertainty quantification in multi-study survival analysis?
• RQ4 How do the stacked estimates of ED05 compare to those from individual AFT models and previous benchmark dose recommendations?
• RQ5 Can this framework be generalized to other domains involving interval-censored time-to-event data, such as carcinogenicity or machine reliability studies?

Key findings

• For peanut allergy, the stacked model estimated an ED05 of 1.1 mg with a 95% credible interval of 0.6–2.0 mg, which is more conservative than previous estimates and better captures tail behavior.
• For sesame allergy, the stacked ED05 estimate was 5.1 mg, with a 95% credible interval of 0.6–15.3 mg, showing strong alignment with the lower bounds of individual AFT models.
• The Log-Laplace distribution received the highest stacking weight in the sesame reanalysis, demonstrating the method’s ability to identify and favor more accurate models.
• The stacked approach produced more conservative ED05 estimates than prior methods, particularly for peanut, where previous estimates were found to be overly optimistic.
• The method successfully incorporated flexible parametric models and frailty components, improving model fit and predictive performance in simulation and real data.
• The framework is generalizable and applicable to other domains involving interval-censored time-to-event data, including medical, epidemiological, and reliability studies.