A flexible quantile mixed-effects model for censored outcomes

2025-11-20

AI Summary

Censored longitudinal data—subject to left, right, or interval censoring—often exhibit skewness, leading to biased quantile estimation and undercoverage of confidence intervals. To address this, we propose a Bayesian quantile mixed-effects model based on the skewed exponential power error distribution. This model decouples the effects of tail thickness and skewness on quantile estimation, offering greater flexibility than conventional skewed Laplace models. It enables efficient Bayesian inference without numerical integration by leveraging analytically tractable likelihood contributions and bridge sampling. Simulation studies demonstrate near-nominal bias and consistent 95% credible interval coverage across diverse censoring mechanisms and skewness levels. Applied to an HIV-1 viral load study, the method significantly improves the stability and accuracy of estimated treatment effect trajectories over time.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We introduce a Bayesian quantile mixed-effects model for censored longitudinal outcomes based on the skew exponential power (SEP) error distribution. The SEP family separates tail behavior and skewness from the targeted quantile and includes the skew Laplace (SL) distribution as a special case. We derive analytic likelihood contributions for left, right, and interval censoring under the SEP model, so censored observations are handled within a single parametric framework without numerical integration in the likelihood. In simulation studies with varying censoring patterns and skewness profiles, the SEP-based quantile mixed-effects model maintains near-nominal bias and credible interval coverage for regression coefficients. In contrast, the SL-based model can exhibit bias and undercoverage when the data's skewness conflicts with the skewness implied by the target quantile. In an HIV-1 RNA viral load case study with left censoring at the assay limit, bridge-sampled marginal likelihoods and simulation-based residual diagnostics favor the SEP specification across quantiles and yield more stable estimates of treatment-specific viral load trajectories than the SL benchmark.

Problem

• Develops Bayesian quantile mixed-effects model for censored longitudinal data
• Handles left/right/interval censoring within unified parametric framework
• Addresses bias issues in skewed data compared to Laplace-based models

Innovation

• Bayesian quantile mixed-effects model for censored data
• Uses skew exponential power distribution for flexible tails
• Analytic likelihood handles censoring without numerical integration