Bayesian Analysis of Censored Linear Mixed-Effects Models for Heavy-Tailed Irregularly Observed Repeated Measures

Area of Science:

• Biostatistics
• Epidemiology
• Computational Biology

Background:

• Longitudinal analysis of human immunodeficiency virus (HIV) and acquired immune deficiency syndrome (AIDS) data commonly uses mixed-effect models.
• HIV/AIDS clinical trial data present complexities such as undetectable viral loads and irregularly recorded patient measures.
• Standard censored mixed-effects models may not adequately handle outlying observations or data collected at irregular intervals.

Purpose of the Study:

• To propose a novel Bayesian analysis for censored linear mixed-effects models.
• To address challenges in HIV/AIDS data, including irregular measurements and non-Gaussian error distributions.
• To incorporate a damped exponential correlation structure for within-subject autocorrelation.

Main Methods:

• Bayesian analysis of censored linear mixed-effects models.
• Utilizing scale mixture of normal family distributions to replace Gaussian assumptions.
• Employing a damped exponential correlation structure for longitudinal data.
• Implementing Stan's No-U-Turn sampler for posterior simulations.

Main Results:

• The proposed Bayesian method effectively accommodates outlying observations and irregularly spaced data.
• Demonstrated feasibility through simulation studies.
• Successfully applied to two acquired immune deficiency syndrome (AIDS) case studies.

Conclusions:

• The developed Bayesian approach offers a more robust and flexible framework for analyzing complex HIV/AIDS longitudinal data.
• This method enhances the analysis of data with non-normal error structures and irregular observations.
• The findings have implications for understanding disease progression and treatment efficacy in HIV/AIDS research.