Multivariate-$t$ nonlinear mixed models with application to censored multi-outcome AIDS studies

Area of Science:

• Biostatistics
• Epidemiology
• Longitudinal Data Analysis

Background:

• Multivariate longitudinal HIV/AIDS studies often involve complex data with outliers and censored viral loads.
• Existing models may not adequately handle the fat-tailed distributions and censorship common in such data.

Purpose of the Study:

• To propose an extended multivariate nonlinear mixed-effects model that accommodates outliers and censored responses.
• To introduce the multivariate-t nonlinear mixed-effects model with censored responses (MtNLMMC) for robust analysis of HIV/AIDS data.

Main Methods:

• The study extends multivariate nonlinear mixed-effects models using a joint multivariate-t distribution for random effects and errors.
• Censoring information from multiple outcomes is incorporated into the model.
• A pseudo-data Expectation Conditional Maximization either (ECME) algorithm, utilizing Taylor-series linearization, is developed for maximum likelihood estimation.

Main Results:

• The proposed MtNLMMC model effectively analyzes multi-outcome longitudinal data with nonlinear patterns, censorship, and fat-tailed distributions.
• Application to two HIV/AIDS study datasets demonstrated favorable performance.
• The MtNLMMC outperformed its Gaussian counterpart and other existing approaches in experimental results.

Conclusions:

• The MtNLMMC provides a robust and effective statistical framework for analyzing complex longitudinal HIV/AIDS data.
• This approach enhances the analysis of data characterized by outliers, censorship, and non-normal error distributions.
• The model offers improved accuracy and reliability in understanding disease progression and treatment effects in HIV/AIDS research.