Influence assessment in censored mixed-effects models using the multivariate Student's-t distribution

Area of Science:

• Biostatistics
• Epidemiology
• Biomedical Data Analysis

Background:

• Longitudinal HIV RNA dynamics studies often involve repeated viral load measurements with detection limits, leading to censored data.
• Standard linear and non-linear mixed-effects censored (LMEC/NLMEC) models assume normality, which can be violated by outliers and heavy tails, compromising inference.
• Robust statistical methods are needed to address potential violations of normality assumptions in analyzing censored longitudinal biomedical data.

Purpose of the Study:

• To develop novel influence diagnostics for LMEC/NLMEC models that accommodate multivariate Student's-t distributions.
• To enhance the robustness of statistical inference in the presence of outliers and heavy-tailed distributions in censored data.
• To provide a more reliable method for identifying influential observations in HIV RNA dynamics studies.

Main Methods:

• Development of influence diagnostics based on the conditional expectation of the complete data log-likelihood using a multivariate Student's-t density.
• Adaptation of existing methods for censored mixed-effects models to reduce complexity.
• Application of the new methodology to a longitudinal HIV dataset and validation through a simulation study.

Main Results:

• The proposed influence diagnostics effectively identify influential observations in LMEC/NLMEC models with Student's-t errors.
• The methodology demonstrates improved robustness compared to traditional approaches when normality assumptions are questionable.
• Simulation studies confirm the accuracy of the proposed measures in detecting influential points under various censoring and perturbation schemes.

Conclusions:

• The developed influence diagnostics offer a robust approach for analyzing censored longitudinal data, particularly in HIV RNA dynamics.
• The use of multivariate Student's-t distributions enhances the reliability of statistical models when dealing with heavy-tailed errors.
• This work provides valuable tools for improving the quality and interpretability of findings from biomedical studies with censored repeated measures.