Bayesian Modeling and Inference for Nonignorably Missing Longitudinal Binary Response Data with Applications to HIV...

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Longitudinal Data Analysis

Background:

• Missing data are common in longitudinal clinical trials, complicating progress monitoring.
• Appropriate handling of missing data is crucial, requiring assessment of ignorable versus nonignorable mechanisms.
• Existing methods face challenges in estimating random effects variance and algorithm convergence.

Purpose of the Study:

• To develop a new probit model for longitudinal binary response data.
• To address difficulties in estimating random effects variance and improve Gibbs sampling algorithm performance.
• To provide a robust statistical framework for analyzing clinical trial data with nonignorable missingness.

Main Methods:

• A novel probit model for longitudinal binary response data is proposed.
• A variation of Jeffreys prior is established to remedy improper posterior distributions arising from nonignorable missingness.
• An efficient Gibbs sampling algorithm utilizing a collapsing technique is developed.
• Model assessment criteria, including deviance information criterion (DIC) and logarithm of the pseudomarginal likelihood (LPML), are employed.

Main Results:

• The proposed model successfully estimates the variance of random effects.
• Significant improvements in convergence and mixing of the Gibbs sampling algorithm are demonstrated.
• The use of a variation of Jeffreys prior rectifies issues with improper posterior distributions.
• Simulations confirm the empirical performance of the developed methods.

Conclusions:

• The new probit model offers a reliable approach for handling nonignorable missing data in longitudinal clinical trials.
• The improved Gibbs sampling algorithm enhances computational efficiency and stability.
• The methodology is validated through simulations and demonstrated on HIV prevention trial data.