Semiparametric Bayesian inference for repeated fractional measurement data.

Area of Science:

• Biostatistics
• Statistical Modeling
• Data Analysis

Background:

• Fractional data (0-1) with boundary masses pose challenges for standard statistical transformations like logit.
• Existing methods struggle with the positive probability at 0 and 1 inherent in many real-world datasets.

Purpose of the Study:

• To develop a flexible statistical model for inference on repeated fractional data, accommodating boundary masses.
• To introduce a Bayesian semiparametric approach capable of capturing complex random effects distributions.

Main Methods:

• Augmentation of the model with latent variables to permit positive probabilities at 0 and 1.
• Application of a linear mixed-effects model to these latent variables.
• Utilizing a Polya tree prior within a Bayesian framework for the random effects distribution.

Main Results:

• The proposed model successfully handles fractional data with point masses at 0 and 1.
• The Bayesian semiparametric approach effectively captures potential multimodality and skewness in random effects.
• Demonstrated utility through a simulation study and a real-world canine cancer dataset.

Conclusions:

• The novel Bayesian approach provides a robust method for analyzing fractional outcome data with boundary issues.
• The model's flexibility in handling random effects distributions enhances its applicability in various scientific fields.
• Effective implementation via Markov chain Monte Carlo simulation facilitates practical use in complex data analyses.