A monotone single index model for missing-at-random longitudinal proportion data

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Beta distributions are standard for proportion data in longitudinal studies.
• Existing models may struggle with complex covariate effects and link function misspecification.

Purpose of the Study:

• Develop semi-parametric Beta regression models for proportion-valued responses in longitudinal studies.
• Flexibly model aggregate covariate effects using interpretable time-varying single index transforms.
• Address missing-at-random data within a Bayesian framework.

Main Methods:

• Utilized single index models for dimension reduction and accommodating link function misspecification.
• Employed Bayesian methodology with Hamiltonian Monte Carlo sampling for inference.
• Incorporated missing-at-random handling for proportion responses.

Main Results:

• Demonstrated the utility of semi-parametric Beta regression for complex longitudinal proportion data.
• Validated the methodology through simulation studies assessing frequentist properties and robustness.
• Successfully applied the model to a longitudinal obesity dataset on body fat proportion.

Conclusions:

• The proposed semi-parametric Beta regression models offer a flexible and robust approach for analyzing longitudinal proportion data.
• The single index transform effectively captures aggregate covariate effects.
• The methodology provides valuable insights for obesity research and similar fields.