Modeling Zero-Inflated Longitudinal Circular Data Using Bayesian Methods: Application to Ophthalmology

TL;DR

This paper develops a Bayesian two-stage model for zero-inflated longitudinal circular data, demonstrated through ophthalmology data, improving analysis of complex circular responses with excess zeros.

Contribution

It introduces the first Bayesian mixed-effects model for zero-inflated longitudinal circular data using a projected normal distribution.

Findings

Proposed method outperforms existing models in simulations

Model effectively analyzes ophthalmology post-operative data

Facilitates better clinical decision-making

Abstract

This paper introduces the modeling of circular data with excess zeros under a longitudinal framework, where the response is a circular variable and the covariates can be both linear and circular in nature. In the literature, various circular-circular and circular-linear regression models have been studied and applied to different real-world problems. However, there are no models for addressing zero-inflated circular observations in the context of longitudinal studies. Motivated by a real case study, a mixed-effects two-stage model based on the projected normal distribution is proposed to handle such issues. The interpretation of the model parameters is discussed and identifiability conditions are derived. A Bayesian methodology based on Gibbs sampling technique is developed for estimating the associated model parameters. Simulation results show that the proposed method outperforms its competitors in various situations. A real dataset on post-operative astigmatism is analyzed to demonstrate the practical implementation of the proposed methodology. The use of the proposed method facilitates effective decision-making for treatment choices and in the follow-up phases.