# Two-stage Circular-circular Regression with Zero-inflation: Application to Medical Sciences

## TL;DR

This paper introduces a novel two-stage Bayesian circular-circular regression model for zero-inflated data, demonstrated with medical case studies, improving analysis accuracy in medical decision-making.

## Contribution

It develops the first model to handle zero-inflated circular responses and covariates simultaneously, using Mobius transformation and Bayesian MCMC estimation.

## Key findings

- Simulation shows superior performance over existing methods.
- Applied to medical datasets on astigmatism and gait abnormalities.
- Enhances decision-making in medical treatments.

## Abstract

This paper considers the modeling of zero-inflated circular measurements concerning real case studies from medical sciences. Circular-circular regression models have been discussed in the statistical literature and illustrated with various real-life applications. However, there are no models to deal with zero-inflated response as well as a covariate simultaneously. The Mobius transformation based two-stage circular-circular regression model is proposed, and the Bayesian estimation of the model parameters is suggested using the MCMC algorithm. Simulation results show the superiority of the performance of the proposed method over the existing competitors. The method is applied to analyse real datasets on astigmatism due to cataract surgery and abnormal gait related to orthopaedic impairment. The methodology proposed can assist in efficient decision making during treatment or post-operative care.