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September 2021 Two-stage circular-circular regression with zero inflation: Application to medical sciences
Jayant Jha, Prajamitra Bhuyan
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Ann. Appl. Stat. 15(3): 1343-1365 (September 2021). DOI: 10.1214/20-AOAS1429


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 Möbius 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 postoperative care.

Funding Statement

The work of Dr. Prajamitra Bhuyan was supported in part by the Lloyd’s Register Foundation programme on data-centric engineering at the Alan Turing Institute, UK.


The authors are thankful to Prof. Anup Dewanji, Dr. Arnab Chakraborty, Prof. Debasis Sengupta, Dr. Jayabrata Biswas, Dr. Sourabh Bhattacharya, and Mr. Sudipta Kundu for many helpful comments and suggestions.


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Jayant Jha. Prajamitra Bhuyan. "Two-stage circular-circular regression with zero inflation: Application to medical sciences." Ann. Appl. Stat. 15 (3) 1343 - 1365, September 2021.


Received: 1 March 2020; Revised: 1 December 2020; Published: September 2021
First available in Project Euclid: 23 September 2021

Digital Object Identifier: 10.1214/20-AOAS1429

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 3 • September 2021
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