  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.
