Modeling Medical Data by Flexible Integer-Valued AR(1) Process with Zero-and-One-Inflated Geometric Innovations

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Traditional integer-valued autoregressive (INAR) models may not adequately capture excess zeros and ones common in medical count data.
• Modeling discrete time series with specific distributional properties, such as overdispersion and inflation at zero and one, presents challenges.

Purpose of the Study:

• Introduce a novel stationary first-order INAR model with zero-and-one-inflated geometric innovations.
• Provide a flexible statistical tool for analyzing medical count data, particularly time series with excess zeros and ones.
• Evaluate the model's performance and applicability to real-world medical datasets.

Main Methods:

• Development of a new INAR process incorporating zero-and-one-inflated geometric innovations.
• Derivation and discussion of fundamental probabilistic and statistical properties.
• Proposal of Conditional Least Squares (CLS) and Maximum Likelihood Estimation (MLE) for parameter estimation.
• Monte Carlo simulations to assess the performance of the proposed estimation techniques.

Main Results:

• The proposed zero-and-one-inflated INAR model demonstrates robust parameter estimation.
• Simulations indicate that the CLS and MLE methods perform well in estimating model parameters.
• Application to COVID-19 and Poliomyelitis data shows the model's practical utility.
• The new model outperforms competing zero-inflated and zero-and-one-inflated INAR models in goodness-of-fit.

Conclusions:

• The novel stationary first-order INAR model with zero-and-one-inflated geometric innovations is a valuable tool for medical count data analysis.
• The proposed estimation methods are effective for parameter estimation in the new model.
• The model provides a superior fit compared to existing INAR models for the analyzed medical time series data.