# Markov Chain-based Cost-Optimal Control Charts for Healthcare Data

## TL;DR

This paper presents a Markov chain-based method for cost-optimal control charts tailored for healthcare data, allowing for random shifts, repairs, and sampling intervals, and optimizing both average cost and its variability.

## Contribution

It introduces a novel Markov chain approach for healthcare monitoring that accounts for randomness in health deterioration, treatment effects, and sampling times, with cost optimization.

## Key findings

- Optimal parameters differ from traditional medical parameters.
- The method effectively monitors cholesterol levels in cardiovascular patients.
- Incorporating cost variability improves control chart performance.

## Abstract

Control charts have traditionally been used in industrial statistics, but are constantly seeing new areas of application, especially in the age of Industry 4.0. This paper introduces a new method, which is suitable for applications in the healthcare sector, especially for monitoring a health-characteristic of a patient. We adapt a Markov chain-based approach and develop a method in which not only the shift size (i.e. the degradation of the patient's health) can be random, but the effect of the repair (i.e. treatment) and time between samplings (i.e. visits) too. This means that we do not use many often-present assumptions which are usually not applicable for medical treatments. The average cost of the protocol, which is determined by the time between samplings and the control limit, can be estimated using the stationary distribution of the Markov chain. Furthermore, we incorporate the standard deviation of the cost into the optimisation procedure, which is often very important from a process control viewpoint. The sensitivity of the optimal parameters and the resulting average cost and cost standard deviation on different parameter values is investigated. We demonstrate the usefulness of the approach for real-life data of patients treated in Hungary: namely the monitoring of cholesterol level of patients with cardiovascular event risk. The results showed that the optimal parameters from our approach can be somewhat different from the original medical parameters.