# Individualized post-crisis monitoring of psychiatric patients via Hidden Markov models

## TL;DR

This paper introduces a method using Hidden Markov models to monitor psychiatric patients after a mental health crisis and determine how long they need close monitoring.

## Contribution

A novel Hidden Markov model-based policy for individualized post-crisis monitoring of psychiatric patients is proposed.

## Key findings

- The policy achieved an F1 score of 0.79 on a real-world dataset of 162 psychiatric patients.
- 67.3% of patients required close monitoring for one week, while 21.6% needed it for two weeks or more.
- The method showed high sensitivity (79.8%) and specificity (88.9%) in identifying unstable patients.

## Abstract

Individuals in the midst of a mental health crisis frequently exhibit instability and face an elevated risk of recurring crises in the subsequent weeks, which underscores the importance of timely intervention in mental healthcare. This work presents a data-driven method to infer the mental state of a patient during the weeks following a mental health crisis by leveraging their historical data. Additionally, we propose a policy that determines the necessary duration for closely monitoring a patient after a mental health crisis before considering them stable.

We model the patient’s mental state as a Hidden Markov Process, partially observed through mental health crisis events. We introduce a closed-form solution that leverages the model parameters to optimally estimate the risk of future mental health crises. Our policy determines a patient should be closely monitored when their estimated risk of crisis exceeds a predefined threshold. The method’s performance is evaluated using both simulated data and a real-world dataset comprising 162 anonymized psychiatric patients.

In the simulations, 96.2% of the patients identified by the policy were in an unstable state, achieving a F1 score of 0.74. In the real-world dataset, the policy yielded an F1 score of 0.79, with a sensitivity of 79.8% and specificity of 88.9%. Under this policy, 67.3% of the patients should undergo close monitoring for one week, 21.6% during 2 weeks or more, while 11.1% do not need close monitoring.

The simulation results provide compelling evidence that the method is effective under the specified assumptions. When applied to actual psychiatric patients, the proposed policy showed significant potential for providing an individualized assessment of the required duration for close and automatic monitoring after a mental health crisis to reduce the relapse risks.