Statistical Physics of Medical Diagnostics: Study of a Probabilistic Model

TL;DR

This paper explores a probabilistic diagnostic model using statistical physics methods, demonstrating that simulation-based strategies can improve diagnostic accuracy by identifying more decisive signs, especially in complex disease landscapes.

Contribution

It introduces a simulation-based diagnostic strategy employing mean-field approximation and Monte Carlo optimization to enhance accuracy over traditional methods.

Findings

Simulation improves diagnosis in complex disease landscapes.

Macroscopic states influence inference quality.

Phase transitions affect diagnostic performance.

Abstract

We study a diagnostic strategy which is based on the anticipation of the diagnostic process by simulation of the dynamical process starting from the initial findings. We show that such a strategy could result in more accurate diagnoses compared to a strategy that is solely based on the direct implications of the initial observations. We demonstrate this by employing the mean-field approximation of statistical physics to compute the posterior disease probabilities for a given subset of observed signs (symptoms) in a probabilistic model of signs and diseases. A Monte Carlo optimization algorithm is then used to maximize an objective function of the sequence of observations, which favors the more decisive observations resulting in more polarized disease probabilities. We see how the observed signs change the nature of the macroscopic (Gibbs) states of the sign and disease probability distributions. The structure of these macroscopic states in the configuration space of the variables affects the quality of any approximate inference algorithm (so the diagnostic performance) which tries to estimate the sign/disease marginal probabilities. In particular, we find that the simulation (or extrapolation) of the diagnostic process is helpful when the disease landscape is not trivial and the system undergoes a phase transition to an ordered phase.