Empirical Bayes Methods for Prior Estimation in Systems Medicine

TL;DR

This paper evaluates empirical Bayes methods for constructing informative priors from multiple patient data to improve personalized predictions in systems medicine, comparing four approaches on toy and biological models.

Contribution

It introduces and compares four empirical Bayes prior estimation methods in systems medicine modeling, demonstrating their effectiveness over non-informative priors.

Findings

Empirical Bayes priors improve patient-specific parameter estimation.

Doubly-smoothed maximum likelihood estimation performs best among tested methods.

Methods are validated on both toy models and a biological ODE model.

Abstract

One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements for single patients is usually limited due to time and cost restrictions. This hampers the process of making patient-specific predictions about the outcome of a treatment. On the other hand, data are often available for many patients, in particular if extensive clinical studies have been performed. Therefore, before applying Bayes' rule \emph{separately} to the data of each patient (which is typically performed using a non-informative prior), it is meaningful to use empirical Bayes methods in order to construct an informative prior from all available data. We compare the performance of four priors -- a non-informative prior and priors chosen by nonparametric maximum likelihood estimation (NPMLE), by maximum penalized likelihood estimation (MPLE) and by doubly-smoothed maximum likelihood estimation (DS-MLE) -- by applying them to a low-dimensional parameter estimation problem in a toy model as well as to a high-dimensional ODE model of the human menstrual cycle, which represents a typical example from systems biology modeling.