Inference in HIV dynamics models via hierarchical likelihood

TL;DR

This paper introduces a hierarchical likelihood approach for inference in complex HIV dynamical models with non-linear ODEs, providing a practical alternative to computationally intensive likelihood methods.

Contribution

It develops a novel h-likelihood method for non-linear mixed-effects HIV models, including asymptotic theory, bias correction, and an efficient algorithm.

Findings

MHLE are nearly unbiased with bootstrap correction.

Simulation confirms good estimator properties.

Method successfully applied to clinical trial data.

Abstract

HIV dynamical models are often based on non-linear systems of ordinary differential equations (ODE), which do not have analytical solution. Introducing random effects in such models leads to very challenging non-linear mixed-effects models. To avoid the numerical computation of multiple integrals involved in the likelihood, we propose a hierarchical likelihood (h-likelihood) approach, treated in the spirit of a penalized likelihood. We give the asymptotic distribution of the maximum h-likelihood estimators (MHLE) for fixed effects, a result that may be relevant in a more general setting. The MHLE are slightly biased but the bias can be made negligible by using a parametric bootstrap procedure. We propose an efficient algorithm for maximizing the h-likelihood. A simulation study, based on a classical HIV dynamical model, confirms the good properties of the MHLE. We apply it to the analysis of a clinical trial.