HIV with contact-tracing: a case study in Approximate Bayesian Computation

TL;DR

This paper introduces an extension of Approximate Bayesian Computation (ABC) for epidemiological models with missing data, demonstrating its effectiveness in HIV contact-tracing analysis and disease progression prediction.

Contribution

It extends ABC to path-valued summary statistics and compares its performance with MCMC in modeling HIV contact-tracing data.

Findings

ABC produces similar posterior distributions to MCMC in SIR models.

The HIV detection system in Cuba has an estimated 40% undetected cases.

ABC effectively predicts disease evolution and system efficiency.

Abstract

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian Computation, an alternative to data imputation methods such as Markov Chain Monte Carlo integration, is proposed for making inference in epidemiological models. It is a likelihood-free method that relies exclusively on numerical simulations. ABC consists in computing a distance between simulated and observed summary statistics and weighting the simulations according to this distance. We propose an original extension of ABC to path-valued summary statistics, corresponding to the cumulated number of detections as a function of time. For a standard compartmental model with Suceptible, Infectious and Recovered individuals (SIR), we show that the posterior distributions obtained with ABC and MCMC are similar. In a refined SIR model well-suited to the HIV contact-tracing data in Cuba, we perform a comparison between ABC with full and binned detection times. For the Cuban data, we evaluate the efficiency of the detection system and predict the evolution of the HIV-AIDS disease. In particular, the percentage of undetected infectious individuals is found to be of the order of 40%.