HIV with contact tracing: a case study in approximate Bayesian computation

• Published in: Biostatistics (Oxford, England) Vol. 11; no. 4; pp. 644 - 660
• Main Authors: Blum, Michael G B, Tran, Viet Chi
• Format: Journal Article
• Language: English
• Published: England Oxford Publishing Limited (England) 01.10.2010; Oxford University Press (OUP)
• Subjects: Acquired immune deficiency syndrome; AIDS; Algorithms; Applications; Bayes Theorem; Bayesian analysis; Biostatistics; Computation; Computer Simulation; Contact Tracing; Cuba - epidemiology; Epidemiology; HIV; HIV Infections - epidemiology; HIV Infections - transmission; Human immunodeficiency virus; Humans; Life Sciences; Linear Models; Markov Chains; Models, Biological; Monte Carlo Method; Monte Carlo simulation; Nonlinear Dynamics; Santé publique et épidémiologie; Statistics; Stochastic Processes; Cuba; Mathematical epidemiology; likelihood-free inference; stochastic SIR model; simulation-based inference; unobserved infectious population
• DOI: 10.1093/biostatistics/kxq022
• ISSN: 1465-4644

Missing data is a recurrent issue in epidemiology where the infection process may be partially observed. Approximate Bayesian computation (ABC), an alternative to data imputation methods such as Markov chain Monte Carlo (MCMC) 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%.