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

Area of Science:

• Epidemiology
• Computational Statistics
• Mathematical Modeling

Background:

• Missing data is a common challenge in epidemiological studies, particularly when infection processes are only partially observed.
• Traditional data imputation methods like Markov chain Monte Carlo (MCMC) can be computationally intensive.
• Approximate Bayesian computation (ABC) presents a likelihood-free alternative for statistical inference.

Purpose of the Study:

• To propose and evaluate an extension of ABC for epidemiological models with time-series data.
• To compare ABC with MCMC for inference in a standard Susceptible-Infectious-Recovered (SIR) model.
• To assess the efficiency of HIV detection systems and predict disease evolution using a refined SIR model and Cuban contact-tracing data.

Main Methods:

• Developed an original extension of ABC to handle path-valued summary statistics (cumulated detections over time).
• Applied ABC to a standard SIR model and compared results with MCMC.
• Utilized a refined SIR model with full and binned detection times for HIV contact-tracing data analysis.

Main Results:

• Posterior distributions from ABC and MCMC were found to be similar in the standard SIR model.
• The extended ABC method was applied to HIV contact-tracing data from Cuba.
• Estimated approximately 40% of infectious individuals remain undetected in the Cuban HIV epidemic.

Conclusions:

• The proposed ABC extension is a viable and effective method for inference in epidemiological models with partially observed data.
• ABC provides comparable results to MCMC, offering a powerful alternative for complex models.
• The study highlights significant levels of undetected infectious individuals, informing public health strategies for HIV-AIDS in Cuba.