In this paper, we develop a Bayesian framework for parameter estimation of a computationally expensive dynamic epidemic model using time series epidemic data. Specifically, we work with a model for A/H1N1 influenza, which is implemented as a deterministic computer simulator, taking as input the underlying epidemic parameters and calculating the corresponding time series of reported infections. To obtain Bayesian inference for the epidemic parameters, the simulator is embedded in the likelihood for the reported epidemic data. However, the simulator is computationally slow, making it impractical to use in Bayesian estimation where a large number of simulator runs is required. We propose an efficient approximation to the simulator using an emulator, a statistical model that combines a Gaussian process prior for the output function of the simulator with a dynamic linear model for its evolution through time. This modeling framework is both flexible and tractable, resulting in efficient posterior inference through Markov Chain Monte Carlo (MCMC). The proposed dynamic emulator is then used in a calibration procedure to obtain posterior inference for the parameters of the influenza epidemic.
Abstract:The application of biomarkers for 'recent' infection in cross-sectional HIV incidence surveillance requires the estimation of critical biomarker characteristics. Various approaches have been employed for using longitudinal data to estimate the Mean Duration of Recent Infection (MDRI) -the average time in the 'recent' state. In this systematic benchmarking of MDRI estimation approaches, a simulation platform was used to measure accuracy and precision of over twenty approaches, in thirty scenarios capturing various study designs, subject behaviors and test dynamics that may be encountered in practice. Results highlight that assuming a single continuous sojourn in the 'recent' state can produce substantial bias. Simple interpolation provides useful MDRI estimates provided subjects are tested at regular intervals. Regression performs the best -while 'random effects' describe the subject-clustering in the data, regression models without random effects proved easy to implement, stable, and of similar accuracy in scenarios considered; robustness to parametric assumptions was improved by regressing 'recent'/'non-recent' classifications rather than continuous biomarker readings. All approaches were vulnerable to incorrect assumptions about subjects' (unobserved) infection times. Results provided show the relationships between MDRI estimation performance and the number of subjects, inter-visit intervals, missed visits, loss to follow-up, and aspects of biomarker signal and noise.
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