In vaccine development, the temporal profiles of relative abundance of subtypes of immune cells (T-cells) is key to understanding vaccine efficacy. Complex and expensive experimental studies generate very sparse time series data on this immune response. Fitting multi-parameter dynamic models of the immune response dynamics-- central to evaluating mechanisms underlying vaccine efficacy-- is challenged by data sparsity. The research reported here addresses this challenge. For HIV/SIV vaccine studies in macaques, we: (a) introduce novel dynamic models of progression of cellular populations over time with relevant, time-delayed components reflecting the vaccine response; (b) define an effective Bayesian model fitting strategy that couples Markov chain Monte Carlo (MCMC) with Approximate Bayesian Computation (ABC)-- building on the complementary strengths of the two approaches, neither of which is effective alone; (c) explore questions of information content in the sparse time series for each of the model parameters, linking into experimental design and model simplification for future experiments; and (d) develop, apply and compare the analysis with samples from a recent HIV/SIV experiment, with novel insights and conclusions about the progressive response to the vaccine, and how this varies across subjects.
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