  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.
