# Sampling-Based Likelihood Approximations for Infectious Disease Models and Other Related Topics

 Title: Sampling-Based Likelihood Approximations for Infectious Disease Models and Other Related Topics Malik, Rajat Department of Mathematics and Statistics Mathematics and Statistics Deardon, Rob Deardon et al. (2010) describe a class of individual-level models (ILMs), fitted in a Bayesian framework using Markov chain Monte Carlo (MCMC) techniques. They are used to model the spread of infectious diseases in discrete time. A key feature of these ILMs is that they take into account covariate information on susceptible and infectious individuals as well as shared covariate information such as geography or contact measures. These models quantify probabilistic outcomes regarding the risk of infection. ILMs are developed and fitted to data sets from two studies on influenza transmission within households in Hong Kong during 2008--2009 and 2009--2010. The goal is to estimate the effect of vaccination on infection risk and choose a model that best fits the infection data. The infectious pressure exerted on susceptible individuals defines the hazard rate (in survival analysis terminology) for individuals. Unfortunately, quantifying this infectious pressure for each individual over time can be computationally burdensome, leading to a time-consuming likelihood calculation and, thus, MCMC-based analysis. Therefore, we introduce sampling methods to speed-up the calculation of the likelihood function. We compare a simple random sampling scheme with a number of spatially-stratified sampling approaches. The performances of the sampling-based likelihood approximations are tested and compared via simulation studies, and using data from the 2001 foot-and-mouth disease (FMD) epidemic in the U.K. Data augmentation is a technique used in Bayesian inference that allows the parameter set to be augmented by parameters representing missing or censored data. Here, infection times are treated as missing information. The problem of computation time worsens when using data augmentation to allow for uncertainty in infection times due to a significant increase in the number of times the likelihood function is calculated at each MCMC step. Therefore, we expand the data-sampling-based likelihood approximating algorithms and develop sampling methods that allow for data augmented infection times parameters. Once again, a simple random sampling approach is initially considered followed by various spatially-stratified schemes. We test and compare the performances of our methods using simulated data, and data from the 2001 FMD epidemic in the U.K. http://hdl.handle.net/10214/8752 2015-03 Attribution-NonCommercial-ShareAlike 2.5 Canada
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