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Data and Statistics: New methods and future challenges Phil O’Neill University of Nottingham

Data and Statistics: New methods and future challenges Phil O’Neill University of Nottingham . Professors: How they spend their time. Professors: How they spend their time. 1. High-resolution genetic data 2. Model assessment . 1. High-resolution genetic data 2. Model assessment .

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Data and Statistics: New methods and future challenges Phil O’Neill University of Nottingham

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  1. Data and Statistics: New methods and future challengesPhil O’NeillUniversity of Nottingham

  2. Professors: How theyspend their time

  3. Professors: How theyspend their time

  4. 1. High-resolution genetic data2. Model assessment

  5. 1. High-resolution genetic data2. Model assessment

  6. Gardy 2011 NEJM

  7. “High-resolution genetic data”: what are they? individual-level data on the pathogen can be taken at single or multiple time points  high-dimensional e.g. whole genome sequences proportion of individuals sampled could be high/low  becoming far more common due to cost reduction

  8. “High-resolution genetic data”: what use are they? better inference about transmission paths more reliable estimates of epi quantities? understand evolution of the pathogen

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  10. . A C C C T T G G G A A A .....

  11. Modelling and Data Analysis methodsTwo kinds of approaches exist:1. Separate genetic and epidemic components (e.g. Volz, Rasmussen) 2. Combine genetic and epidemic components (e.g. Ypma, Worby, Morelli)

  12. 1. Separate genetic and epidemic componentse.g: - estimate phylogenetic tree - given the tree, fit epidemic modelor - cluster individuals into genetically similar groups - given the groups, fit multi-type epidemic model

  13. 1. Separate genetic and epidemic components + “Simple” approach + Avoids complex modelling- Ignores any relationship between transmission and genetic information

  14. 2. Combine genetic and epidemic componentse.g: - model genetic evolution explicitly - define model featuring both genetic and epidemic parts

  15. 2. Combine genetic and epidemic components + “Integrated” approach - Is modelling too detailed? - Initial conditions: typical sequence?+/- Model differences between individuals instead?

  16. 1. High-resolution genetic data2. Model assessment

  17. “Model assessment”: what is it? Does our model fit the data? Is there a better model?

  18. “Model assessment”: why do it? Poor fit sheds doubt on conclusions from modelling Model choice can be a tool for directly addressing questions of interest

  19. Linear regression: yk= axk + b + ek, ek ~ N(0,v)Minimise distance of model mean from observed data

  20. Linear regression: yk= axk + b + ek, ek ~ N(0,v)Minimise distance of model mean from observed data

  21. For outbreak data: What are the right residuals? Should observed or unobserved data be compared to the model? (Streftaris and Gibson) Mean model may only be available via simulation Is the mean the right quantity to consider?

  22. For outbreak data: What are the right residuals? Should observed or unobserved data be compared to the model? (Streftaris and Gibson) Mean model may only be available via simulation Is the mean the right quantity to consider?

  23. Simulation-based approaches to model fit: Forward simulation – “close” to data? Choice of summary statistics? Close ties to ABC methods (McKinley, Neal)

  24. Approaches to model choice  Hypermodels/saturated models Bayesian non-parametric methods Bayesian methods e.g. RJMCMC Mixture models

  25.  Hypermodels/saturated modelse.g. Infection rates βS or βSI or βSI0.5 in an SIR model? Instead use βSI and estimate  (O’Neill and Wen)

  26.  Bayesian non-parametric methodse.g. Infection rate β(t)SI or β(t) in an SIR model; Estimate β(t) in a Bayesian non-parametric manner using Gaussian process machinery (Kypraios,O’Neill and Xu; Knock and Kypraios)

  27.  Reversible Jump MCMCe.g. Distinct models (usually small number), estimate Bayes factors by running MCMC on union of parameter spaces (O’Neill; Neal and Roberts; Knock and O’Neill)

  28.  Mixture modelse.g. Given two models (f, g), create mixture model f(x) =  g(x) + (1-  ) h(x);estimation of  enables estimation of Bayes Factors (Kypraios and O’Neill)

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