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Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-0526-1061
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-9228-7357
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-0423-6702
2018 (English)In: Biostatistics, ISSN 1465-4644, E-ISSN 1468-4357Article in journal (Refereed) Epub ahead of print
Abstract [en]

Despite the wide application of dynamic models in infectious disease epidemiology, the particular modeling of variability in the different model components is often subjective rather than the result of a thorough model selection process. This is in part because inference for a stochastic transmission model can be difficult since the likelihood is often intractable due to partial observability. In this work, we address the question of adequate inclusion of variability by demonstrating a systematic approach for model selection and parameter inference for dynamic epidemic models. For this, we perform inference for six partially observed Markov process models, which assume the same underlying transmission dynamics, but differ with respect to the amount of variability they allow for. The inference framework for the stochastic transmission models is provided by iterated filtering methods, which are readily implemented in the R package pomp by King and others (2016, Statistical inference for partially observed Markov processes via the R package pomp. Journal of Statistical Software 69, 1–43). We illustrate our approach on German rotavirus surveillance data from 2001 to 2008, discuss practical difficulties of the methods used and calculate a model based estimate for the basic reproduction number R0 using these data.

Place, publisher, year, edition, pages
2018.
Keywords [en]
iterated filtering, model selection, parameter inference, partially observed Markov process, rotavirus surveillance data, seasonal age-stratified SIRS model
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-161483DOI: 10.1093/biostatistics/kxy057OAI: oai:DiVA.org:su-161483DiVA, id: diva2:1259162
Funder
Swedish Research Council, 2015 05182 VRAvailable from: 2018-10-28 Created: 2018-10-28 Last updated: 2019-08-15
In thesis
1. Stochastic dynamic modelling and statistical analysis of infectious disease spread and cancer treatment
Open this publication in new window or tab >>Stochastic dynamic modelling and statistical analysis of infectious disease spread and cancer treatment
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Mathematical models have proven valuable for public health decision makers as they can provide insights into the understanding, control and, ultimately, the prevention of diseases. This thesis contains four manuscripts dealing with stochastic dynamic modelling and statistical analysis of infectious disease spread and optimization of cancer treatment.

Paper I is concerned with deriving a patient- and organ-specific measure for the estimated negative side effects of radiotherapy using a stochastic logistic birth-death process. Our analysis shows that the region of a maximum tolerable radiation dose can be related to the solution of a logistic differential equation; we illustrate our results for brachytherapy for prostate cancer.

Paper II and III deal with inference for stochastic epidemic models. Parameter estimation for this model class can be challenging as disease spread is usually only partially observed, e.g. in the form of accumulated reported incidences within specified time periods. To perform inference for these types of models, a useful method for maximum likelihood estimation is iterated filtering which takes advantage of the fact that it is relatively easy to generate samples from the underlying transmission process while the likelihood function for the given data is intractable.

Paper II is an application-oriented introduction to iterated filtering via the R package pomp (King et al., 2016) which contains a wide collection of simulation-based inference methods for partially observed Markov processes. We review the theoretical background of the method and discuss by two examples its performance and some associated practical difficulties.

Paper III is concerned with model selection for partially observed epidemic models that differ with respect to the amount of variability they allow for and parameter estimation of those models from routinely collected surveillance data. We illustrate the model selection and inference framework via the R package pomp for rotavirus transmission in Germany, however, the method can be easily adapted to other diseases.

In Paper IV we develop a transmission model for hepatitis C virus (HCV) infection among people who inject drugs (PWIDs) to enable countries to monitor their progress towards HCV elimination. In the scope of the WHO’s commitment to viral hepatitis elimination, this topic is highly relevant to public health since injection drug use is the main route of transmission in many countries. From the model and using surveillance data, we derive estimates of four key HCV-indicators. Furthermore, the model can be used to investigate the impact of two interventions, direct-acting antiviral drug treatment and needle exchange programs, on the disease dynamics. In order to make the model and its output accessible to relevant users, it is made available through a Shiny app.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2018
Keywords
Mathematical modelling, infectious disease spread, cancer treatment, statistical inference, population dynamics, birth-death process, partially observed Markov process
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-161485 (URN)978-91-7797-484-0 (ISBN)978-91-7797-485-7 (ISBN)
Public defence
2018-12-13, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2015_05182_VR
Available from: 2018-11-20 Created: 2018-10-29 Last updated: 2018-11-14Bibliographically approved

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