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Stochastic dynamic modelling and statistical analysis of infectious disease spread and cancer treatment
Stockholm University, Faculty of Science, Department of Mathematics. (Mathematical Statistics)ORCID iD: 0000-0002-0526-1061
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 [en]
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: urn:nbn:se:su:diva-161485ISBN: 978-91-7797-484-0 (print)ISBN: 978-91-7797-485-7 (electronic)OAI: oai:DiVA.org:su-161485DiVA, id: diva2:1259327
Public defence
2018-12-13, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2015_05182_VRAvailable from: 2018-11-20 Created: 2018-10-29 Last updated: 2018-11-14Bibliographically approved
List of papers
1. A stochastic model for the normal tissue complication probability (NTCP) and applications
Open this publication in new window or tab >>A stochastic model for the normal tissue complication probability (NTCP) and applications
2017 (English)In: Mathematical Medicine and Biology, ISSN 1477-8599, E-ISSN 1477-8602, Vol. 34, no 4, p. 469-492Article in journal (Refereed) Published
Abstract [en]

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth–death process to define an organ-specific and patient-specific NTCP. We emphasize an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework is based on simple modelling assumptions and it prepares a framework for the use of the NTCP model in clinical practice. As example, we consider side effects of prostate cancer brachytherapy such as increase in urinal frequency, urinal retention and acute rectal dysfunction.

Keywords
normal tissue complication, probability logistic birth death process, tumour control probability, radiation treatment, side effects, TCP, NTCP, brachytherapy, prostate cancer
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-137846 (URN)10.1093/imammb/dqw013 (DOI)000418360900002 ()
Available from: 2017-01-12 Created: 2017-01-12 Last updated: 2018-10-31Bibliographically approved
2. Iterated filtering methods for Markov process epidemic models
Open this publication in new window or tab >>Iterated filtering methods for Markov process epidemic models
2019 (English)In: Handbook of Infectious Disease Data Analysis / [ed] Leonhard Held, Niel Hens, Philip D. O’Neill, Jacco Wallinga, CRC Press, 2019Chapter in book (Refereed)
Abstract [en]

Dynamic epidemic models have proven valuable for public health decision makers as they provide useful insights into the understanding and prevention of infectious diseases. However, inference for these types of models can be difficult because the disease spread is typically only partially observed e.g. in form of reported incidences in given time periods. This chapter discusses how to perform likelihood-based inference for partially observed Markov epidemic models when it is relatively easy to generate samples from the Markov transmission model while the likelihood function is intractable. The first part of the chapter reviews the theoretical background of inference for partially observed Markov processes (POMP) via iterated filtering. In the second part of the chapter the performance of the method and associated practical difficulties are illustrated on two examples. In the first example a simulated outbreak data set consisting of the number of newly reported cases aggregated by week is fitted to a POMP where the underlying disease transmission model is assumed to be a simple Markovian SIR model. The second example illustrates possible model extensions such as seasonal forcing and over-dispersion in both, the transmission and observation model, which can be used, e.g., when analysing routinely collected rotavirus surveillance data. Both examples are implemented using the R-package pomp (King et al., 2016) and the code is made available online.

Place, publisher, year, edition, pages
CRC Press, 2019
Keywords
simulation-based inference, iterated filteringinfectlous disease surveillance data, partially observed Markov processes
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-161490 (URN)9781138626713 (ISBN)
Funder
Swedish Research Council, 2015_05182_VR
Note

The book is in press (not published yet).

Available from: 2018-10-29 Created: 2018-10-29 Last updated: 2018-10-31
3. Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany
Open this publication in new window or tab >>Model selection and parameter estimation for dynamic epidemic models via iterated filtering: application to rotavirus in Germany
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.

Keywords
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:nbn:se:su:diva-161483 (URN)10.1093/biostatistics/kxy057 (DOI)
Funder
Swedish Research Council, 2015 05182 VR
Available from: 2018-10-28 Created: 2018-10-28 Last updated: 2018-11-27
4. Dynamic modelling of hepatitis C transmission among people who inject drugs: A tool to support WHO elimination targets
Open this publication in new window or tab >>Dynamic modelling of hepatitis C transmission among people who inject drugs: A tool to support WHO elimination targets
(English)Manuscript (preprint) (Other academic)
Abstract [en]

To reach the WHO goal of hepatitis C elimination, it is essential to identify the number of people unaware of their hepatitis C virus (HCV) infection and to investigate the effect of interventions on the disease transmission dynamics. In developed countries, one of the primary routes of HCV transmission is via contaminated needles shared by people who inject drugs (PWIDs). However, substantial underreporting combined with high uncertainty regarding the size of this difficult to reach population, makes it challenging to estimate the core indicators recommended by the WHO. To help enable countries to monitor their progress towards the elimination goal, we present a novel multi-layered dynamic transmission model for HCV transmission within a PWIDs population. The model explicitly accounts for disease stage (acute and chronic), injection drug use status (active and former PWIDs), status of diagnosis (diagnosed and undiagnosed) and country of disease acquisition (domestic or abroad). First, based on this model, and using routine surveillance data, we estimate the number of undiagnosed PWIDs, the true incidence, the average time until diagnosis, the reproduction numbers and associated uncertainties. Second, we examine the impact of two interventions on disease dynamics: 1) direct-acting antiviral drug treatment, and 2) needle exchange programs. To make the model accessible to relevant users and to support communication of our results to public health decision makers, the model and its output are made available through a Shiny app. As a proof of concept, we illustrate our results for a specific data set; however, through the app our model can be easily adapted to other high-income countries with similar transmission patterns among PWIDs where the disease is endemic.

Keywords
dynamic modelling, hepatitis C virus, treatment, needle exchange programs, surveillance data, inference, Shiny app
National Category
Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-161486 (URN)
Funder
Swedish Research Council, 2015_05182_VRSwedish Research Council, 2015_05015_VR
Available from: 2018-10-28 Created: 2018-10-28 Last updated: 2018-10-31Bibliographically approved

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