Evaluation of real time methods for epidemic forecasting 1

This study evaluates dierent models and methods for epidemic forecast-ing with real-time data.. Chapter 1Introduction This project investigates statistical models of the Inuenza A-H1N120

Evaluation of Real-time Methods for

Epidemic Forecasting

Lee Huey Chyi October 12, 2011

I would like to express my gratitude to all who made the completion of this thesis possible I am deeply indebted to my supervisor Dr Alex Cook for his guidance, encouragement and patience throughout the course of research and

my graduate studies I would also like to thank Jimmy Ong, Mark Chen, Vernon Lee, Raymond Lin, Paul Ananth Tambyah and Goh Lee Gan for their interest and valuable feedback in the course of our collaboration Furthermore, I want to thank my examiners Dr Adrian Roellin and Dr Leontine Alkema for their time and suggestions for improvement I appreciate also the support of my friends, classmates and seniors, Zheng Xiaohui, Oi Puay Leng, Victor Ong, Yong Yee May, Elizabeth Chong, Loke Chok Kang, Philip Ho, Jiang Binyan and Liu Cheng for their constant encouragement

1.1 Methods commonly used in modeling epidemiology 6

1.2 The inuenza A-H1N1(2009) pandemic 8

2 Methods 15 2.1 Data source 15

2.2 Models for disease dynamics 19

2.2.1 Richards model 21

2.2.2 Deterministic SIR compartmental model 23

2.2.3 Stochastic SIR compartmental model 27

2.2.4 The observation model 28

2.3 Statistical methodology 29

2.3.1 Bayesian paradigm 29

2.3.2 Markov Chain Monte Carlo 31

2.3.3 Importance Sampling 34

2.3.4 Particle lter 39

3 Results 46 3.1 Parameters and predictions for each model 47

3.2 Evaluation of predictive performances 62

3.3 Eects of prior 64

2

This study evaluates dierent models and methods for epidemic forecast-ing with real-time data We propose the Richards model, and two com-partmental SIR modelsone deterministic, the other stochasticunder a Bayesian simulation-based inferential framework to model the 2009 inuenza A-H1N1 pandemic Real-time data collection was based on reporting of cases

of inuenza-like-illnesses by doctors in a network of general practice/family doctor clinics we established in Singapore in the weeks before community transmission became widespread, as we have previously reported The ap-proaches used to derive estimates of the posterior distribution of epidemic model parameters are Markov chain Monte Carlo methods, importance sam-pling and particle ltering We assess the predictive performance of the three models quantitatively by using several performance metrics The eects of informative and non-informative priors on the predictions are also assessed Our conclusion is that stochastic SIR model with particle lter is the most eective among our models and can be applied together with a real-time surveillance system to deliver predictions for future pandemic outbreaks We also conclude that deterministic SIR model performs well but requires more computational time, whereas the non-compartmental Richards model is un-able to predict eectively in advance of the peak

Chapter 1

Introduction

This project investigates statistical models of the Inuenza A-H1N1(2009) pandemic in Singapore; it builds upon our previous published study (Ong

et al., 2010; Cook et al., 2010) which provides real-time monitoring and forecasting of the pandemic using the particle lter method In this study, we will be proposing alternative models and statistical methods, and evaluating their performance against the existing one

Modeling of disease dynamics is important in modern epidemiology as a quantitative method in assessing the spread of infectious diseases, as infec-tious disease agents adapt and evolve quickly over time, resulting in emer-gence of new infectious diseases and re-emeremer-gence of some existing diseases (Anderson and May, 1991) In recent years, much emphasis has been placed

on epidemiological modeling of diseases as a cost eective way of assessing disease management, methods to control spread and an aid in public health policy decision making (Keeling et al., 2001; Lipsitch et al., 2003)

Epidemiological modeling allows us to explore the eect of dierent

as-4

sumptions and can be used to estimate underlying key parameters which govern the disease spread For instance, the estimated reproductive number can be used to determine whether the disease will persist or die out, and therefore the level of control strategies to be administered (Roberts, 2007) The underlying parameters of the disease are determined by disease-related factors such as the infectious agent, mode of transmission, latent period, infectious period, susceptibility and resistance, as well as social, cultural, demographic, economic and geographic factors (Hethcote, 2009)

We have chosen to study Inuenza A-H1N1(2009) in the context of Sin-gapore, and as a consequence the models we consider do not have to include parameters accounting for factors which vary across dierent countries Ad-ditionally, as we will be relying on quite coarse data  daily inuenza-like illness (ILI) data from participating general practice/family doctor clinics in Singapore during a 3 months outbreak, and with the goal of assessing predic-tive performance at a similar level of coarseness, we do not need to account for several other complicating factors such as demography or social culture, although those have been demonstrated to be important in other scenarios (Weiss and McMichael, 2004)

1.1 Methods commonly used in modeling

epi-demiology

Various statistical methods have been developed to examine the evolution of infectious diseases and to address questions pertaining to disease control The advantages and disadvantages of some commonly used methods in parameter estimation and epidemic prediction are summarized below

The data augmentation method has been proposed to deal with partially observed data; this method introduces unobserved data that simplify calcu-lation of the observation likelihood while permitting calcucalcu-lation of the newly introduced hidden process likelihood The Gaussian diusion is one of the proximation methods based on the idea that the likelihood function of the ap-proximating process can be expressed as the density of a multivariate normal distribution with tractable mean and variance (Ross et al., 2008) Moment closure is another approximation method, which is employed to approximate the likelihood of a non-linear stochastic process (Gillespie, 2007) A popu-lar though not very statistically rigorous approach uses exponential-growth approximations Lastly, least-squares tting and non-parametric methods (Wallinga and Teunis, 2004) are also used in some instances to model epi-demics

The advantage of the data augmentation method is its general scope of applicability, however the simulations can be computationally intensive, and

a large sample is required for augmentation (Puggioni, 2008) In Gaussion

diusion, the likelihood function of the approximating process is simpler than the likelihood function of the original process, but the drawback of this approach however is low accuracy unless some corrective measures are applied

to it (Siegmund, 1979), especially when the process occurs near boundary conditions (Pagendam and Pollett, 2009)

The moment closure approach has the advantage of being robust near boundary conditions, but is more suitable for simple epidemic models without

a wide range of dynamics (Krishnarajah et al., 2005) It has been used to show for instance, that a small number of optimally chosen observations could yield almost as much information as more closely monitored data (Cook et al., 2007) The exponential growth approximation works well in the initial phase of epidemic but requires ad hoc division of the series into exponential and post-exponential phases (Aparicio and Pascual, 2006)

The least-squares tting has the benet of simplicity (Chowell et al., 2007), however, by using a deterministic model to account for stochastic event, the method fails to account properly for the distinction between stochas-ticity and measurement error (Tan, 2000) The non-parametric methods do not rely on distributional assumptions and therefore serve as an eective mea-sure to estimate shapes of underlying distribution, however the shortcomings are increased computation time and issues in estimating residual variability (Bustad et al., 2006)

1.2 The inuenza A-H1N1(2009) pandemic

Inuenza is a viral infection which has caused signicant morbidity and mor-tality in its history (Cox and Subbarao, 2000) Inuenza epidemics show seasonality in temperate regions, and predominantly aect the elderly and people with chronic medical conditions (Thompson et al., 2003) However,

if a novel strain which is suciently dierent from previously circulating viruses emerges, it will potentially result in a widespread infection and can

be classied as a pandemic (Rothberg and Haessler, 2010) As existing vac-cines are not targeted at the new strain, one of the few treatments available upon emergence of the new virus strain is antiviral drugs, and many countries maintain antiviral stockpiles for such scenarios, though current prices make stockpiles costly for developing countries (Carrasco et al., 2011) Although antiviral drugs are usually stockpiled to be used as the rst line of defence, the large-scale use of these drugs might exert a strong selection pressure on the virus that may lead to the emergence of more drug-resistant strains in the future (Débarre et al., 2007), albeit presumably at a tness cost relative

to the wild type

On 24 April 2009, the World Health Organization (WHO) reported

con-rmed cases of Swine Inuenza A/H1N1 in the United States and Mexico

on its Global Alert and Response network (WHO, 2009) The rst case of Inuenza A in Singapore was conrmed on May 27, 2009 to be a female pa-tient who travelled from New York City and is admitted to Communicable

Disease Centre in Tan Tock Seng Hospital for treatment (Liang et al., 2009) The virus originated when its external proteins hemagglutinin (HA), which allows attachment and membrane fusion of virus with host cells, and neuraminidase (NA), which digests sialic acid which most cells have on their surface to gain entry into host cells, undergo genetic mutation or recombi-nation (Wagner et al., 2002) The new H1N1 virus is a reassortant virus containing genetic material from dierent species; where pigs act as a mix-ing vessel which allows avian, swine and human viruses to undergo mixmix-ing and genetic changes to generate the novel virus strain (Smith et al., 2009) Although it bears some similarities to historical strains that circulate prior

to 1957, there was little existing immunity in the population except in some elderly groups (Katz et al., 2009), and as a result, the new H1N1 virus was able to spread easily and rapidly between humans to cause the rst inuenza pandemic of the 21st century

The initial case denition to specify the clinical manifestation of inuenza A-H1N1(2009) was developed to include hospitalized patient with severe acute respiratory illness and individuals with acute respiratory illness; later

it was expanded to include individuals with fever, cough, headache, and at least one of the following symptoms: rhinorrhea, coryza, arthralgia, myal-gia, prostration, sore throat, chest pain, abdominal pain, or nasal congestion (Cordova et al., 2009), symptoms that are common to other inuenza strains The incubation period prior to development of symptoms for the inuenza A-H1N1(2009) appears to be 1.5 to 3 days generally, and virus shedding can

10 occur from 1 day before the onset of symptoms through 4 to 8 days after the onset of symptoms or until symptoms resolve (De Serres et al., 2010); in some instances such as in young children and severely ill patients, the infectious period might be longer (Louie et al., 2009)

The two classes of inuenza antiviral drugs licensed for use in most coun-tries are adamantanes (amantadine and rimantadine) and neuraminidase in-hibitors (oseltamivir and zanamivir), since the inuenza A-H1N1(2009) virus

is resistant to the adamantanes, neuraminidase inhibitors, oseltamivir in par-ticular, was widely prescribed for both treatment and prophylaxis of the virus (Abramson, 2011) In Singapore, the prescription of oseltamivir is shown to

be eective in shortening the duration of viral shedding (Ling et al., 2010), especially when prescribed during the rst 3 days of illness, and in contain-ment of inuenza A-H1N1(2009) outbreaks in semiclosed environcontain-ment (Lee

et al., 2010) Infectious disease modeling has been used to assess the use of antivirals and other control measures (Carrasco et al., 2011), so that health-care policy makers can decide on the quantity of antiviral drugs to stockpile, and the type of drugs to administer to patients

Figure 1.1: Map for Public Health Information and Geographic Information Systems on the spread of Inuenza H1N1, cumu-lative cases of laboratory conrmed inuenza A-H1N1(2009) are shown in red circles in aected countries (source: http://www.who.int/csr/disease/swineu/h1n1_maps_june/en/index.html)

The World Health Organization (WHO) ocially announced the inuenza A-H1N1(2009) pandemic on 11th June 2009, and produced a map to show the number of laboratory conrmed cases reported by each country (Figure 1.1) as of 12th June (WHO, 2009) The time line for the development of inuenza A-H1N1(2009) in Singapore is shown in the table below:

12 Date Event

17 March First identied case of inuenza A-H1N1(2009) in Mexico

(Domínguez-Cherit et al., 2009)

29 April Ministry of Health raises alert in the Disease Outbreak Response System

(DORSCON) from green to yellow (MOH, 2009)

1 May DORSCON alert is raised to orange (MOH, 2009)

3 May Home Quarantine Order is issued to any person who is a known or

suspected close contact of a probable or conrmed case of inuenza A-H1N1(2009), as well as persons who arrived in Singapore within 7 days after having departed from Mexico This measure is based on the containment strategy proposed by the government to limit the spread of inuenza A-H1N1(2009) (MOH, 2009)

11 May Alert level formally returned to DORSCON yellow (MOH, 2009)

26 May First imported case of inuenza A-H1N1(2009) detected in Singapore

(Liang et al., 2009)

18 June First community case of inuenza A-H1N1(2009) detected in Singapore

(Mukherjee et al., 2010)

25 June Starting of data submissions of acute respiratory infection (ARI) cases

from general practice/family doctor clinics who responded to appeals to participate in our study (Ong et al., 2010)

2 July Singapore commences transition to Mitigation Phase Persons with

inuenza-like symptoms can consult polyclinic or Pandemic Preparedness Clinic doctors, who will make a preliminary assessment Only severely ill or high-risk patients will be tested for the inuenza A-H1N1(2009) virus, and be hospitalized if needed (Tay et al., 2010)

9 July Singapore enters full Mitigation phase Contact tracing of infected

individuals was stepped down and Home Quarantine Orders no longer issued, except to patients deemed to be a risk to the community (Tay et al., 2010)

11 July Thermal scanning at checkpoints discontinued (Tay et al., 2010)

18 July First inuenza A-H1N1(2009)-related death in Singapore The

49-year-old patient with multiple health problems died of a heart attack, contributed by severe pneumonia and H1N1 infection (Cutter et al., 2010)

26 July - 1 Aug Polyclinic attendances for ARI reached peak of 24,477 Proportion of ILI

among ARI cases in polyclinics peaked at 22.9% (Tay et al., 2010) 2Aug - 8 Aug Proportion of inuenza A-H1N1(2009) among ILI cases in GP (General

Physicians) clinics and polyclinics peaked at 65.5% (Tay et al., 2010)

24 September End of real-time data submitted by general practice/family doctor

clinics used in this report

30 September A cumulative total of 18 inuenza A-H1N1(2009)-related deaths

(Cutter et al., 2010)