on 09-Dec-2019 (Mon)

Among the 27 population-based forecasting studies, 16 used weekly predictions of weekly incidence 1 or more weeks into the future in the validation (Table 3). Nine studies predicted the timing of the epidemic peak or incidence at the peak; all performed validation using at least some forecasts made at least 4 weeks before the actual peak [10–13,16–18,29,31]. The facility-based forecasting studies used 1-step-ahead [37–39] or n-step-ahead [40] predictions of visit counts over step sizes of 1 day [40] to 1 month [39]. The regional or global pandemic spread forecasting studies used early data from the 2009 influenza A(H1N1)pdm09 pandemic to predict outcomes at national level across countries, including pandemic arrival, and peak incidence and time of peak.

The branching process approximation is a CTMC, but near the disease-free equilibrium, the rates are linear (Table 2).

Three important assumptions underlie the branching process approximation:

1. Each infectious individual behavior is independent from other infectious individuals. Reasonable if a small number of infectious individuals is introduced into a large homogeneously-mixed population (assumption (3)).
2. Each infectious individual has the same probability of recovery and the same probability of transmitting an infection. Reasonable in a homogeneously-mixed population with constant transmission and recovery rates, b and g.
3. The susceptible population is sufficiently large.

Technologies that translate raw, unprocessed data into struc- tured formats would be particularly useful. For instance, software could extract data from line lists of cases or clinical notes in electronic health records, or convert data stored in non-standard formats into machine-readable data. Digitizing handwritten text reliably, quickly and securely from clinical or epidemiological records will be a persistent need for the foreseeable future.

Over the past several years, academic research on infectious disease forecasting has grown and models have successfully generated predictions for pathogens such as influenza[19–2] , dengue[13], Zika[22], and Ebola[2]. But, scaling academic research to support public health decision-makers in real-time has received little attention and relatively scarce resources.

In this paper, an epidemic forecast generated by a model/data-driven approach is quantified based on epidemiologically relevant features which we refer to as Epi-features. Further, the accuracy of a model’s estimate of a particular Epi-feature is quantified by evaluating its error with respect to the Epi-features extracted from the ground truth. This is enabled by using functions that capture their dissimilarity, which we refer to as error measures.

In the case of count data, the predictive distribution is discrete which means the PIT is no longer uniform under the hypothesis of an ideal forecast

Few research funding agencies provide substantial and sustained support for this type of translational work, despite a strong track record of research productivity emerging from the CDC FluSight challenge and other governmental forecasting challenges[28]. Nor have donor foundations shown leadership in this crucial area of epidemic response. If not provided with sufficient resources, public health will remain decades behind most other sectors in its use of advanced analytics.

Forecasting results must be communicated effectively to ensure they produce actionable insights. Visualizations play a key role. Academic groups have built data visualization tools to communicate forecasts[29], but these largely rely on customized code. Analysts who develop forecast models typically have limited time to spend on visualization and lack advanced design skills.

decision makers incorporated information from infectious disease models, with early forecasts indicating that incidence would continue to grow rapidly unless aggressive interventions were implemented. For example, a forecast gener- ated by the CDC predicted up to 1.4 million Ebola cases with no additional interventions or changes in community behavior 5 . These forecasts likely contributed to the acceleration of the international response and provided guidance for how resources might be effectively deployed.

the integration of those analyses into the decision-making cycle for the Ebola 2014–2016 epidemic was not seamless, a pattern repeated across many recent outbreaks, including Zika 6

Modeling and outbreak data analysis efforts typically occur in silos with limited communication of methods and data between model developers and end users. Modeling “cross talk” across stakeholders within and between countries is also typically limited, often occurring within a landscape of legal and ethical uncertainty. Specifically, the ethics of performing research using surveillance and health data[7], limited knowledge of what types of questions models can help inform, data sharing restrictions[8], and the incentive in academia to quickly publish modeling results in peer-reviewed journals contribute to a complex collaborative environment with different and sometimes conflicting stakeholder goals and priorities.

This new track of outbreak science describes the functional use of models, clinical knowledge, laboratory results, data science, statistics, and other advanced analytical methods to specifically support public health decision making between and during outbreak threats. Outbreak scientists work with decision makers to turn outbreak data into actionable information for decisions about how to anticipate the course of an outbreak, allocate scarce resources, and prioritize and implement public health interventions.

Here, we make three specific recommen- dations to get the most out of modeling efforts during outbreaks and epidemics. Together these recommendations constitute the foundation of an integrative field that is “outbreak science”:

we therefore recommend that epidemic modeling capability be enhanced and honed not during rapidly-evolving public health emergencies, but rather between major epidemics.

Currently, limited information is available on how those on the frontlines of public health perceive and use models in epidemic decision-making. Understanding the functional relationship between the public health end-users and model developers is critical to improving capacity during outbreaks.

Developing and implementing epidemic models under the “fog of war” is an enterprise far removed from the controlled conventional academic setting of epidemiology and biostatistics.

The goal of this paper is to demonstrate how to apply the Epi-features and error measures on the output of a fore- casting algorithm to evaluate its performance and com- pare it with other methods.

Definitions of different Epidemiologically Relevant features (Epi-features)

Peak value: Maximum number of new infected cases in a given week in the epidemic time-series

Peak time: The week when peak value is attained

Total attack rate: Fraction of individuals ever infected in the whole population

Age-specific attack rate: Fraction of individuals ever infected belonging to a specific age window

First-take-off-(value): Sharp increase in the number of new infected case counts over a few consecutive weeks

First-take-off-(time): The start time of sudden increase in the number of new infected case counts

Intensity duration: The number of weeks (usually consecutive) where the number of new infected case counts is more than a specific threshold

Speed of epidemic: Rate at which the case counts approach the peak value

Start-time of disease season: Time at which the fraction of infected individuals exceeds a specific threshold

For permission to photocopy or use material electronically from this work,

INVESTIGATIONS ⦁ Antinuclear antibodies (positive in >95% cases): • Anticentromere autoantibodies (fewer than half of patients with limited disease) • Anti-topoisomerase (half of patients with diffuse disease) • Antinucleolar antibodies (fewer than half of patients with diffuse disease) ⦁ Electrocardiogram (ECG) – arrhythmias, conduction defects ⦁ Echocardiogram – to assess fibrosis, effusions ⦁ Thoracic high-resolution computed tomography – to assess pulmonary fibrosis ⦁ Pulmonary function tests ⦁ Biopsy and histological examination if diagnosis unclear

a SSM is a stochastic process that makes use of a latent variable representation to describe dynamical phenomena (Sch¨on and Lindsten, 2017). It has two components: a latent process, denoted by {X_t}_t≥1 representing the underlying dynamics; and an observed process denoted by {Y_t}_t≥1

In this thesis, the state process is assumed Markovian over time, hence the subset of SSMs analysed can be also classified in the category of partially observed Markov processs (POMPs) (King, Nguyen, and Ionides, 2016) or hidden Markov models (HMMs) (Churchill, 2005). From now onwards, unless otherwise specified, SSM will refer to Markovian SSM.

For a SSM: The state process X is often called the dynamic parameter, while θ is often referred to as static parameter(s) and the observational process Y are called the measurements.

A SSM can also be represented by a graphical model which is a probabilistic model where a graph G = (V, E) represents the conditional independence structure (edges E) between random variables (r.v.s) (nodes V).

State inference problems can take any of the following forms (Lindsten, 2013):

• the distribution of of the state process at t conditionally on the data up until t, is called marginal filtering;
• the distribution of the whole state process up until t conditionally on the data up until t, is called joint filtering and is often constructed sequentially;
• the distribution of the state process for future intervals until time t + s, conditionally on the data up until t, is called prediction;
• the distribution of the whole state process up until T conditionally on the full data, is called joint smoothing;
• the distribution of the state process at t conditionally on the full data, is called marginal smoothing.

This thesis, and this chapter, mainly addresses filtering problems. Such filtering can be approached exploiting Bayes’ theorem, conditional independence, and the Markovianity of the system.

Where does this come from?

Most of the results reported below can be found in common textbooks on MC and/or SMC methods (Brooks et al., 2011; Robert and Casella, 2013) as well as in key papers (Andrieu, Doucet, and Holenstein, 2010; Arulampalam et al., 2002; Gilks and Berzuini, 2001).

All distributions in this section are assumed conditional on θ, the static parameter, and for ease of presentation, this dependence is omitted, denoting p(x_t|θ) by p(x_t), p(x_t | y_1:t, θ) by p(x_t | y_1:t), etc.

SMC algorithms, such as the sequential importance sam- pler, re-sampler and the BPF, provide a method to approximate the likelihood, i.e. the data distribution conditional on a parameter value θ.

Since the focus of this section is the inference of the static parameter, θ is reintroduced in the notation below.

Sequential importance sampling (Arulampalam et al., 2002) can be used to approximate the distribution of the hidden states conditionally on the data, by decomposing the problem into simpler, lower-dimensional, approximation steps.

To obtain samples from this target distribution, assume that, at time t, a weighted sample n x (n) 0:t−1 , w (n) t−1 o N n=1 , of the target distribution at t − 1, p(x 0:t−1 |y 1:t−1 ), is avail- able. Letting δ a (x) define a Dirac point mass in a, the sample provides the following approximation to the target distribution at t − 1: bp(x 0:t−1 |y 1:t−1 ) = N X n=1 δ x (n) 0:t−1 (x)w (n) t−1 To propose values for the next approximation step, assume an importance distribution q(x 0:t |y 1:t ) that is factorisable as follows: q(x 0:t |y 1:t ) = q t (x t |x t−1 , y t )q(x 0:t−1 |y 1:t−1 ) = q t (x t |x t−1 , y t )q t−1 (x t−1 |x t−2 , y t−1 )q(x 0:t−2 |y 1:t−2 ) = . . . = q 0 (x 0 ) t Y s=1 q s (x s |x s−1 , y s )

With increasing dimensionality of the target distribution, however, the weights degenerate: a small number of particles are assigned relatively large weights and most of the particles have weight zero. To overcome weight degeneracy, resampling steps can be inserted in order to rejuvenate the sequential sample

The BPF is a sequential importance re-sampling algorithm where specific choices of the importance distribution (and hence of the weights) are made. This algorithm was first introduced by Stewart and McCarthy Jr (1992) and by Gordon, Salmond, and Smith (1993), taking for the first time its current name. The BPF targets the joint filtering distribution p(x_0:t | y_1:t).

The key idea of the BPF algorithm is to generate a set of N particles and apply three steps sequentially (over times t = 1, 2, . . . ):

1. resample to obtain a equally-weighted sample from the target distribution at t − 1
2. propagate this sample from the importance distribution, chosen to be the state equation of the SSM
3. weight the proposed sample according to the target and importance density

the BPF is simply a sequential importance re-sampler having the state equation as importance distribution

Algorithm 2: Sequential Importance Re-sampling

Algorithm 3: Bootstrap Particle Filter

There are many flavours that can be added to enhance the basic BPF, such as the use of auxiliary variables (Pitt and Shephard, 1999) that improves matching between the importance and target distributions.

Methods belonging to the non-Bayesian literature aim at obtaining the maximum- likelihood estimate and provide point and interval estimates. These methods include Multiple Iterated Filtering (Ionides, Bret´o, and King, 2006), as well grid-search methods.

Pseudo-marginal algorithms are aimed at exploring only the posterior distribution of the parameter, marginally from the distribution of the states, and they are based on the classical Metropolis Hastings (MH) algorithm (Hastings, 1970; Metropolis et al., 1953). Nevertheless, differently from the original MH algorithm, here the unnormalised poste- rior distribution is approximated by the product of the prior and a SMC approximation of the likelihood in the acceptance ratio.

Two algorithms are employed throughout this thesis: grouped independence Metropo- lis Hastings (GIMH) (Beaumont, 2003) and Monte Carlo within Metropolis (MCWM) (Andrieu and Roberts, 2009).

In GIMH, at iteration i, when a new value θ' is proposed, an SMC algorithm is run to estimate the likelihood p(θ'), which is plugged into the numerator of the acceptance ratio, together with prior and proposal density. The denominator is composed of the previously-retained estimated likelihood for the initial parameter p(θⁱ) and the respective prior and proposal density. Upon acceptance, the proposed parameter θ' and its estimated likelihood p(θ') are retained; upon rejection the old parameter θⁱ and its likelihood p(θⁱ) are retained.

grouped independence Metropolis Hastings (GIMH)

Monte Carlo within Metropolis (MCWM)

The MCWM algorithm re-approximates the likelihood of the parameter θⁱ when computing the acceptance ratio instead of storing it and re-using it every time.

GIMH was proved an exact algorithm in Andrieu and Roberts (2009), targeting the exact posterior distribution.

despite MCWM being biased for small approximation size N, this bias decreases and becomes irrelevant as N increases (McKinley et al., 2014)

If the likelihood approximation is precise enough, GIMH and MCWM would perform equally well.

the works purposefully represent themselves as first-person accounts of an event of significance from which an audience is supposed to learn some important information, whether the "truth" of historical events, a religious moral, or simply some lesson which was thought useful to those hearing the tales

The word naru is used as a name for various objects, originally boundary stones, memorial stones and monuments. Two sorts of inscribed objects received the designation naru at the dawn of the second millennium: tablets accompanying presents and tablets used for building inscriptions

At the end of the third millennium the naru chiefly played a part in religious transactions; at the beginning of the second millennium it was to become not only actually but also symbolically the bearer of memory. (90)

He presents himself as having been born the illegitimate son of a priestess, set adrift on the Euphrates River soon after his birth, rescued by a gardener and then, through the help of the goddess Inanna, rising to become king of Akkad