Simulations for Designing and Interpreting Intervention Trials in Infectious Diseases

M. Elizabeth Halloran, Kari Auranen, Sarah Baird, Nicole E. Basta, Steve Bellan, Ron Brookmeyer, Ben Cooper, Victor DeGruttola, James Hughes, Justin Lessler, Eric T. Lofgren, Ira M. Longini, Jukka-Pekka Onnela, Berk Ozler, George Seage, Thomas A. Smith, Alessandro Vespignani, Emilia Vynnycky, Marc Lipsitch

BMC Medicine

December 29, 2017

ABSTRACT

Here we urge the adoption of a new paradigm for the design and interpretation of intervention trials in infectious diseases, particularly in emerging infectious disease, that more accurately reflects the dynamics of the transmission process. Interventions in infectious diseases can have indirect effects on those not receiving the intervention as well as direct effects on those receiving the intervention. Combinations of interventions can have complex interactions at the population level. These often cannot be adequately addressed with standard study designs and analytic methods. Simulations can help to accurately represent transmission dynamics in an increasingly complex world which is critical for proper trial design and interpretation. Some ethical aspects of a trial can also be quantified using simulations. After a trial has been conducted, simulations can be used to explore possible explanations for the observed effects. A great deal is to be gained through a multidisciplinary approach that builds collaborations among experts in infectious disease dynamics, epidemiology, statistical science, economics, simulation methods and the conduct of clinical trials.

Models and analyses to understand threats to polio eradication

James S. Koopman

BMC Medicine

December 22, 2017

ABSTRACT

To achieve complete polio eradication, the live oral poliovirus vaccine (OPV) currently used must be phased out after the end of wild poliovirus transmission. However, poorly understood threats may arise when OPV use is stopped. To counter these threats, better models than those currently available are needed. Two articles recently published in BMC Medicine address these issues. Mercer et al. (BMC Med 15:180, 2017) developed a statistical model analysis of polio case data and characteristics of cases occurring in several districts in Pakistan to inform resource allocation decisions. Nevertheless, despite having the potential to accelerate the elimination of polio cases, their analyses are unlikely to advance our understanding OPV cessation threats. McCarthy et al. (BMC Med15:175, 2017) explored one such threat, namely the emergence and transmission of serotype 2 circulating vaccine derived poliovirus (cVDPV2) after OPV2 cessation, and found that the risk of persistent spread of cVDPV2 to new areas increases rapidly 1–5 years after OPV2 cessation. Thus, recently developed models and analysis methods have the potential to guide the required steps to surpass these threats. ‘Big data’ scientists could help with this; however, datasets covering all eradication efforts should be made readily available.

Online Bayesian Phylogenetic Inference: Theoretical Foundations via Sequential Monte Carlo

Vu Dinh, Aaron E Darling, Frederick A Matsen IV

Systematic Biology

December 13, 2017

ABSTRACT

Phylogenetics, the inference of evolutionary trees from molecular sequence data such as DNA, is an enterprise that yields valuable evolutionary understanding of many biological systems. Bayesian phylogenetic algorithms, which approximate a posterior distribution on trees, have become a popular if computationally expensive means of doing phylogenetics. Modern data collection technologies are quickly adding new sequences to already substantial databases. With all current techniques for Bayesian phylogenetics, computation must start anew each time a sequence becomes available, making it costly to maintain an up-to-date estimate of a phylogenetic posterior. These considerations highlight the need for an online Bayesian phylogenetic method which can update an existing posterior with new sequences. Here, we provide theoretical results on the consistency and stability of methods for online Bayesian phylogenetic inference based on Sequential Monte Carlo (SMC) and Markov chain Monte Carlo. We first show a consistency result, demonstrating that the method samples from the correct distribution in the limit of a large number of particles. Next, we derive the first reported set of bounds on how phylogenetic likelihood surfaces change when new sequences are added. These bounds enable us to characterize the theoretical performance of sampling algorithms by bounding the effective sample size (ESS) with a given number of particles from below. We show that the ESS is guaranteed to grow linearly as the number of particles in an SMC sampler grows. Surprisingly, this result holds even though the dimensions of the phylogenetic model grow with each new added sequence.

Comparative epidemiology of poliovirus transmission

Navideh Noori, John M. Drake, Pejman Rohani

Scientific Reports

December 12, 2017

ABSTRACT

Understanding the determinants of polio transmission and its large-scale epidemiology remains a public health priority. Despite a 99% reduction in annual wild poliovirus (WPV) cases since 1988, tackling the last 1% has proven difficult. We identified key covariates of geographical variation in polio transmission patterns by relating country-specific annual disease incidence to demographic, socio-economic and environmental factors. We assessed the relative contributions of these variables to the performance of computer-generated models for predicting polio transmission. We also examined the effect of spatial coupling on the polio extinction frequency in islands relative to larger land masses. Access to sanitation, population density, forest cover and routine vaccination coverage were the strongest predictors of polio incidence, however their relative effect sizes were inconsistent geographically. The effect of climate variables on polio incidence was negligible, indicating that a climate effect is not identifiable at the annual scale, suggesting a role for climate in shaping the transmission seasonality rather than intensity. We found polio fadeout frequency to depend on both population size and demography, which should therefore be considered in policies aimed at extinction. Our comparative epidemiological approach highlights the heterogeneity among polio transmission determinants. Recognition of this variation is important for the maintenance of population immunity in a post-polio era.

Effective Online Bayesian Phylogenetics via Sequential Monte Carlo with Guided Proposals

Mathieu Fourment, Brian C Claywell, Vu Dinh, Connor McCoy, Frederick A Matsen IV, Aaron E Darling

Systematic Biology

November 27, 2017

ABSTRACT

Modern infectious disease outbreak surveillance produces continuous streams of sequence data which require phylogenetic analysis as data arrives. Current software packages for Bayesian phylogenetic inference are unable to quickly incorporate new sequences as they become available, making them less useful for dynamically unfolding evolutionary stories. This limitation can be addressed by applying a class of Bayesian statistical inference algorithms called sequential Monte Carlo (SMC) to conduct online inference, wherein new data can be continuously incorporated to update the estimate of the posterior probability distribution. In this article, we describe and evaluate several different online phylogenetic sequential Monte Carlo (OPSMC) algorithms. We show that proposing new phylogenies with a density similar to the Bayesian prior suffers from poor performance, and we develop “guided” proposals that better match the proposal density to the posterior. Furthermore, we show that the simplest guided proposals can exhibit pathological behavior in some situations, leading to poor results, and that the situation can be resolved by heating the proposal density. The results demonstrate that relative to the widely used MCMC-based algorithm implemented in MrBayes, the total time required to compute a series of phylogenetic posteriors as sequences arrive can be significantly reduced by the use of OPSMC, without incurring a significant loss in accuracy.

Selection on non-antigenic gene segments of seasonal influenza A virus and its impact on adaptive evolution

Jayna Raghwani, Robin Thompson, Katia Koelle

Virus Evolution

November 9, 2017

ABSTRACT

Most studies on seasonal influenza A/H3N2 virus adaptation have focused on the main antigenic gene, haemagglutinin. However, there is increasing evidence that the genome-wide genetic background of novel antigenic variants can influence these variants' emergence probabilities and impact their patterns of dominance in the population. This suggests that non-antigenic genes may be important in shaping the viral evolutionary dynamics. To better understand the role of selection on non-antigenic genes in the adaptive evolution of seasonal influenza viruses, we here develop a simple population genetic model that considers a virus with one antigenic and one non-antigenic gene segment. By simulating this model under different regimes of selection and reassortment, we find that the empirical patterns of lineage turnover for the antigenic and non-antigenic gene segments are best captured when there is both limited viral coinfection and selection operating on both gene segments. In contrast, under a scenario of only neutral evolution in the non-antigenic gene segment, we see persistence of multiple lineages for long periods of time in that segment, which is not compatible with the observed molecular evolutionary patterns. Further, we find that reassortment, occurring in coinfected individuals, can increase the speed of viral adaptive evolution by primarily reducing selective interference and genetic linkage effects mediated by the non-antigenic gene segment. Together, these findings suggest that, for influenza, with 6 internal or non-antigenic gene segments, the evolutionary dynamics of novel antigenic variants are likely to be influenced by the genome-wide genetic background as a result of linked selection among both beneficial and deleterious mutations.

Silent circulation of poliovirus in small populations

Celeste Vallejo,  James Keesling, James Koopman, Burton Singer

Infectious Disease Modeling

November 8, 2017

ABSTRACT

Background
Small populations that have been isolated by conflict make vaccination and surveillance difficult, threatening polio eradication. Silent circulation is caused by asymptomatic infections. It is currently not clear whether the dynamics of waning immunity also influence the risk of silent circulation in the absence of vaccination. Such circulation can, nevertheless, be present following a declaration of elimination as a result of inadequate acute flaccid paralysis surveillance (AFPS) or environmental surveillance (ES).

Methods
We have constructed a stochastic model to understand how stochastic effects alter the ability of small populations to sustain virus circulation in the absence of vaccination. We analyzed how the stochastic process determinants of the duration of silent circulation that could have been detected by ES were affected by R0, waning dynamics, population size, and AFPS sensitivity in a discrete individual stochastic model with homogeneous contagiousness and random mixing. We measured the duration of silent circulation both by the interval between detected acute flaccid paralysis (AFP) cases and the duration of circulation until elimination.

Results
As R0 increased and population size increased, the interval between detected AFP cases and the duration of circulation until elimination increased. As AFPS detection rates decreased, the interval between detected AFP cases increased. There was up to a 22%chance of silent circulation lasting for more than 3 years with 100% AFP detection. The duration of silent circulation was not affected by the waning immunity dynamics.

Conclusion
We demonstrated that small populations have the potential to sustain prolonged silent circulation. Surveillance in these areas should be intensified before declaring elimination. To further validate these conclusions, it is necessary to realistically relax the simplifying assumptions about mixing and waning.

What Controls the Acute Viral Infection Following Yellow Fever Vaccination?

James Moore, Hasan Ahmed, Jonathan Jia, Rama Akondy, Rafi Ahmed, Rustom Antia

Bulletin of Mathematical Biology

November 6, 2017

ABSTRACT

Does target cell depletion, innate immunity, or adaptive immunity play the dominant role in controlling primary acute viral infections? Why do some individuals have higher peak virus titers than others? Answering these questions is a basic problem in immunology and can be particularly difficult in humans due to limited data, heterogeneity in responses in different individuals, and limited ability for experimental manipulation. We address these questions for infections following vaccination with the live attenuated yellow fever virus (YFV-17D) by analyzing viral load data from 80 volunteers. Using a mixed effects modeling approach, we find that target cell depletion models do not fit the data as well as innate or adaptive immunity models. Examination of the fits of the innate and adaptive immunity models to the data allows us to select a minimal model that gives improved fits by widely used model selection criteria (AICc and BIC) and explains why it is hard to distinguish between the innate and adaptive immunity models. We then ask why some individuals have over 1000-fold higher virus titers than others and find that most of the variation arises from differences in the initial/maximum growth rate of the virus in different individuals.

Combining Participatory Influenza Surveillance with Modeling and Forecasting: Three Alternative Approaches

John S Brownstein, Shuyu Chu,  Achla Marathe, Madhav V Marathe, Andre T Nguyen, Daniela Paolotti, Nicola Perra, Daniela Perrotta, Mauricio Santillana, Samarth Swarup, Michele Tizzoni, Alessandro Vespignani,
Anil Kumar S Vullikanti, Mandy L Wilson, Qian Zhang

JMIR Public Health and Surveillance

November 1, 2017

ABSTRACT

Background: Influenza outbreaks affect millions of people every year and its surveillance is usually carried out in developed countries through a network of sentinel doctors who report the weekly number of Influenza-like Illness cases observed among the visited patients. Monitoring and forecasting the evolution of these outbreaks supports decision makers in designing effective interventions and allocating resources to mitigate their impact.

Objective: Describe the existing participatory surveillance approaches that have been used for modeling and forecasting of the seasonal influenza epidemic, and how they can help strengthen real-time epidemic science and provide a more rigorous understanding of epidemic conditions.

Methods: We describe three different participatory surveillance systems, WISDM (Widely Internet Sourced Distributed Monitoring), Influenzanet and Flu Near You (FNY), and show how modeling and simulation can be or has been combined with participatory disease surveillance to: i) measure the non-response bias in a participatory surveillance sample using WISDM; and ii) nowcast and forecast influenza activity in different parts of the world (using Influenzanet and Flu Near You).

Results: WISDM-based results measure the participatory and sample bias for three epidemic metrics i.e. attack rate, peak infection rate, and time-to-peak, and find the participatory bias to be the largest component of the total bias. The Influenzanet platform shows that digital participatory surveillance data combined with a realistic data-driven epidemiological model can provide both short-term and long-term forecasts of epidemic intensities, and the ground truth data lie within the 95 percent confidence intervals for most weeks. The statistical accuracy of the ensemble forecasts increase as the season progresses. The Flu Near You platform shows that participatory surveillance data provide accurate short-term flu activity forecasts and influenza activity predictions. The correlation of the HealthMap Flu Trends estimates with the observed CDC ILI rates is 0.99 for 2013-2015. Additional data sources lead to an error reduction of about 40% when compared to the estimates of the model that only incorporates CDC historical information.

Conclusions: While the advantages of participatory surveillance, compared to traditional surveillance, include its timeliness, lower costs, and broader reach, it is limited by a lack of control over the characteristics of the population sample. Modeling and simulation can help overcome this limitation as well as provide real-time and long-term forecasting of influenza activity in data-poor parts of the world.

Spatio-Temporal Analysis of Surveillance Data

Jon Wakefield, Tracy Qi Dong, Vladimir N. Minin

arXiv

November 1, 2017

ABSTRACT

In this chapter, we consider space-time analysis of surveillance count data. Such data are ubiquitous and a number of approaches have been proposed for their analysis. We first describe the aims of a surveillance endeavor, before reviewing and critiquing a number of common models. We focus on models in which time is discretized to the time scale of the latent and infectious periods of the disease under study. In particular, we focus on the time series SIR (TSIR) models originally described by Finkenstadt and Grenfell in their 2000 paper and the epidemic/endemic models first proposed by Held, Hohle, and Hofmann in their 2005 paper. We implement both of these models in the Stan software and illustrate their performance via analyses of measles data collected over a 2-year period in 17 regions in the Weser-Ems region of Lower Saxony, Germany.

Evolution-informed forecasting of seasonal influenza A (H3N2)

Xiangjun Du, Aaron A. King, Robert J. Woods, Mercedes Pascual

Science Translational Medicine

October 25, 2017

ABSTRACT

Interpandemic or seasonal influenza A, currently subtypes H3N2 and H1N1, exacts an enormous annual burden both in terms of human health and economic impact. Incidence prediction ahead of season remains a challenge largely because of the virus’ antigenic evolution. We propose a forecasting approach that incorporates evolutionary change into a mechanistic epidemiological model. The proposed models are simple enough that their parameters can be estimated from retrospective surveillance data. These models link amino acid sequences of hemagglutinin epitopes with a transmission model for seasonal H3N2 influenza, also informed by H1N1 levels. With a monthly time series of H3N2 incidence in the United States for more than 10 years, we demonstrate the feasibility of skillful prediction for total cases ahead of season, with a tendency to underpredict monthly peak epidemic size, and an accurate real-time forecast for the 2016/2017 influenza season.

Resource-driven encounters among consumers and implications for the spread of infectious disease

 

Rebecca K. Borchering, Steve E. Bellan, Jason M. Flynn, Juliet R. C. Pulliam, Scott A. McKinley

Royal Society Interface

October 11, 2017

ABSTRACT

Animals share a variety of common resources, which can be a major driver of conspecific encounter rates. In this work, we implement a spatially explicit mathematical model for resource visitation behaviour in order to examine how changes in resource availability can influence the rate of encounters among consumers. Using simulations and asymptotic analysis, we demonstrate that, under a reasonable set of assumptions, the relationship between resource availability and consumer conspecific encounters is not monotonic. We characterize how the maximum encounter rate and associated critical resource density depend on system parameters like consumer density and the maximum distance from which consumers can detect and respond to resources. The assumptions underlying our theoretical model and analysis are motivated by observations of large aggregations of black-backed jackals at carcasses generated by seasonal outbreaks of anthrax among herbivores in Etosha National Park, Namibia. As non-obligate scavengers, black-backed jackals use carcasses as a supplemental food resource when they are available. While jackals do not appear to acquire disease from ingesting anthrax carcasses, changes in their movement patterns in response to changes in carcass abundance do alter jackals' conspecific encounter rate in ways that may affect the transmission dynamics of other diseases, such as rabies. Our theoretical results provide a method to quantify and analyse the hypothesis that the outbreak of a fatal disease among herbivores can potentially facilitate outbreaks of an entirely different disease among jackals. By analysing carcass visitation data, we find support for our model's prediction that the number of conspecific encounters at resource sites decreases with additional increases in resource availability. Whether or not this site-dependent effect translates to an overall decrease in encounters depends, unexpectedly, on the relationship between the maximum distance of detection and the resource density.

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Jonathan Fintzi, Xiang Cui, Jon Wakefield, Vladimir Minin

Journal of Computational and Graphical Statistics

October 9, 2017

ABSTRACT

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school.

A Surrogate Function for One-Dimensional Phylogenetic Likelihoods

Brian C Claywell, Vu Dinh, Mathieu Fourment, Connor O McCoy, Frederick A Matsen IV

Molecular Biology and Evolution

September 26, 2017

ABSTRACT

Phylogenetics has seen a steady increase in data set size and substitution model complexity, which require increasing amounts of computational power to compute likelihoods. This motivates strategies to approximate the likelihood functions for branch length optimization and Bayesian sampling. In this article, we develop an approximation to the 1D likelihood function as parametrized by a single branch length. Our method uses a four-parameter surrogate function abstracted from the simplest phylogenetic likelihood function, the binary symmetric model. We show that it offers a surrogate that can be fit over a variety of branch lengths, that it is applicable to a wide variety of models and trees, and that it can be used effectively as a proposal mechanism for Bayesian sampling. The method is implemented as a stand-alone open-source C library for calling from phylogenetics algorithms; it has proven essential for good performance of our online phylogenetic algorithm sts.

The RAPIDD Ebola forecasting challenge: Model description and synthetic data generation

Marco Ajelli, Qian Zhang, Kaiyuan Sun, Stefano Merler, Laura Fumanelli, Gerardo Chowell, Lone Simonsen, Cecile Viboud, Alessandro Vespignani

Epidemics

September 20, 2017

ABSTRACT

The Ebola forecasting challenge organized by the Research and Policy for Infectious Disease Dynamics (RAPIDD) program of the Fogarty International Center relies on synthetic disease datasets generated by numerical simulations of a highly detailed spatially-structured agent-based model. We discuss here the architecture and technical steps of the challenge, leading to datasets that mimic as much as possible the data collection, reporting, and communication process experienced in the 2014–2015 West African Ebola outbreak. We provide a detailed discussion of the model's definition, the epidemiological scenarios’ construction, synthetic patient database generation and the data communication platform used during the challenge. Finally we offer a number of considerations and takeaways concerning the extension and scalability of synthetic challenges to other infectious diseases.

Preliminary results of models to predict areas in the Americas with increased likelihood of Zika virus transmission in 2017.

Jason Asher, Christopher Barker, Grace Chen, Derek Cummings, Matteo Chinazzi, Shelby Daniel-Wayman, Marc Fischer, Neil Ferguson, Dean Follman, M. Elizabeth Halloran, Michael Johansson, Kiersten Kugeler, Jennifer Kwan, Justin Lessler, Ira M. Longini, Stefano Merler, Andrew Monaghan, Ana Pastore y Piontti, Alex Perkins, D. Rebecca Prevots, Robert Reiner, Luca Rossi, Isabel Rodriguez-Barraquer, Amir S. Siraj, Kaiyuan Sun, Alessandro Vespignani, Qian Zhang

bioRxiv

September 18, 2017

ABSTRACT

Numerous Zika virus vaccines are being developed. However, identifying sites to evaluate the efficacy of a Zika virus vaccine is challenging due to the general decrease in Zika virus activity. We compare results from three different modeling approaches to estimate areas that may have increased relative risk of Zika virus transmission during 2017. The analysis focused on eight priority countries (i.e., Brazil, Colombia, Costa Rica, Dominican Republic, Ecuador, Mexico, Panama, and Peru). The models projected low incidence rates during 2017 for all locations in the priority countries but identified several sub-national areas that may have increased relative risk of Zika virus transmission in 2017. Given the projected low incidence of disease, the total number of participants, number of study sites, or duration of study follow-up may need to be increased to meet the efficacy study endpoints.

The RAPIDD ebola forecasting challenge: Synthesis and lessons learnt

Cécile Viboud, Kaiyuan Sun, Robert Gaffey, Marco Ajelli, Laura Fumanelli, Stefano Merler, Qian Zhang, Gerardo Chowell, Lone Simonsen, Alessandro Vespignani, the RAPIDD Ebola Forecasting Challenge group

Epidemics

August 26, 2017

ABSTRACT

Infectious disease forecasting is gaining traction in the public health community; however, limited systematic comparisons of model performance exist. Here we present the results of a synthetic forecasting challenge inspired by the West African Ebola crisis in 2014–2015 and involving 16 international academic teams and US government agencies, and compare the predictive performance of 8 independent modeling approaches. Challenge participants were invited to predict 140 epidemiological targets across 5 different time points of 4 synthetic Ebola outbreaks, each involving different levels of interventions and “fog of war” in outbreak data made available for predictions. Prediction targets included 1–4 week-ahead case incidences, outbreak size, peak timing, and several natural history parameters. With respect to weekly case incidence targets, ensemble predictions based on a Bayesian average of the 8 participating models outperformed any individual model and did substantially better than a null auto-regressive model. There was no relationship between model complexity and prediction accuracy; however, the top performing models for short-term weekly incidence were reactive models with few parameters, fitted to a short and recent part of the outbreak. Individual model outputs and ensemble predictions improved with data accuracy and availability; by the second time point, just before the peak of the epidemic, estimates of final size were within 20% of the target. The 4th challenge scenario − mirroring an uncontrolled Ebola outbreak with substantial data reporting noise − was poorly predicted by all modeling teams. Overall, this synthetic forecasting challenge provided a deep understanding of model performance under controlled data and epidemiological conditions. We recommend such “peace time” forecasting challenges as key elements to improve coordination and inspire collaboration between modeling groups ahead of the next pandemic threat, and to assess model forecasting accuracy for a variety of known and hypothetical pathogens.

Dependency of Vaccine Efficacy on Pre-Exposure and Age: A Closer Look at a Tetravalent Dengue Vaccine

Yang Yang, Ya Meng, M. Elizabeth Halloran, Ira M. Longini, Jr.

Clinical Infectious Diseases

August 24, 2017

ABSTRACT

Background

A recombinant, live-attenuated, tetravalent dengue vaccine (CYD-TDV) was licensed for children of 9 years old or older in a few countries, but the dependence of vaccine efficacy on baseline immunity status and age groups has not been fully characterized.

Methods

Combining the two phase III trials, CYD14 and CYD15, we estimated the vaccine efficacy for each of the four serotypes of dengue virus (DENV), as well as all serotypes combined, simultaneously stratified by baseline immunity status and age group, while accounting for uncertainty in the baseline immunity status of subjects.

Results

Baseline seropositive subjects showed high efficacy for all serotypes, 70.2% (95% confidence interval [CI]: 57.4, 80.1) for dengue 1 (DENV-1), 67.9% (95% CI: 49.9, 82.0) for DENV-2, 77.5% (95% CI: 64.3, 90.2) for DENV-3, 89.9% (95% CI: 79.8, 99.9) for DENV-4, and 75.4% (95% CI: 68.3, 81.6) overall. In contrast, baseline seronegative subjects showed moderate efficacy against DENV-4, 51.2% [95% CI: 20.0, 72.8] but no significant efficacy against other serotypes. Among seropositive children, the overall efficacy tended to increase with age, 35.9% (95% CI: -7.6, 69.3) for children ≤5 years old, 65.6% (95% CI: 40.3, 84.2) for 6 – 8 years old, 73.4% (95% CI: 62.6, 82.1) for 9 – 11 years old, and 80.6% (95% CI: 72.9, 87.3) for 12 years or older.

Conclusions

The CYD-TDV vaccine was highly efficacious for all dengue serotypes among children older than 5 years who have acquired baseline immunity from previous exposure. Increasing vaccine efficacy with age was not fully explained by increasing prevalence of baseline immunity with age.

Birth/birth-death processes and their computable transition probabilities with biological applications

Lam Si Tung Ho, Jason Xu, Forrest W. Crawford, Vladimir N. Minin, Marc A. Suchard

Journal of Mathematical Biology

July 24, 2017

ABSTRACT

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.

Monte Carlo profile confidence intervals for dynamic systems

E. L. Ionides, C. Breto, J. Park, R. A. Smith, A. A. King

Royal Society Interface

July 5, 2017

ABSTRACT

Monte Carlo methods to evaluate and maximize the likelihood function enable the construction of confidence intervals and hypothesis tests, facilitating scientific investigation using models for which the likelihood function is intractable. When Monte Carlo error can be made small, by sufficiently exhaustive computation, then the standard theory and practice of likelihood-based inference applies. As datasets become larger, and models more complex, situations arise where no reasonable amount of computation can render Monte Carlo error negligible. We develop profile likelihood methodology to provide frequentist inferences that take into account Monte Carlo uncertainty. We investigate the role of this methodology in facilitating inference for computationally challenging dynamic latent variable models. We present examples arising in the study of infectious disease transmission, demonstrating our methodology for inference on nonlinear dynamic models using genetic sequence data and panel time-series data. We also discuss applicability to nonlinear time-series and spatio-temporal data.