An empirically adjusted approach to reproductive number estimation for stochastic compartmental models: A case study of two Ebola outbreaks.

The various thresholding quantities grouped under the "Basic Reproductive Number" umbrella are often confused, but represent distinct approaches to estimating epidemic spread potential, and address different modeling needs. Here, we contrast several common reproduction measures applied to stochastic compartmental models, and introduce a new quantity dubbed the "empirically adjusted reproductive number" with several advantages. These include: more complete use of the underlying compartmental dynamics than common alternatives, use as a potential diagnostic tool to detect the presence and causes of intensity process underfitting, and the ability to provide timely feedback on disease spread. Conceptual connections between traditional reproduction measures and our approach are explored, and the behavior of our method is examined under simulation. Two illustrative examples are developed: First, the single location applications of our method are established using data from the 1995 Ebola outbreak in the Democratic Republic of the Congo and a traditional stochastic SEIR model. Second, a spatial formulation of this technique is explored in the context of the ongoing Ebola outbreak in West Africa with particular emphasis on potential use in model selection, diagnosis, and the resulting applications to estimation and prediction. Both analyses are placed in the context of a newly developed spatial analogue of the traditional SEIR modeling approach.

A spatial epidemic model for disease spread over a heterogeneous spatial support.

Data from the Iowa mumps epidemic of 2006 were collected on a spatial lattice over a regular temporal interval. Without access to a person-to-person contact graph, it is sensible to analyze these data as homogenous within each areal unit and to use the spatial graph to derive a contact structure. The spatio-temporal partition is fine, and the counts of new infections at each location at each time are sparse. Therefore, we propose a spatial compartmental epidemic model with general latent time distributions (spatial PS SEIR) that is capable of smoothing the contact structure, while accounting for spatial heterogeneity in the mixing process between locations. Because the model is an extension of the PS SEIR model, it simultaneously handles non-exponentially distributed latent and infectious time distributions. The analysis within focuses on the progression of the disease over both space and time while assessing the impact of a large proportion of the infected people dispersing at the same time because of spring break and the impact of public awareness on the spread of the mumps epidemic. We found that the effect of spring break increased the mixing rate in the population and that the spatial transmission of the disease spreads across multiple conduits.

A path-specific SEIR model for use with general latent and infectious time distributions.

Most current Bayesian SEIR (Susceptible, Exposed, Infectious, Removed (or Recovered)) models either use exponentially distributed latent and infectious periods, allow for a single distribution on the latent and infectious period, or make strong assumptions regarding the quantity of information available regarding time distributions, particularly the time spent in the exposed compartment. Many infectious diseases require a more realistic assumption on the latent and infectious periods. In this article, we provide an alternative model allowing general distributions to be utilized for both the exposed and infectious compartments, while avoiding the need for full latent time data. The alternative formulation is a path-specific SEIR (PS SEIR) model that follows individual paths through the exposed and infectious compartments, thereby removing the need for an exponential assumption on the latent and infectious time distributions. We show how the PS SEIR model is a stochastic analog to a general class of deterministic SEIR models. We then demonstrate the improvement of this PS SEIR model over more common population averaged models via simulation results and perform a new analysis of the Iowa mumps epidemic from 2006.

Approximate Bayesian computation for spatial SEIR(S) epidemic models.

Approximate Bayesia n Computation (ABC) provides an attractive approach to estimation in complex Bayesian inferential problems for which evaluation of the kernel of the posterior distribution is impossible or computationally expensive. These highly parallelizable techniques have been successfully applied to many fields, particularly in cases where more traditional approaches such as Markov chain Monte Carlo (MCMC) are impractical. In this work, we demonstrate the application of approximate Bayesian inference to spatially heterogeneous Susceptible-Exposed-Infectious-Removed (SEIR) stochastic epidemic models. These models have a tractable posterior distribution, however MCMC techniques nevertheless become computationally infeasible for moderately sized problems. We discuss the practical implementation of these techniques via the open source ABSEIR package for R. The performance of ABC relative to traditional MCMC methods in a small problem is explored under simulation, as well as in the spatially heterogeneous context of the 2014 epidemic of Chikungunya in the Americas.

Estimating the reproductive number, total outbreak size, and reporting rates for Zika epidemics in South and Central America.

As South and Central American countries prepare for increased birth defects from Zika virus outbreaks and plan for mitigation strategies to minimize ongoing and future outbreaks, understanding important characteristics of Zika outbreaks and how they vary across regions is a challenging and important problem. We developed a mathematical model for the 2015/2016 Zika virus outbreak dynamics in Colombia, El Salvador, and Suriname. We fit the model to publicly available data provided by the Pan American Health Organization, using Approximate Bayesian Computation to estimate parameter distributions and provide uncertainty quantification. The model indicated that a country-level analysis was not appropriate for Colombia. We then estimated the basic reproduction number to range between 4 and 6 for El Salvador and Suriname with a median of 4.3 and 5.3, respectively. We estimated the reporting rate to be around 16% in El Salvador and 18% in Suriname with estimated total outbreak sizes of 73,395 and 21,647 people, respectively. The uncertainty in parameter estimates highlights a need for research and data collection that will better constrain parameter ranges.

The Effect of Receiving Treatment Within a Clinical Trial Setting on Survival and Quality of Care Perception in Advanced Stage Non-Small Cell Lung Cancer.

OBJECTIVES: Treatment outcomes of advanced stage (IIIB and IV) non-small cell lung cancer (NSCLC) are poor. In this study, we explore the survival outcomes and the perception of the quality of care delivered in stage IIIB and IV NSCLC patients treated within versus outside a clinical trial. MATERIALS AND METHODS: Data were obtained from the Cancer Care Outcomes Research and Surveillance Consortium (CanCORS). Baseline characteristics according to clinical trial participation were determined. The association between clinical trial enrollment and survival was assessed using a Cox proportional hazard model after adjusting for age, income, primary data collection and research site, comorbidities, self-reported performance status, presence of brain metastasis, stage IIIB versus IV, and cancer histology. RESULTS: Of 815 stage IIIB and IV NSCLC patients, 56 (7%) were enrolled in clinical trials. Median survival for the patients treated within versus outside a clinical trial was 20.5 versus 16.7 months, respectively (P=0.21). Using a multivariate survival model, clinical trial enrollment did not correlate with longer survival (P=0.81). Comparing patients according to clinical trial enrollment, patients treated within a clinical trial setting perceived a better overall quality of care (P<0.01). CONCLUSIONS: Management of stage IIIB and IV NSCLC patients within a clinical trial setting conveyed a perception of superior care that did not translate into survival benefit. These findings suggest that providing cancer care within a clinical trial should not imply a survival benefit when counseling stage IIIB and IV NSCLC patients about entering clinical trials.

A multivariate CAR model for mismatched lattices.

In this paper, we develop a multivariate Gaussian conditional autoregressive model for use on mismatched lattices. Most current multivariate CAR models are designed for each multivariate outcome to utilize the same lattice structure. In many applications, a change of basis will allow different lattices to be utilized, but this is not always the case, because a change of basis is not always desirable or even possible. Our multivariate CAR model allows each outcome to have a different neighborhood structure which can utilize different lattices for each structure. The model is applied in two real data analysis. The first is a Bayesian learning example in mapping the 2006 Iowa Mumps epidemic, which demonstrates the importance of utilizing multiple channels of infection flow in mapping infectious diseases. The second is a multivariate analysis of poverty levels and educational attainment in the American Community Survey.