David A. Rolls

The impact of injecting networks on hepatitis C transmission and treatment in people who inject drugs

With the development of new highly efficacious direct‐acting antiviral (DAA) treatments for hepatitis C virus (HCV), the concept of treatment as prevention is gaining credence. To date, the majority of mathematical models assume perfect mixing, with injectors having equal contact with all other injectors. This article explores how using a networks‐based approach to treat people who inject drugs (PWID) with DAAs affects HCV prevalence. Using observational data, we parameterized an exponential random graph model containing 524 nodes. We simulated transmission of HCV through this network using a discrete time, stochastic transmission model. The effect of five treatment strategies on the prevalence of HCV was investigated; two of these strategies were (1) treat randomly selected nodes and (2) “treat your friends,” where an individual is chosen at random for treatment and all their infected neighbors are treated. As treatment coverage increases, HCV prevalence at 10 years reduces for both the high‐ and low‐efficacy treatment. Within each set of parameters, the treat your friends strategy performed better than the random strategy being most marked for higher‐efficacy treatment. For example, over 10 years of treating 25 per 1,000 PWID, the prevalence drops from 50% to 40% for the random strategy and to 33% for the treat your friends strategy (6.5% difference; 95% confidence interval: 5.1‐8.1). Conclusion: Treat your friends is a feasible means of utilizing network strategies to improve treatment efficiency. In an era of highly efficacious and highly tolerable treatment, such an approach will benefit not just the individual, but also the community more broadly by reducing the prevalence of HCV among PWID. (Hepatology 2014;60:1860–1869)

Hepatitis C Virus Phylogenetic Clustering Is Associated with the Social-Injecting Network in a Cohort of People Who Inject Drugs

It is hypothesized that social networks facilitate transmission of the hepatitis C virus (HCV). We tested for association between HCV phylogeny and reported injecting relationships using longitudinal data from a social network design study. People who inject drugs were recruited from street drug markets in Melbourne, Australia. Interviews and blood tests took place three monthly (during 2005–2008), with participants asked to nominate up to five injecting partners at each interview. The HCV core region of individual isolates was then sequenced and phylogenetic trees were constructed. Genetic clusters were identified using bootstrapping (cut-off: 70%). An adjusted Jaccard similarity coefficient was used to measure the association between the reported injecting relationships and relationships defined by clustering in the phylogenetic analysis (statistical significance assessed using the quadratic assignment procedure). 402 participants consented to participate; 244 HCV infections were observed in 238 individuals. 26 genetic clusters were identified, with 2–7 infections per cluster. Newly acquired infection (AOR = 2.03, 95% CI: 1.04–3.96, p = 0.037, and HCV genotype 3 (vs. genotype 1, AOR = 2.72, 95% CI: 1.48–4.99) were independent predictors of being in a cluster. 54% of participants whose infections were part of a cluster in the phylogenetic analysis reported injecting with at least one other participant in that cluster during the study. Overall, 16% of participants who were infected at study entry and 40% of participants with newly acquired infections had molecular evidence of related infections with at least one injecting partner. Likely transmission clusters identified in phylogenetic analysis correlated with reported injecting relationships (adjusted Jaccard coefficient: 0.300; p<0.001). This is the first study to show that HCV phylogeny is associated with the injecting network, highlighting the importance of the injecting network in HCV transmission.

Hepatitis C Transmission and Treatment in Contact Networks of People Who Inject Drugs

Hepatitis C virus (HCV) chronically infects over 180 million people worldwide, with over 350,000 estimated deaths attributed yearly to HCV-related liver diseases. It disproportionally affects people who inject drugs (PWID). Currently there is no preventative vaccine and interventions feature long treatment durations with severe side-effects. Upcoming treatments will improve this situation, making possible large-scale treatment interventions. How these strategies should target HCV-infected PWID remains an important unanswered question. Previous models of HCV have lacked empirically grounded contact models of PWID. Here we report results on HCV transmission and treatment using simulated contact networks generated from an empirically grounded network model using recently developed statistical approaches in social network analysis. Our HCV transmission model is a detailed, stochastic, individual-based model including spontaneously clearing nodes. On transmission we investigate the role of number of contacts and injecting frequency on time to primary infection and the role of spontaneously clearing nodes on incidence rates. On treatment we investigate the effect of nine network-based treatment strategies on chronic prevalence and incidence rates of primary infection and re-infection. Both numbers of contacts and injecting frequency play key roles in reducing time to primary infection. The change from “less-” to “more-frequent” injector is roughly similar to having one additional network contact. Nodes that spontaneously clear their HCV infection have a local effect on infection risk and the total number of such nodes (but not their locations) has a network wide effect on the incidence of both primary and re-infection with HCV. Re-infection plays a large role in the effectiveness of treatment interventions. Strategies that choose PWID and treat all their contacts (analogous to ring vaccination) are most effective in reducing the incidence rates of re-infection and combined infection. A strategy targeting infected PWID with the most contacts (analogous to targeted vaccination) is the least effective.

Hepatitis C transmission and treatment as prevention – The role of the injecting network

BACKGROUND The hepatitis C virus (HCV) epidemic is a major health issue; in most developed countries it is driven by people who inject drugs (PWID). Injecting networks powerfully influence HCV transmission. In this paper we provide an overview of 10 years of research into injecting networks and HCV, culminating in a network-based approach to provision of direct-acting antiviral therapy. METHODS Between 2005 and 2010 we followed a cohort of 413 PWID, measuring HCV incidence, prevalence and injecting risk, including network-related factors. We developed an individual-based HCV transmission model, using it to simulate the spread of HCV through the empirical social network of PWID. In addition, we created an empirically grounded network model of injecting relationships using exponential random graph models (ERGMs), allowing simulation of realistic networks for investigating HCV treatment and intervention strategies. Our empirical work and modelling underpins the TAP Study, which is examining the feasibility of community-based treatment of PWID with DAAs. RESULTS We observed incidence rates of HCV primary infection and reinfection of 12.8 per 100 person-years (PY) (95%CI: 7.7-20.0) and 28.8 per 100 PY (95%CI: 15.0-55.4), respectively, and determined that HCV transmission clusters correlated with reported injecting relationships. Transmission modelling showed that the empirical network provided some protective effect, slowing HCV transmission compared to a fully connected, homogenous PWID population. Our ERGMs revealed that treating PWID and all their contacts was the most effective strategy and targeting treatment to infected PWID with the most contacts the least effective. CONCLUSION Networks-based approaches greatly increase understanding of HCV transmission and will inform the implementation of treatment as prevention using DAAs.

Modelling a disease-relevant contact network of people who inject drugs

Abstract This study uses social network analysis to model a contact network of people who inject drugs (PWID) relevant for investigating the spread of an infectious disease (hepatitis C). Using snowball sample data, parameters for an exponential random graph model (ERGM) including social circuit dependence and four attributes (location, age, injecting frequency, gender) are estimated using a conditional estimation approach that respects the structure of snowball sample designs. Those network parameter estimates are then used to create a novel, model-dependent estimate of network size. Simulated PWID contact networks are created and compared with Bernoulli graphs. Location, age and injecting frequency are shown to be statistically significant attribute parameters in the ERGM. Simulated ERGM networks are shown to fit the collected data very well across a number of metrics. In comparison with Bernoulli graphs, simulated networks are shown to have longer paths and more clustering. Results from this study make possible simulation of realistic networks for investigating treatment and intervention strategies for reducing hepatitis C prevalence.

A simulation study comparing epidemic dynamics on exponential random graph and edge-triangle configuration type contact network models

We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure.

Minimum distance estimators of population size from snowball samples using conditional estimation and scaling of exponential random graph models

New distance-based estimators of population size for snowball sample network data using exponential random graph models (ERGMs) are presented. After ERGM parameters are obtained using conditional estimation it is possible to simulate networks from the ERGM across a range of hypothesized sizes and then estimate the population’s size. This is done by creating simulated snowball samples from the simulated networks and then minimizing their distances from an observed network statistic across network sizes. The number of nodes in the snowball sample (snowball size) combined with a moment-based distance is shown to be an effective estimator. For ERGM conditional estimate parameters, the moment-based snowball size estimator can outperform a multivariate Mahalanobis estimator, where the latter would be a maximum likelihood estimator under the assumption the network statistics are multivariate Gaussian. “Extreme” ERGM scaling across network sizes, which prevents finding a minimum-distance estimate, is also discussed.

An Improved Test for Continuous Local Martingales

We present a new test for the “continuous martingale hypothesis”. That is, a test for the hypothesis that observed data are from a process which is a continuous local martingale. The basis of the test is an embedded random walk at first passage times, obtained from the well-known representation of a continuous local martingale as a continuous time-change of Brownian motion. With a variety of simulated diffusion processes our new test shows higher power than existing tests using either the crossing tree or the quadratic variation, including the situation where non-negligible drift is present. The power of the test in the presence of jumps is also explored with a variety of simulated jump diffusion processes. The test is also applied to two sequences of high-frequency foreign exchange trade-by-trade data. In both cases the continuous martingale hypothesis is rejected at times less than hourly and we identify significant dependence in price movements at these small scales.

Large Deviations: Advanced Probability for Undergrads

In the branch of probability called “large deviations,” rates of convergence (e.g. of the sample mean) are considered. The theory makes use of the moment generating function. So, particularly for sums of independent and identically distributed random variables, the theory can be made accessible to senior undergraduates after a first course in stochastic processes. This paper describes a directed independent study in large deviations offered to a strong senior, providing a sample outline and discussion of resources. Learning points are also highlighted.