Improving and Extending STERGM Approximations Based on Cross-Sectional Data and Tie Durations.

Temporal exponential-family random graph models (TERGMs) are a flexible class of models for network ties that change over time. Separable TERGMs (STERGMs) are a subclass of TERGMs in which the dynamics of tie formation and dissolution can be separated within each discrete time step and may depend on different factors. The Carnegie et al. (2015) approximation improves estimation efficiency for a subclass of STERGMs, allowing them to be reliably estimated from inexpensive cross-sectional study designs. This approximation adapts to cross-sectional data by attempting to construct a STERGM with two specific properties: a cross-sectional equilibrium distribution defined by an exponential-family random graph model (ERGM) for the network structure, and geometric tie duration distributions defined by constant hazards for tie dissolution. In this paper we focus on approaches for improving the behavior of the Carnegie et al. approximation and increasing its scope of application. We begin with Carnegie et al.'s observation that the exact result is tractable when the ERGM is dyad-independent, and then show that taking the sparse limit of the exact result leads to a different approximation than the one they presented. We show that the new approximation outperforms theirs for sparse, dyad-independent models, and observe that the errors tend to increase with the strength of dependence for dyad-dependent models. We then develop theoretical results in the dyad-dependent case, showing that when the ERGM is allowed to have arbitrary dyad-dependent terms and some dyad-dependent constraints, both the old and new approximations are asymptotically exact as the size of the STERGM time step goes to zero. We note that the continuous-time limit of the discrete-time approximations has the desired cross-sectional equilibrium distribution and exponential tie duration distributions with the desired means. We show that our results extend to hypergraphs, and we propose an extension of the Carnegie et al. framework to dissolution hazards that depend on tie age.

The value of implementing a nursing and midwifery clinical accreditation programme at two NHS trusts.

Unit/ward accreditation programmes have been widely implemented by nursing and midwifery teams across healthcare providers in the UK over the recent years and have many associated benefits. These include promoting quality improvement on a wider scale across the organisation, strengthening oversight and accountability of quality and safety from ward to board and vice versa, promoting shared learning, and providing opportunities for sharing and celebrating excellence. The Royal Wolverhampton NHS Trust and Walsall Healthcare NHS Trust have recognised the value of this approach, launching a clinical accreditation programme in April 2023. This initially focused on nursing and midwifery, with plans to widen the approach to other disciplines and specialist teams. Up to the time of writing, 56 visits had been undertaken with 30 clinical areas accredited. The remaining visited areas are awaiting their accreditation outcome. The approach has positively contributed to improvements in patient outcomes, such as more patient observations being completed on time, a reduction in patient falls and improvements in pressure ulcers. Colleagues participating in the programme and frontline staff working in the clinical areas assessed have reported how positive the approach has been, providing opportunities for shared learning and celebrating excellence.

Partnership types and coital frequency as predictors of gonorrhea and chlamydia among young MSM and young transgender women.

BACKGROUND: Sexually transmitted infections pose a major public health challenge in the United States and this burden is especially acute in subpopulations like young men who have sex with men (YMSM) and young transgender women (YTW). Yet, the direct behavioral antecedents of these infections are not well understood making it difficult to identify the cause of recent increases in incidence. This study examines how variations in partnership rates and the number of condomless sex acts are associated with STI infections among YMSM-YTW. METHOD: This study leveraged 3 years of data from a large longitudinal cohort of YMSM-YTW. A series of generalized linear mixed models examined the association between the number of condomless anal sex acts, number of one-time partners, number of casual partners, and number of main partners and chlamydia, gonorrhea, or any STI. RESULTS: Results indicated the number of casual partners was associated with gonorrhea [aOR = 1.17 (95% CI: 1.08, 1.26)], chlamydia [aOR = 1.12 (95% CI: 1.05, 1.20)], and any STI [aOR = 1.14 (95% CI: 1.08, 1.21)] while the number of one-time partners was only associated with gonorrhea [aOR = 1.13 (95% CI: 1.02, 1.26)]. The number of condomless anal sex acts was not associated with any outcome. CONCLUSION: These findings suggest the number of casual partners is a consistent predictor of STI infection among YMSM-YTW. This may reflect the quick saturation of risk within partnerships making the number of partners, rather than the number of acts, the more relevant factor for STI risk.

Comparing Sexual Network Mean Active Degree Measurement Metrics Among Men Who Have Sex With Men.

BACKGROUND: Mean active degree is an important proxy measure of cross-sectional network connectivity commonly used in HIV/sexually transmitted infection epidemiology research. No current studies have compared measurement methods of mean degree using a cross-sectional study design for men who have sex with men (MSM) in the United States. We compared mean degree estimates based on reported ongoing main and casual sexual partnerships (current method) against dates of first and last sex (retrospective method). METHODS: We used data from ARTnet, a cross-sectional survey of MSM in the United States (2017-2019). ARTnet collected data on the number and types of sexual partners in the past year, limited to the 5 most recent partners (data truncation). We quantified partnerships for months 0 to 12 before the survey date (retrospective method) and compared that with ongoing partnerships on the day of survey (current method). We used linear regression to understand the impact of truncated partnership data on mean degree estimation. RESULTS: The retrospective method yielded similar degree estimates to the current for months proximate to the day of survey. The retrospective method mean degree systematically decreased as the month increased from 0 to 12 months before survey date. This was driven by data truncation: among participants with >5 partners in the past year compared with those with ≤5, the average change in main partnership degree between 12 and 0 months before survey date was -0.05 (95% confidence interval, -0.08 to -0.03) after adjusting for race/ethnicity, age, and education. The adjusted average change in casual partnership degree was -0.40 (95% confidence interval, -0.45 to -0.35). CONCLUSIONS: The retrospective method underestimates mean degree for MSM in surveys with truncated partnership data, especially for casual partnerships. The current method is less prone to bias from partner truncation when the target population has high rate of partners per year.

Impact of Survey Design on Estimation of Exponential-Family Random Graph Models from Egocentrically-Sampled Data.

Egocentric sampling of networks selects a subset of nodes ("egos") and collects information from them on themselves and their immediate network neighbours ("alters"), leaving the rest of the nodes in the network unobserved. This design is popular because it is relatively inexpensive to implement and can be integrated into standard sample surveys. Recent methodological developments now make it possible to statistically analyse this type of network data with Exponential-family Random Graph Models (ERGMs). This provides a framework for principled statistical inference, and the fitted models can in turn be used to simulate complete networks of arbitrary size that are consistent with the observed sample data, allowing one to infer the distribution of whole-network properties generated by the observed egocentric network statistics. In this paper, we discuss how design choices for egocentric network studies impact statistical estimation and inference for ERGMs. The design choices include both measurement strategies (for ego and alter attributes, and for ego-alter and alter-alter ties) and sampling strategies (for egos and alters). We discuss the importance of harmonising measurement specifications across egos and alters, and conduct simulation studies to demonstrate the impact of sampling design on statistical inference, specifically stratified sampling and degree censoring.

HIV and Sexually Transmitted Infection Epidemic Potential of Networks of Men Who Have Sex With Men in Two Cities.

BACKGROUND: The speed with which a pathogen circulates in a sexual network is a function of network connectivity. Cross-sectional connectivity is a function of network features like momentary degree and assortative mixing. Temporal connectivity is driven by partner acquisition rates. The forward-reachable path (FRP) has been proposed as a summary measure of these two aspects of transmission potential. We use empirical data from San Francisco and Atlanta to estimate the generative parameters of the FRP and compare results to the HIV/sexually transmitted infection epidemics in each city. METHODS: We used temporal exponential random graph models to estimate the generative parameters for each city's dynamic sexual network from survey data. We then simulated stochastic dynamic networks from the fitted models and calculated the FRP for each realization, overall, and stratified by partnership type and demographics. RESULTS: The overall mean and median paths were higher in San Francisco than in Atlanta. The overall paths for each city were greater than the sum of the paths in each individual partnership network. In the casual partnership network, the mean path was highest in the youngest age group and lowest in the oldest age group, despite the fact that the youngest group had the lowest mean momentary degree and past-year partner counts. CONCLUSIONS: The FRP by age group revealed the additional utility of the measure beyond the temporal and cross-sectional network connectivity measures. Other nonnetwork factors are still necessary to infer total epidemic potential for any specific pathogen.

A Behavioral Cascade of HIV Seroadaptation Among US Men Who Have Sex with Men in the Era of PrEP and U = U.

Seroadaptive behaviors help reduce HIV risk for some men who have sex with men (MSM), and have been well documented across MSM populations. Advancements in biomedical prevention have changed the contexts in which seroadaptive behaviors occur. We thus sought to estimate and compare the prevalence of four stages of the "seroadaptive cascade" by PrEP use in the recent era: knowledge of own serostatus, knowledge of partner serostatus; serosorting (matching by status), and condomless anal intercourse. Serosorting overall appeared to remain common, especially with casual and one-time partners. Although PrEP use did not impact status discussion, it did impact serosorting and the likelihood of having condomless anal intercourse. For respondents not diagnosed with HIV and not on PrEP, condomless anal intercourse occurred in just over half of relationships with HIV-positive partners who were not on treatment. Biomedical prevention has intertwined with rather than supplanted seroadaptive behaviors, while contexts involving neither persist.

RESUMEN: Los comportamientos seroadaptivos ayudan a reducir el riesgo de VIH en algunos hombres que tienen sexo con otros hombres (HSH) y han sido bien documentados en varias comunidades de HSH. Los avances en prevención biomédica han cambiado los contextos de los comportamientos seroadaptivos. Por ello buscamos estimar y comparar la prevalencia de cuatro fases de la 'cascada seroadaptiva' mediante el uso de PrEP en la era reciente: conocimiento del seroestatus personal, conocimiento del seroestatus del compañero, serosorting (emparejamiento por estatus) y coito anal sin condón. En general, el serosorting parece seguir siendo común especialmente con parejas casuales o de una noche. A pesar de que el uso de PrEP no impactó la discusión sobre el estatus, sí impactó el serosorting y la probabilidad de coito anal sin condón. Los encuestados no diagnosticados con VIH y sin PrEP tuvieron coito anal sin condón en la mitad de las relaciones con parejas VIH-positivo que no estaban bajo tratamiento. La prevención biomédica se ha entremezclado en lugar de suplantar los comportamientos seropositivos, mientras persisten los contextos en los que no aparece ninguno.

Temporal Variation in One-Time Partnership Rates Among Young Men Who Have Sex With Men and Transgender Women.

BACKGROUND: Volatility in sexual contact rates has been recognized as an important factor influencing HIV transmission dynamics. One-time partnerships may be particularly important given the potential to quickly accumulate large number of contacts. Yet, empirical data documenting individual variation in contact rates remain rare. This study provides much needed data on temporal variation in one-time partners to better understand behavioral dynamics and improve the accuracy of transmission models. METHODS: Data for this study were obtained from a longitudinal cohort study of young men who have sex with men and transgender women in Chicago. Participants provided sexual network data every 6 months for 2 years. A series of random effects models examined variation in one-time partnership rates and disaggregated within and between associations of exposure variables. Exposure variables included prior number of one-time partners, number of casual partners, and having a main partner. RESULTS: Results indicated substantial between-person and within-person variation in one-time partners. Casual partnerships were positively associated and main partnerships negatively associated with one-time partnership rates. There remained a small positive association between prior one-time partnerships and the current number of one-time partnerships. CONCLUSIONS: Despite the preponderance of a low number of one-time partners, substantial variation in one-time partnership rates exists among young men who have sex with men and transgender women. Accordingly, focusing on high contact rate individuals alone may be insufficient to identify periods of highest risk. Future studies should use these estimates to more accurately model how volatility impacts HIV transmission and better understand how this variation influences intervention effectiveness.

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, would allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (iii) focus on requirements for data collection, particularly in low-to-middle-income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

Egocentric sexual networks of men who have sex with men in the United States: Results from the ARTnet study.

In this paper, we present an overview and descriptive results from one of the first egocentric network studies of men who have sex with men (MSM) from across the United States: the ARTnet study. ARTnet was designed to support prevention research for human immunodeficiency virus (HIV) and other sexually transmitted infections (STIs) that are transmitted across partnership networks. ARTnet implemented a population-based egocentric network study design that sampled egos from the target population and asked them to report on the number, attributes, and timing of their sexual partnerships. Such data provide the foundation needed for parameterizing stochastic network models that are used for disease projection and intervention planning. ARTnet collected data online from 2017 to 2019, with a final sample of 4904 participants who reported on 16198 sexual partnerships. The aims of this paper were to characterize the joint distribution of three network parameters needed for modeling: degree distributions, assortative mixing, and partnership age, with heterogeneity by partnership type (main, casual and one-time), demography, and geography. Participants had an average of 1.19 currently active partnerships ("mean degree"), which was higher for casual partnerships (0.74) than main partnerships (0.45). The mean rate of one-time partnership acquisition was 0.16 per week (8.5 partners per year). Main partnerships lasted 272.5 weeks on average, while casual partnerships lasted 133.0 weeks. There was strong but heterogenous assortative mixing by race/ethnicity for all groups. The mean absolute age difference for all partnership types was 9.5 years, with main partners differing by 6.3 years compared to 10.8 years for casual partners. Our analysis suggests that MSM may be at sustained risk for HIV/STI acquisition and transmission through high network degree of sexual partnerships. The ARTnet network study provides a robust and reproducible foundation for understanding the dynamics of HIV/STI epidemiology among U.S. MSM and supporting the implementation science that seeks to address persistent challenges in HIV/STI prevention.

Effects of Cationic Polyacrylamide and Cationic Starch on Aquatic Life.

Geotextile tubes with polyacrylamide flocculants are widely used in dewatering applications. Due to variations in solid concentrations during dredging, excess flocculant is sometimes released into the environment, where it might have toxic effects. This study determined optimum doses for a cationic polyacrylamide (CPAM) and a natural-based polymer alternative, cationic starch (C. Starch). Slurry samples were treated with optimum and 50% overdoses of each compound, and residual polymer concentrations were measured. Overdosed C. Starch resulted in low residuals (<2 ppm), but overdosed CPAM resulted in 17.4 ppm residual polymer. The relative toxicity of CPAM and C. Starch was also tested using zebrafish embryos. 100% of embryos that had their chorion removed and 71.8% of embryos that retained their chorions, were dead or dying after 7 days of exposure to CPAM. In contrast, there was no statistically significant difference in the numbers of embryos that were dead or dying, when exposed to C. Starch, compared to controls. These data strongly suggest that C. Starch should be considered as a replacement to CPAM in dewatering applications.

Monitoring HIV Preexposure Prophylaxis Use Among Men Who Have Sex With Men in Washington State: Findings From an Internet-Based Survey.

BACKGROUND: Many state and local health departments now promote and support the use of HIV preexposure prophylaxis (PrEP), yet monitoring use of the intervention at the population level remains challenging. METHODS: We report the results of an online survey designed to measure PrEP use among men who have sex with men (MSM) in Washington State. Data on the proportion of men with indications for PrEP based on state guidelines and levels of awareness, interest, and use of PrEP are presented for 1080 cisgender male respondents who completed the survey between January 1 and February 28, 2017. We conducted bivariate and multivariable logistic regression to identify factors associated with current PrEP use. To examine patterns of discontinuation, we conducted Cox proportional hazards regression and fit a Kaplan-Meier curve to reported data on time on PrEP. RESULTS: Eighty percent of respondents had heard of PrEP, 19% reported current use, and 36% of men who had never used PrEP wanted to start taking it. Among MSM for whom state guidelines recommend PrEP, 31% were taking it. In multivariable analysis, current PrEP use was associated with older age, higher education, and meeting indications for PrEP use. Our data suggest that 20% of PrEP users discontinue within 12 months, and men with lower educational attainment were more likely to discontinue. CONCLUSIONS: Despite high levels of use, there is significant unmet need for PrEP in Washington. Our experience indicates that Internet surveys are feasible and informative for monitoring PrEP use in MSM.

Multilevel network data facilitate statistical inference for curved ERGMs with geometrically weighted terms.

Multilevel network data provide two important benefits for ERG modeling. First, they facilitate estimation of the decay parameters in geometrically weighted terms for degree and triad distributions. Estimating decay parameters from a single network is challenging, so in practice they are typically fixed rather than estimated. Multilevel network data overcome that challenge by leveraging replication. Second, such data make it possible to assess out-of-sample performance using traditional cross-validation techniques. We demonstrate these benefits by using a multilevel network sample of classroom networks from Poland. We show that estimating the decay parameters improves in-sample performance of the model and that the out-of-sample performance of our best model is strong, suggesting that our findings can be generalized to the population of interest.

Correction: A New Method for Estimating the Number of Undiagnosed HIV Infected Based on HIV Testing History, with an Application to Men Who Have Sex with Men in Seattle/King County, WA.

[This corrects the article DOI: 10.1371/journal.pone.0129551.].

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers.

INFERENCE FOR SOCIAL NETWORK MODELS FROM EGOCENTRICALLY SAMPLED DATA, WITH APPLICATION TO UNDERSTANDING PERSISTENT RACIAL DISPARITIES IN HIV PREVALENCE IN THE US.

Egocentric network sampling observes the network of interest from the point of view of a set of sampled actors, who provide information about themselves and anonymized information on their network neighbors. In survey research, this is often the most practical, and sometimes the only, way to observe certain classes of networks, with the sexual networks that underlie HIV transmission being the archetypal case. Although methods exist for recovering some descriptive network features, there is no rigorous and practical statistical foundation for estimation and inference for network models from such data. We identify a subclass of exponential-family random graph models (ERGMs) amenable to being estimated from egocentrically sampled network data, and apply pseudo-maximum-likelihood estimation to do so and to rigorously quantify the uncertainty of the estimates. For ERGMs parametrized to be invariant to network size, we describe a computationally tractable approach to this problem. We use this methodology to help understand persistent racial disparities in HIV prevalence in the US. We also discuss some extensions, including how our framework may be applied to triadic effects when data about ties among the respondent's neighbors are also collected.

Epidemic potential by sexual activity distributions.

For sexually transmitted infections like HIV to propagate through a population, there must be a path linking susceptible cases to currently infectious cases. The existence of such paths depends in part on the degree distribution. Here, we use simulation methods to examine how two features of the degree distribution affect network connectivity: Mean degree captures a volume dimension, while the skewness of the upper tail captures a shape dimension. We find a clear interaction between shape and volume: When mean degree is low, connectivity is greater for long-tailed distributions, but at higher mean degree, connectivity is greater in short-tailed distributions. The phase transition to a giant component and giant bicomponent emerges as a positive function of volume, but it rises more sharply and ultimately reaches more people in short-tail distributions than in long-tail distributions. These findings suggest that any interventions should be attuned to how practices affect both the volume and shape of the degree distribution, noting potential unanticipated effects. For example, policies that primarily affect high-volume nodes may not be effective if they simply redistribute volume among lower degree actors, which appears to exacerbate underlying network connectivity.

Forward reachable sets: Analytically derived properties of connected components for dynamic networks.

Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration. FRS are defined as the set of nodes that can be reached from an initial seed via a path of temporally ordered edges; a natural extension of connected component measures to dynamic networks. Working in a stochastic framework, we derive closed-form expressions for the mean and variance of the exponential growth rate of the FRS for temporal networks with both edge and node dynamics. For networks with node dynamics, we calculate thresholds for the growth of the FRS. The effects of finite population size are explored via simulation and approximation. We examine how these properties vary by edge duration and different cross-sectional degree distributions that characterize a range of scientifically interesting normative outcomes (Poisson and Bernoulli). The size of the forward reachable set gives an upper bound for the epidemic size in disease transmission network models, relating this work to epidemic modeling (Ferguson, 2000; Eames, 2004).

Effectiveness of combination packages for HIV-1 prevention in sub-Saharan Africa depends on partnership network structure: a mathematical modelling study.

OBJECTIVES: Combination packages for HIV prevention can leverage the effectiveness of biomedical and behavioural elements to lower disease incidence with realistic targets for individual and population risk reduction. We investigated how sexual network structures can maximise the effectiveness of a package targeting sexually active adults in sub-Saharan Africa (SSA) with intervention components for medical male circumcision (MMC) and sexual partnership concurrency (having >1 ongoing partner). METHODS: Network-based mathematical models of HIV type 1 (HIV-1) transmission dynamics among heterosexual couples were used to explore how changes to MMC alone and in combination with changes to concurrency impacted endemic HIV-1 prevalence and incidence. Starting from a base model parameterised from empirical data from West Africa, we simulated the prevalence of circumcision from 10% to 90% and concurrency was modelled at four discrete levels corresponding to values observed across SSA. RESULTS: MMC and concurrency could contribute to the empirical variation in HIV-1 disease prevalence across SSA. Small reductions in concurrency resulted in large declines in HIV-1 prevalence. Scaling up circumcision in low-concurrency settings yields a greater relative benefit, but the absolute number of infections averted depends on both the circumcision coverage and baseline incidence. Epidemic extinction with this package will require substantial scale-up of MMC in low-concurrency settings. CONCLUSIONS: Dynamic sexual network structure should be considered in the design and targeting of MMC within combination HIV-1 prevention packages. Realistic levels of coverage for these packages within southern Africa could lead to a reduction of incidence to the low levels observed in western Africa, and possibly, epidemic extinction.