Sexual partnership durations over the life-course in network models for epidemics: insights from survival analysis and a new strategy from STERGMs

Emily Pollock, Steven Goodreau, Martina Morris


The duration of sexual relationships across a population generates the network structure that is largely responsible for either exposing individuals to or protecting individuals from sexually transmitted infections (STIs). In particular, relationship durations relative to the pathogen-specific duration of infection are an important driver of how quickly STIs can spread throughout a population. Moreover, when partnerships overlap, transmission pathways increase even among those individuals with few lifetime partners, and this effect is even greater when the duration of overlap is large. The distribution of relationship durations across the life-course is also important because STIs often have distinct age patterns in terms of prevalence. Numerous dynamic network models, including Separable Temporal Exponential Random Graph Models (STERGMs), have been developed to understand the influence of heterogeneity in sexual behavior on transmission patterns of these infections. However, while faithfully representing the duration of partnerships is a central objective of temporal network dynamics, for convenience these models often rely on a simplifying assumption that relationship dissolution is governed by a constant hazard. While recent models have begun to address this simplification by modeling marriages and cohabitations separately from casual partnerships, this approach is still unlikely to approximate the full distribution accurately, especially as one considers variation in relational duration over the life-course. In this study, we first use empirical data from the USA’s National Survey of Family Growth (NSFG) and tools from survival analysis to investigate the limitations of assuming an exponential distribution of relationship durations both at the population level and amongst age groups. We then take a step back from the exploratory analyses and return to first principles, considering relationship formation and dissolution from a life-course and systems-based perspective. We use this to generate a dynamic network simulation using the EpiModel API that explicitly encompasses many of the processes that generate observed relationship durations over the life-course. Individuals enter and exit the population at specific boundary ages but can also exit due to a background age-specific mortality rate. Partner selection is influenced by the age of a potential partner relative to one’s own (age mixing). The rate at which individuals form relationships over time is influenced by their age, but it is also influenced by the number of relationships they are currently in. Crucially, relationships are not automatically labeled as a marriage, cohabitation, or causal, but instead transition between states over time. To encompass this feature, we propose a new STERGM framework to simulate relationships and sample over time given these rules. We compare sampled relationships from this scenario to a scenario based on the current standard practice (modeling marriages/cohabitations and casual relationships on separate networks) and finally we compare results from both scenarios to the empirical distribution of relationship lengths by age in the NSFG. We expect that these advances in model framework will prove to be a more reasonable approximation of the distribution of relationship lengths across the life-course, and in turn improve our understanding of STI transmission in future epidemic models.

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