Bridging Statistical Inference and Mechanistic Network Models for HIV/AIDS

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Network models are used to investigate the spread of HIV/AIDS, but rather than assuming that the members of a population of interest are fully mixed, the network approach enables individual-level specification of contact patterns by considering the structure of connections among the members of the population. By representing individuals as nodes and contacts between pairs of individuals as edges, this network depiction enables identification of individuals who drive the epidemic, allows for accurate assessment of study power in cluster- randomized trials, and makes it possible to evaluate the impact of interventions on the individuals themselves, their partners, and the broader network. There are currently two major mathematical paradigms to the modeling of networks: the statistical approach and the mechanistic approach. In the statistical approach, one specifies a model that states the likelihood of observing a given network, whereas in the mechanistic approach one specifies a set of domain-specific mechanistic rules at the level of individual nodes, the actors in the network, that are used to evolve the network over time. Given that mechanistic models directly model individual-level behaviors – modification of which is the foundation of most prevention measures – they are a natural fit for infectious diseases. Another attractive feature of mechanistic models is their scalability as they can be implemented for networks consisting of thousands or even millions of nodes, making it possible to simulate population-wide implementation of interventions. Lack of statistical methods for calibrating these models to empirical data has however impeded their use in real-world settings, a limitation that stems from the fact that there are typically no closed-form likelihood functions available for these models due the exponential increase in the number of ways, as a function of network size, of arriving at a given observed network. We propose to overcome this gap by advancing inferential and model selection methods for mechanistic network models, and by developing a framework for investigating their similarities with statistical network models. We base our approach on approximate Bayesian computation (ABC), a family of methods developed specifically for settings where likelihood functions are intractable or unavailable. Our specific aims are the following. Aim 1: To develop a statistically principled framework for estimating parameter values and their uncertainty for mechanistic network models. Aim 2: To develop a statistically principled method for model choice between two competing mechanistic network models and estimating the uncertainty surrounding this choice. Aim 3: To establish a framework for mapping mechanistic network models to statistical models. We also propose to implement these methods in open source software, using a combination of Python and C/C++, to facilitate their dissemination and adoption. We believe that the research proposed here can help harness mechanistic network models – and with that leverage some of the insights developed in the network science community over the past decade and more – to help eradicate this disease.