Statistical Methods for Sparse Network Data and Mechanistic Models of Infectious Disease: Latent Space and Likelihood-Free Inference

Abstract

Networks are central to the study of infectious disease: who interacts with whom, how social ties form and dissolve, and how those connections are distributed across a population shape whether and how a pathogen spreads. This is particularly true for sexually transmitted infections, where outbreak dynamics are driven by heterogeneous partnership patterns of close contact. Working with network data in the setting, however, presents a set of intertwined statistical challenges. Sexual contact networks tend to be sparse, with many isolated or low-degree nodes whose information standard models struggle to incorporate. The full structure of the network is rarely directly observable or fully captured; investigators typically only have partial, egocentric views observed via non-random snowball sampling. Yet, simulated mechanistic network models with realistic partnership dynamics have intractable likelihoods, complicating both estimation and uncertainty quantification. Finally, the latent structures that anchor many statistical network models must themselves be estimated, often alongside high-dimensional node attributes, creating error-in-variables problems that downstream inference frequently ignores. In this dissertation, we develop three methods that address these challenges through mechanistic model simulation, joint latent space modeling with covariate selection, and simulation-based conformal inference, with applications drawn from infectious disease epidemiology and network-based social science. In Chapter 1, we ask how the timing and intensity of public health interventions jointly shape the trajectory of an emerging sexually transmitted outbreak. Motivated by the 2022 mpox outbreak among gay, bisexual, and other men who have sex with men (GBMSM), we develop a dynamic agent-based network model with three partnership types (main, casual, and one-time) parameterized using empirical survey data on GBMSM partnership dynamics in the United States.[67,37] Simulating a broad range of vaccination and behavior-change scenarios, we find that both types of interventions reduce transmission, that earlier implementation has a disproportionately large effect, and that interventions targeted only at the highest-activity subset of the population can still substantially reduce cumulative infection. By tracking the source of every infection, we also show that main and casual partnerships drive early spread, while one-time partnerships connect otherwise disjoint parts of the network over time. In Chapter 2, we address the problem of fitting statistical network models to sparse networks when investigators have collected a large number of node covariates, only some of which are informative about the network's structure. Building on the joint latent space framework of Zhang et al.[70], in which the adjacency matrix of the network and node attributes are generated conditionally on shared latent positions, we propose a two-stage procedure that combines group-lasso screening with a measurement-error-aware ridge stabilization term to account for the fact that the latent positions used as predictors are themselves estimated with error. We establish prediction error rates for the covariate component when latent positions are treated as observed and when estimated with bounded error; under uniform control across $q$ covariates and $n$ nodes, the rate is order $O(\log q / n)$, with an additional term due to latent position estimation error. Simulations demonstrate stable predictive performance as covariate sparsity grows, while the performance of naive approaches degrades. Applied to household social networks from 75 Indian villages, our method screens a large covariate battery via an emulated pilot study, substantially reducing subsequent data collection by nearly 70% without sacrificing predictive accuracy. In Chapter 3, we develop a method for obtaining calibrated parameter estimates and prediction regions from egocentric snowball-sampled network data when the underlying mechanistic network model has an intractable likelihood. Classical moment and RDS-II estimators are unbiased for node-level prevalence estimands and rely on asymptotic uncertainty quantification that does not extend cleanly to network-structure parameters such as partnership-style mixing. We adapt the ABCD-Conformal framework of Baragatti et al.[9] to this setting by (i) using a graph neural network with DeepSets aggregation to produce permutation-invariant summaries of the unordered set of ego subgraphs, (ii) applying an additive log-ratio reparameterization to simplex-valued parameters so that split-conformal prediction regions remain valid in their natural geometry, and (iii) deriving closed-form expressions for expected snowball size and inter-sample collision rates in the configuration model of interest. Across 1,000 simulated test networks, the GNN-Conformal estimator achieves nominal 95% coverage for all parameters and yields the narrowest conformal intervals for 7 of 11 parameters, outperforming naive and RDS-II moment estimators, particularly for constrained simplex-valued parameters and the dispersion parameter of the long-tailed one-time partnership distribution. These three projects provide complementary tools for the study of disease transmission on sparse contact networks: a mechanistic simulation framework for evaluating interventions in emerging outbreaks, a covariate selection procedure for joint latent space models that respects sparsity and estimation error, and a simulation-based inference procedure with finite-sample coverage guarantees for egocentric network samples. Together, they work towards making the network structure of disease transmission more tractable statistically and computationally.