4 Simulation In this section we describe simulation of a contagion process on a network in an observational study setting to estimate the effect of an intervention on that process. We use this simulation study to investigate the usefulness of our method to adjust for baseline confounding factors in order to reduce both bias and variance of estimates of effects of exposure. As before, we assume that individuals are nested within a collection of independent clusters, each with its own contact network structure, and that the outcome of interest arises from a contagion process propagating through network ties. We also assume that the intervention will reduce the rate of the contagion by varying amounts. We first describe the network generation and the contagious spreading processes as well as the effect of the exposure (or intervention) on the latter. We also describe the process by which individuals would be sampled for an observational study. To estimate the average exposure effect, we apply the doubly-robust augmented GEE described above and compare results to a standard GEE and the effect of the simulation conditions on them. The structure of our simulation is very general and could apply to many settings, including that of the microfinance intervention study. It can also apply to observational studies of interventions, such as vaccines for control of infectious diseases. Among the settings that we consider is one that closely matches the characteristics of the microfinance study. At the end of this section, we describe the simulation results for this specific setting. The network generation model in our simulation study is the degree-corrected stochastic block model with degree correlation. Because of the complexity of this model, it is not possible to analytically obtain an estimate of the improvement in efficiency resulting from incorporation of network information in analyses. The original stochastic block model 13 assumes that, in a given network, each node j belongs to only one block b$_{j}$ in a partition of nodes B = { 1 , ..., B } ; the set of node memberships is given by the vector b = { b$_{1}$, ..., b$_{n}$ } . In this model, the probability of an edge between nodes j and j ′ depends only on their block membership P ( e$_{jj}$ ′ = 1) = p$_{b}$$_{j}$$_{b}$$_{j}$$_{′}$ . An extension of this model, the so-called degree-corrected stochastic block model , allows each node j to have arbitrary expected degree θ$_{j}$ :=$_{E}$( k$_{j}$ ) , where k$_{j}$ is the observed degree ∑ j $_{′}$e$_{jj}$ ′ for node j $^{14}$. The likelihood associated with this model assumes that the mean number of edges ν$_{jj}$ ′ between any two nodes j and j ′ is the product of the expected degrees of nodes j and j ′ ( θ$_{j}$ and θ$_{j}$ ′ , respectively), multiplied by the expected amount of mixing Simulated Contact Networks 8