In an observational study, obtaining unbiased estimates of an exposure effect requires adjusting for all potential confounders. When this condition is met, leveraging additional covariates related to the outcome may produce less variable estimates of the effect of exposure. For contagion processes operating on a contact network, transmission can only occur through ties that connect exposed and unexposed individuals; the outcome of such a process is known to depend intimately on the structure of the network. In this paper, we investigate the use of contact network features as both confounders and efficiency covariates in exposure effect estimation. Using doubly-robust augmented generalized estimating equations (GEE), we estimate how gains in efficiency depend on the network structure and spread of the contagious agent or behavior. We apply this approach to estimate the effects of two distinct exposures, the proportion of leaders in a village and the proportion of households participating in a self-help program, for the spread of a microfinance program in a collection of villages in Karnataka, India. We compare these results to simulated observational trials using a stochastic compartmental contagion model on a collection of model-based contact networks and compare the bias and variance of the estimated exposure effects using an assortment of network covariate adjustment strategies.
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