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## Estimation Performance Metrics 

In principle, our doubly-robust approach to estimation should remove bias as well as reduce variance in the estimation of β$_{A}$ . Based on the simulation specifications, we define estimation metrics for the average exposure effect β$_{A}$ . For r = 1 , ..., R replicates, the estimate of exposure effect is denoted ̂ β$_{r}$ and the estimated standard deviation ̂ sd ($_{̂}$ β$_{r}$ ) . These standard deviation estimates are compared with the empirical bootstrap estimates evaluated as the standard deviations of all the estimates ̂ β$_{r}$ in the R replicates. Empirical power and coverage are derived from these simulation study point estimates and confidence intervals. Although the contagious spreading rates in unexposed and exposed groups are specified as p$_{0}$ and p$_{1}$ , the true value for the average exposure effect must be determined through simulation$^{20}$. Because the doubly-robust GEE yields consistent exposure effect estimates 21 under appropriate assumptions, the true value for β ∗ is estimated as the average of all exposure effect estimates calculated with correctly specified models (known in simulation), β ∗ A := 1 R ∑ R r =1 ̂ β $^{∗}$$_{r}$. We define improvement in estimation efficiency as the percent reduction in root mean squared error (RMSE) for each covariate set in the outcome model, comparing the augmentation adjustment ̂ RMSE$_{adj}$ to that of the unadjusted GEE ( ̂ RMSE$_{GEE}$): 

## Sensitivity Analysis 

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To estimate the sensitivity of estimation performance on simulation features, we vary six aspects of the simulation in two ways each: mean degree (values 2 and 10), degree distribution (Poisson or power law distribution), assortativity (values -0.3 and 0.3), block mixing structure (random or heterogenous), infectivity (unit or degree), and infection prevalence at baseline (values (S,B) are low (1,2)% or high (10, 25)%). It leads to a total of 2 6 = 64 scenarios. 

