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## 4 Extended Simulation Results 

In this section, we present an expanded set of results from Section 4 of the main paper. Specifically, we provide tables for the exposure effect size, bias, estimated and robust standard errors, reduction in RMSE, statistical power, and statistical coverage. 

For r = 1 , ..., R trials, we compute the augmented GEE estimates of exposure effect size ̂ β$_{r}$ and estimate standard deviation ̂ sd$_{r}$ ($_{̂}$ β$_{r}$ ) . After calculating β as detailed in the paper, we obtain the estimated empirical bias and empirical variance of the exposure effect estimate, where 

<img src='content_image/303195.jpg'>

To combine the amount of bias and size of the standard error in a single composite measure, we compute the root mean squared error for each trial, defined as: 

<img src='content_image/303194.jpg'>

Our metric for the gained improvement by the augmentation term is the percent reduction in RMSE for each adjustment covariate set, comparing the augmentation adjustment ̂ RMSE$_{adj}$ to that of the unadjusted GEE ( ̂ RMSE$_{GEE}$: 

<img src='content_image/303193.jpg'>

Statistical coverage is the probability that the estimated confidence intervals cover the true exposure effect, which must be 95% or greater for valid inference: 

<img src='content_image/303192.jpg'>

Finally, in our setting with the null hypothesis β = 0 , power is the probability that the confidence interval is significantly different from zero given that the exposure effect is not zero: 

The average values for these estimands are given in the main paper. T 

<img src='content_image/303191.jpg'>

