Figure 3.

Similarity of federated and central estimation for the DR estimate with not-yet-treated individuals as the control group

(A) Simulation setup. The federated setup involved 6 servers. Three servers had 134 (536) individuals (observations), and three had 133 (532) individuals (observations). Individuals were either never treated or treated in period two or three, with all observations of an individual on one server.

(B) Equality of central and federated point estimates. The x axis shows central (non-federated) estimates,¹⁴ while the y axis shows federated estimates. The 45° line indicates equal results when aligned.

(C) Equality of central and federated asymptotic standard errors. The x axis shows central asymptotic standard errors, and the y axis shows federated standard errors. The 45° line is shown for reference.

(D) Comparison of bootstrapped standard errors. Percentiles of the distribution function compare the distribution of federated (blue) and central (green) bootstrapped standard errors. Two central learning distributions establish reference differences, with 500 bootstrapped standard errors analyzed.

(E) Treatment effect estimates. Point estimates (dots) and 95% confidence intervals for post-treatment periods are shown. Federated package estimates are in blue; estimates from one server are in green. This figure has been designed using resources from Flaticon.com.