We outline a way to deploy a privacy-preserving protocol for multiparty Randomized Controlled Trials on the scale of 500 million rows of data and more than a billion gates. Randomized Controlled Trials (RCTs) are widely used to improve business and policy decisions. A Randomized Controlled Trial is a scientifically rigorous method to measure the effectiveness of a treatment. This is accomplished by randomly allocating subjects to two or more groups, treating them differently, and then comparing the outcomes across groups. In many scenarios, multiple parties hold different parts of the data for conducting and analyzing RCTs. Given privacy requirements and expectations of each of these parties, it is often challenging to have a centralized store of data to conduct and analyze RCTs.
We accomplish this by a three-stage solution. The first stage uses the Private Secret Share Set Intersection (PS3 I)  solution to create a joined set and establish secret shares without revealing membership, while discarding individuals who were placed into more than one group. The second stage runs multiple instances of a general purpose MPC over a sharded database to aggregate statistics about each experimental group while discarding individuals who took an action before they received treatment. The third stage adds distributed and calibrated Differential Privacy (DP) noise to the aggregate statistics and uncertainty measures, providing formal two-sided privacy guarantees.
We also evaluate the performance of multiple open source general purpose MPC libraries for this task. We additionally demonstrate how we have used this to create a working ads effectiveness measurement product capable of measuring hundreds of millions of individuals per experiment.