  In this paper, 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 in various sectors such as
healthcare, education, criminology, and marketing. 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 (PS$^3$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.
