LinkUp is a social app (≈12M DAUs) that grows primarily through friend referrals. The team wants to test a new referral incentive: when a user invites a friend, both get premium features for 7 days. The concern is interference: treating one user can change outcomes for their friends (e.g., treated inviters bring in more friends, and those friends may engage more because their inviter is active).
You run a 14-day experiment on the existing user base. The primary metric is whether an existing user is active at least once during the 14-day window (binary). Users are connected in an undirected friendship graph.
A naive user-level randomization (50/50) was initially considered, but you suspect it will bias the estimated treatment effect because of spillovers.
The graph has been partitioned into 400 disjoint clusters using a community detection algorithm (clusters are non-overlapping; edges across clusters are rare but not zero).
| Item | Value |
|---|---|
| Total existing users | 2,000,000 |
| Number of clusters | 400 |
| Mean cluster size | 5,000 |
| Median cluster size | 3,900 |
| Treatment assignment | 200 clusters treated, 200 control |
| Control users (sum over control clusters) | 1,012,400 |
| Treated users (sum over treated clusters) | 987,600 |
| Active users in control clusters | 202,480 |
| Active users in treated clusters | 212,334 |
| Cross-cluster edge rate (fraction of edges crossing clusters) | 2.5% |
| Significance level | 0.05 |
Design and analyze an experiment that accounts for network interference. Use the provided cluster-randomized results to estimate the effect of the new incentive, quantify uncertainty, and explain what assumptions are required for the estimate to be causal.