Design a free-month experiment

An online subscription product is considering a promotion that gives eligible new users their first month free instead of charging immediately.

Design an experiment and an analysis plan to estimate the causal impact of the promotion. Your answer should address:

• the randomization unit and experiment setup;
• the primary decision metric and why simple metrics such as signup rate or retention among signups are not sufficient on their own;
• secondary funnel and guardrail metrics;
• how to measure short-term and long-term impact when the free month changes both the signup composition and the timing of revenue;
• how to estimate ROI when the first month is free and some downstream data are missing or only partially observed;
• key pitfalls such as conditioning on post-treatment variables, selection bias, delayed conversion, seasonality, cannibalization, heterogeneous treatment effects, and repeat churn/reactivation;
• what assumptions or sensitivity analyses you would use if the dataset is limited;
• how you would present the recommendation to a non-technical stakeholder.

You may assume the company can run a randomized controlled experiment on eligible users, but the dataset available to you is imperfect and does not contain every field you would ideally want.