Efficient Multi-Cohort Inference for Long-Term Effects and Lifetime Value in A/B Testing with User Learning

TL;DR

This paper presents a new method for estimating long-term effects and lifetime value in A/B testing, addressing the challenge of user churn and limited experimental horizons on streaming platforms.

Contribution

The authors introduce an efficient multi-cohort inference framework that combines cohort estimates to accurately assess long-term treatment effects and residual lifetime value.

Findings

Improved precision in estimating long-term treatment effects and residual lifetime value.

Identification of scenarios where short-term or long-term metrics alone can mislead decisions.

A parametric decay model captures the asymptotic treatment effect and cumulative value over time.

Abstract

In streaming platforms churn is extremely costly, yet A/B tests are typically evaluated using outcomes observed within a limited experimental horizon. Even when both short- and predicted long-term engagement metrics are considered, they may fail to capture how a treatment affects users' retention. Consequently, an intervention may appear beneficial in the short term and neutral in the long term while still generating lower total value than the control due to users churn. To address this limitation, we introduce a method that estimates long-term treatment effects (LTE) and residual lifetime value change ($\Delta ERLV$) in short multi-cohort A/B tests under user learning. To estimate time-varying treatment effects efficiently, we introduce an inverse-variance weighted estimator that combines multiple cohorts estimates, reducing variance relative to standard approaches in the literature. The estimated treatment trajectory is then modeled as a parametric decay to recover both the asymptotic treatment effect and the cumulative value generated over time. Our framework enables simultaneous evaluation of steady-state impact and residual user value within a single experiment. Empirical results show improved precision in estimating LTE and $\Delta ERLV$ and identify scenarios in which relying on either short-term or long-term metrics alone would lead to incorrect product decisions.