Estimating the True Effect Size Distribution with SIMEX

Abstract

Large-scale online experimentation produces noisy effect estimates, which can overstate gains and complicate decisions about launches and testing policies. We propose a nonparametric method based on SIMulation-EXtrapolation (SIMEX) to estimate the latent distribution of true effects from estimated average treatment effects with known variances. The method evaluates quantiles after adding progressively more simulated measurement noise and extrapolates the resulting inverse cumulative distribution function to the zero-noise setting while enforcing monotonicity of the quantiles. In a synthetic example with normally distributed true effects and measurement error, the method recovers the underlying effect distribution and performs nearly as well as a parametric empirical Bayes normal means approach. This provides a flexible way to characterize effect-size distributions without fully specifying a parametric model.