surrogate-index 0.1.1

Efficient-Influence-Function (EIF) utilities for surrogate-index causal inference.

surrogate-index

Introduction

This package provides an implementation of the Surrogate Index Estimator introduced by Athey et al. (2016), a causal inference method for estimating long-term treatment effects using short-term randomized controlled trials (e.g., A/B tests).

The core idea is to combine a randomized experimental dataset with an external observational dataset to estimate the Average Treatment Effect (ATE) on a long-term outcome that is not directly observed in the experiment (e.g., annual revenue, long-term retention). This is particularly useful in settings where long-term metrics are delayed, costly, or infeasible to measure during the experiment window.

This package implements an estimator based on the Efficient Influence Function (EIF) derived by Chen & Ritzwoller (2023), leveraging the Double/Debiased Machine Learning (DML) framework of Chernozhukov et al. (2016). EIF-based estimators enable valid inference while incorporating flexible machine learning models for nuisance components, such as short-term outcome regressions and propensity scores, without compromising asymptotic efficiency or introducing first-order bias.

Brief Mathematical Background

Given the terms:

• $w\in\{0,1\}$: binary treatment indicator
• $s$: a vector of an arbitrary number of short-term outcomes (typically used as the "metrics of interest" in an A/B Test)
• $x$: a vector of pre-treatment covariates.
• $y$: long-term outcome
• $g$: binary indicator for if the user is in the observational sample ($g=1$) or the experimental sample ($g=0$)

the corresponding influence function for the ATE $\tau_0$ is as follows:

$$\xi_0(b,\tau_0,\varphi)=\frac{g}{1-\pi}\left[\frac{1-\gamma(s,x)}{\gamma(s,x)}\cdot\frac{(\varrho(s,x)-\varrho(x))(y-\nu(s,x))}{\varrho(x)(1-\varrho(x))}\right]+\frac{1-g}{1-\pi}\left[\frac{w(\nu(s,x)-\bar\nu_1(x))}{\varrho(x)}-\frac{(1-w)(\nu(s,x)-\bar\nu_0(x))}{1-\varrho(x)}+(\bar\nu_1(x)-\bar\nu_0(x))-\tau_0\right]$$

where:

• $\nu(s,x)=E[Y|S,X,G=1]$
• $\varrho(s,x)=P(W=1|S,X,G=0)$
• $\varrho(x)=P(W=1|X,G=0)$
• $\gamma(s,x)=P(G=1|S,X)$
• $\pi=P(G=1)$
• $\bar\nu_w(x)=E[\nu(S,X)|W=w, X,G=0]$

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Table of Contents

• Installation
• Usage
• Planned Features
• License

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Installation

# simplest
pip install surrogate-index

# with ML extras (e.g. XGBoost)
pip install "surrogate-index[ml]"

# Conda users
conda install -c conda-forge xgboost scikit-learn pandas numpy
pip install surrogate-index

Usage

from surrogate_index import efficient_influence_function

df_exp = ...  # experimental sample
df_obs = ...  # observational sample

results_df = efficient_influence_function(
    df_exp=df_exp,
    df_obs=df_obs,
    y="six_month_revenue",
    w="treatment",
    s_cols=[...],   # list of surrogate metrics
    x_cols=[...],   # list of covariate names
    classifier=..., # e.g., GradientBoostingClassifier()
    regressor=...,  # e.g., XGBRegressor()
)
print(results_df)

Planned Features

• Convert structure to an Object-based one (scikit-learn style)
• Add diagnostic checks
• Add alternative estimators provided in Athey et al. 2016
• etc.

License

Distributed under the MIT License. See LICENSE for details.