{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Heterogenous Effect Mixture Model (HEMM) Demo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Contents\n", "\n", "### 1. [Introduction](#Introduction) \n", "#### 1.1 [Subgroup Discovery and Heterogenous Treatment Effect Problem](#introsgdisc)\n", "#### 1.2 [HEMM Description and Plate Notation](#introhemm)\n", "\n", " \n", "### 2. [Synthetic Data Example](#syndata)\n", "\n", "\n", "#### 2.1 [Data Description and Generative Process](#syndatagen)\n", "\n", "#### 2.2 [Estimation of Counterfactual Outcomes, PEHE Estimation](#syndatapehe)\n", "\n", "#### 2.3 [Subgroup Discovery](#syndatasg)\n", "\n", "#### 2.4 [Bootstrapping PEHE Estimates](#syndatabs)\n", "\n", "\n", "### 3. [IHDP Data Example](#IHDPdata)\n", "\n", "#### 3.1 [Data Description](#IHDPdatadesc)\n", "\n", "#### 3.1 Estimation of Counterfactual Outcomes, PEHE Estimation\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## 1. Introduction\n", "\n", "In a large number of decision problems, estimating Heterogenous Outcomes to a treatment is not sufficient from a decision making perspective. A Neural Network might be able to approximate the Outcome and Corresponding Counterfactuals well, but deployment for real world decision making would be limited by lack of transparency and exaplinability of the Neural Model. \n", "The Heterogenous Effect Mixture Model approach was originally proposed in the paper\n", "[\"***Interpretable Subgroup Discovery in Treatment Effect Estimation with Application to Opioid Prescribing Guidelines***\"](https://arxiv.org/abs/1905.03297) in order to mitigate this challenge and allow decision makers more insight. \n", "\n", "\n", "### 1.1 Subgroup Discovery and Heterogenous Treatment Effect Problem\n", "\n", "\n", "The idea behind HEMM is involves assuming a low dimensional clustering or a latent $\\mathcal{Z}$ for each individual in the dataset. An intuitive visual example of the following phenomenon is below in **Figure A**. Notice that, almost all instances receiving treatment in $\\mathcal{Z}_1$ have a positive outcome, while very few in $\\mathcal{Z}_3$ do. We are interested in recovering such latent subgroups. \n", " \n", "\n", "
Fig A. Example of the Heterogenous Effect Subgroup ProblemFig B. The HEMM Model in Plate Notation |