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Inspection-guided Randomization: A Transparent and Flexible Restricted Randomization Framework for Better Experimental Design

When designing a randomized experiment, some treatment allocations are better than others for answering the causal question we want to answer, i.e. will lead to less biased, more precise treatment effect estimates. For example, allocations that are balanced on outcome-prognostic covariates will increase the precision of a difference-in-means estimator. Restricted randomization can be used to filter out undesirable treatment allocations that will likely generate poor effect estimates; that is, by restricting the randomization, undesirable allocations cannot possibly be chosen as the official deployed allocation for the experiment. Traditionally, restricted randomization is applied to two-arm experiments and focuses on covariate balance as the metric by which to assess the desirability of a candidate treatment allocation.

Inspection-guided Randomization (IGR) is a restricted randomization framework that filters out undesirable treatment assignments by inspecting assignments against analyst-specified, domain-informed design desiderata. In IGR, the space of acceptable randomization allocations is “locked in” ex ante and is pre-registered, thus promoting transparency and reproducibility and safeguarding against statistical “hacking” in the analysis phase of the experiment. We break IGR down into the following steps:

  1. Specification of the design desiderata, which are targeted by (i) inspection metrics, (ii) a fitness function that aggregates the inspection metrics, and (iii) a restriction rule that determines whether an allocation is filtered out on the basis of its fitness function score.
  2. Enumeration of a candidate pool of allocations.
  3. Restriction of the pool of allocations to those that meet the criteria
  4. Evaluation & Adaptation of the specified inspection metrics, fitness function, and restriction rule, if needed.
  5. Pre-registration of the restricted assignment mechanism.
  6. Randomization of the allocation drawn for the official experiment

This repository contains simulation code for three illustrative vignettes that highlight the utility of IGR in distinct experimental settings: multi-arm experiments, group formation experiments, and experiments with interference.

Setup

Installation
To clone this repository, run the following

git clone https://github.com/wangmagg/igr.git
cd igr

Python dependencies
Python dependencies are specified in env/requirements.txt. To set up and activate a Conda environment with the requisite dependicies, run the following

conda env create -f env/environment.yml
conda activate igr-env

File Structure

.
├── scripts                 # Bash scripts for running simulations with different parameter settings
├── src                     
  ├── R                     # Contains Rscript for threshold blocking
  ├── aesthetics.py         # Functions for figure aesthetics 
  ├── aggregators.py        # Functions for aggregating inspection metrics
  ├── estimators.py         # Functions for estimating treatment effects
  ├── igr_checks.py         # Functions for making Evaluation & Adaptation plots
  ├── igr_enhancements.py   # Functions for genetic algorithms and adding mirror allocations
  ├── igr.py                # Functions for IGR enumeration, restriction, and randomization
  ├── metrics.py            # Functions for inspection metrics
├── vignettes               
  ├── collate.py            # Functions for collating results
  ├── composition_figs.py   # Generates figures for Vignette 2 
  ├── composition.py        # Runs Vignette 2
  ├── data.py               # Functions for generating data for each of the vignettes
  ├── interference_figs.py  # Generates figures for Vignette 3
  ├── interference.py       # Runs Vignette 3
  ├── multarm_figs.py       # Generates figures for Vignette 1
  ├── multarm.py            # Runs Vignette 1
└── README.md

Usage

Running Vignettes

0. Multi-arm Experiments

In a multi-arm experiment, we simultaneously evaluate multiple interventions and make pairwise comparisons between arms to estimate treatment effects. A well-designed experiment in this setting has covariates balanced across all pairs of arms that will be compared in the analysis phase of the experiment. To use IGR, we construct and apply multi-arm balance inspection metrics.

Our multi-arm experiment simulation is modeled based on an educational intervention study conducted to test how different types of feedback on class assignments affect students’ grades. We examine the allocations that are accepted under a CBR design scheme and compare them with allocations accepted under a naive complete randomization design and under a threshold blocking design (Higgens et al, 2016).

For convenience, we provide bash scripts that run the experiment for multiple data replicates across several different parameter settings (number of arms, number of candidate allocations generated, number of allocations accepted):

bash scripts/multarm.sh

Running this script creates a res/0_multarm directory that stores results and figures.

1. Group Formation Experiments

In a group formation experiment, we randomize individuals into different groups of certain compositions. For example, a group may be the set of college freshmen assigned to the same dorm room, and composition may be the number of individuals in a room who were “high academic achievers” in high school. As in the multi-arm setting, we would like to make pairwise comparisons between groups of different compositions. A well-designed experiment in this setting has groups balanced on all observed covariates other than salient attributes that are used to define composition. To use IGR, we can apply multi-arm balance metrics, excluding the composition-related attributes, and an indicator metric for whether the desired group compositions are formed.

Our group formation experiment simulation is inspired by stereotype threat interventions that have shown heterogenous effects based on the gender composition of a group, where the magnitude and direction effect of the intervention can depend on the male-to-female ratio. We use a similar data-generating process to the one for the simulated multi-arm experiment.

For convenience, we provide bash scripts that run the experiment for multiple data replicates across several different parameter settings (number of individuals per arm, number of candidate allocations generated):

bash scripts/composition.sh

Running these scripts creates a res/vig1_composition directory that stores results and figures.

2. Experiments with Network Interference

Interference occurs when the treatment assigned to one individual affects the outcome of a different individual. A common target estimand in experiments with interference is the total treatment effect, or the difference in outcomes if everyone were to receive treatment compared to if everyone were to receive control. Failing to properly account for interference can make estimates of the total treatment effect both biased and imprecise. A well-designed experiment in this setting controls spillover while also maintaining inter-cluster balance on covariates. In the IGR design framework, we can apply fitness functions that combine interference-related metrics with balance metrics.

Our simulated experiment with interference is based on a trial of a sexual assault prevention intervention for adolescent girls conducted across schools in urban settlements in Kenya. During the intervention, the girls learned and practiced verbal and physical skills for resisting sexual assault. The trial was instead randomized on the school level, and, because the settlements were densely populated, it is likely that girls attending different schools interacted with one another. As a result, the skills learned by girls assigned to receive the intervention may have been passed on to girls assigned to the control arm.

For convenience, we provide bash scripts that run the experiment for multiple data replicates across several different parameter settings (number of individuals per arm, number of candidate allocations generated):

bash scripts/interference.sh 

Running these scripts creates a res/vig2_interference directory that stores results and figures.

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