Design-based Causal Inference for Incomplete Block Designs

2024-05-29

AI Summary

In multi-treatment, multi-site trials, practical constraints often prevent full treatment implementation within each block, necessitating incomplete block designs (IBD/BIBD) without collapsing treatment levels. Method: We develop finite-population causal inference theory for IBD/BIBD that preserves the original number of treatments. Within the design-based inference framework, we rigorously establish unbiasedness and asymptotic normality of IBD/BIBD estimators, propose a model-robust, conservative variance estimator, and analytically characterize its precision trade-offs relative to complete block, cluster-randomized, and completely randomized designs. Results: Monte Carlo simulations and empirical analysis confirm that IBD achieves a favorable balance between practical feasibility and statistical efficiency while retaining all treatments. Our work delivers ready-to-use closed-form variance formulas and rigorous theoretical guarantees—filling a critical gap in causal inference for multi-treatment incomplete block designs.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Researchers often turn to block randomization to increase the precision of their inference or due to practical considerations, such as in multi-site trials. However, if the number of treatments under consideration is large it might not be practical or even feasible to assign all treatments within each block. We develop novel inference results under the finite-population design-based framework for natural alternatives to the complete block design that do not require reducing the number of treatment arms, the incomplete block design (IBD) and the balanced incomplete block design (BIBD). This includes deriving the properties of two estimators and proposing conservative variance estimators. To assist practitioners in understanding the trade-offs of using these designs, precision comparisons are made to standard estimators for the complete block, cluster-randomized, and completely randomized designs. Simulations and a data illustration further demonstrate the trade-offs. This work highlights IBDs as practical and currently underutilized designs.

Problem

• Developing causal inference for incomplete block designs
• Addressing feasibility issues with many treatment arms
• Comparing design-based and model-based estimators performance

Innovation

• Design-based inference for incomplete blocks
• Novel estimators and central limit theorem
• Conservative variance estimation methods