Design-based Causal Inference for Incomplete Block Designs

TL;DR

This paper develops novel design-based inference methods for incomplete block designs, enabling effective treatment comparisons without reducing treatment arms, supported by theoretical properties, simulations, and data analysis.

Contribution

It introduces new inference results and estimators for incomplete block designs within a finite-population framework, expanding practical options for treatment assignment.

Findings

Derived properties of two design-based estimators

Developed a finite-population central limit theorem

Demonstrated estimator performance through simulations and data

Abstract

Researchers often turn to block randomization to increase the precision of their inference or due to practical considerations, such as in multisite trials. However, if the number of treatments under consideration is large it might not be feasible or practical 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. This includes deriving the properties of two design-based estimators, developing a finite-population central limit theorem, and proposing conservative variance estimators. Comparisons of the design-based estimators are made to linear model-based estimators. Simulations and a data illustration further demonstrate performance of IBD estimators. This work highlights IBDs as practical and currently underutilized designs.