Assumption-Lean Analysis of Cluster Randomized Trials in Infectious Diseases for Intent-to-Treat Effects and Spillover Effects Among A Vulnerable Subpopulation

Cluster randomized trials (CRTs) are a popular design to study the effect of interventions in infectious disease settings. However, standard analysis of CRTs primarily relies on strong parametric methods, usually a Normal mixed effect models to account for the clustering structure, and focus on the overall intent-to-treat (ITT) effect to evaluate effectiveness. The paper presents two methods to analyze two types of effects in CRTs, the overall and heterogeneous ITT effects and the spillover effect among never-takers who cannot or refuse to take the intervention. For the ITT effects, we make a modest extension of an existing method where we do not impose parametric models or asymptotic restrictions on cluster size. For the spillover effect among never-takers, we propose a new bound-based method that uses pre-treatment covariates, classification algorithms, and a linear program to obtain sharp bounds. A key feature of our method is that the bounds can become dramatically narrower as the classification algorithm improves and the method may also be useful for studies of partial identification with instrumental variables. We conclude by reanalyzing a CRT studying the effect of face masks and hand sanitizers on transmission of 2008 interpandemic influenza in Hong Kong.