Open Access
June 2024 As treated analyses of cluster randomized trials
Ari I. F. Fogelson, Kirsten E. Landsiedel, Suzanne M. Dufault, Nicholas P. Jewell
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Ann. Appl. Stat. 18(2): 1506-1518 (June 2024). DOI: 10.1214/23-AOAS1846


Test-negative designs have rapidly become an appealing approach to assess disease interventions when randomization is not feasible and specifically used to measure the effectiveness of vaccines in the field (Vaccine 31 (2013) 2165–2168). An innovative extension of the test-negative design was recently used to assess the impact of a mosquito intervention where the intervention was applied at a cluster level with cluster assignment chosen at random, the AWED (applying Wolbachia to eliminate dengue) trial. The primary analysis reported was intention-to-treat (ITT) (Trials 19 (2018) 302; N. Engl. J. Med. 384 (2021) 2177–2186). However, the level of uptake of the intervention on mosquitoes was routinely captured in all clusters over time, and, furthermore, participants’ mobility across clusters was measured in the time immediately preceding the onset of symptoms (whether test-positive or test-negative). Combinations of these measurements provide proxies for the true exposure to the intervention, thereby permitting an “as treated” assessment. We consider the use of marginal generalized estimating equations (GEE) and conditional generalized inear mixed models (GLMM) to estimate as treated efficacy, contrasting both with the ITT. We illustrate the strengths and challenges of these methods in the context of the AWED trial, highlighting several ways that common approaches to analysis of clustered data can yield incorrect results that can in turn be obscured and compounded by limitations in routine software. In addition, we estimate a greater level of intervention efficacy than shown in the ITT analysis.

Funding Statement

The second, third, and final authors were supported by grant #R01-AI148127 from the National Institute for Allergy and Infectious Diseases.


We acknowledge with deep appreciation the contribution of all investigators in the AWED Study Group to the implementation of the trial and collection of trial data and to the Tahija Foundation as funders of the AWED trial.


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Ari I. F. Fogelson. Kirsten E. Landsiedel. Suzanne M. Dufault. Nicholas P. Jewell. "As treated analyses of cluster randomized trials." Ann. Appl. Stat. 18 (2) 1506 - 1518, June 2024.


Received: 1 January 2023; Revised: 1 September 2023; Published: June 2024
First available in Project Euclid: 5 April 2024

Digital Object Identifier: 10.1214/23-AOAS1846

Keywords: As treated , cluster randomized trial , dengue , GEE , GLMM , per-protocol , test-negative design , Wolbachia

Rights: Copyright © 2024 Institute of Mathematical Statistics

Vol.18 • No. 2 • June 2024
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