Randomization Inference for Cluster-Randomized Test-Negative Designs with Application to Dengue Studies: Unbiased estimation, Partial compliance, and Stepped-wedge design

In 2019, the World Health Organization identified dengue as one of the top ten global health threats. For the control of dengue, the Applying Wolbachia to Eliminate Dengue (AWED) study group conducted a cluster-randomized trial in Yogyakarta, Indonesia, and used a novel design, called the cluster-randomized test-negative design (CR-TND). This design can yield valid statistical inference with data collected by a passive surveillance system and thus has the advantage of cost-efficiency compared to traditional cluster-randomized trials. We investigate the statistical assumptions and properties of CR-TND under a randomization inference framework, which is known to be robust and efficient for small-sample problems. We find that, when the differential healthcare-seeking behavior comparing intervention and control varies across clusters (in contrast to the setting of Dufault and Jewell, 2020 where the differential healthcare-seeking behavior is constant across clusters), current analysis methods for CR-TND can be biased and have inflated type I error. We propose the log-contrast estimator that can eliminate such bias and improve precision by adjusting for covariates. Furthermore, we extend our methods to handle partial intervention compliance and a stepped-wedge design, both of which appear frequently in cluster-randomized trials. Finally, we demonstrate our results by simulation studies and re-analysis of the AWED study.