  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.
