Analysis of cluster-randomized test-negative designs: cluster-level methods

Abstract

Intervention trials of vector control methods often require community level randomization with appropriate inferential methods. For many interventions, the possibility of confounding due to the effects of health-care seeking behavior on disease ascertainment remains a concern. The test-negative design, a variant of the case-control method, was introduced to mitigate this issue in the assessment of the efficacy of influenza vaccination (measured at an individual level) on influenza infection. Here, we introduce a cluster-randomized test-negative design that includes randomization of the intervention at a group level. We propose several methods for estimation and inference regarding the relative risk (RR). The inferential methods considered are based on the randomization distribution induced by permuting intervention assignment across two sets of randomly selected clusters. The motivating example is a current study of the efficacy of randomized releases of Wolbachia-infected Aedes aegypti mosquitoes to reduce the incidence of dengue in Yogyakarta City, Indonesia. Estimation and inference techniques are assessed through a simulation study.

Cluster-Randomized Test-Negative Design Trials: A Novel and Efficient Method to Assess the Efficacy of Community-Level Dengue Interventions

“…Inference can be based on the permutation distribution that considers all possible cluster intervention assignments. An approximate version of this test uses an estimate of the variance of the estimated odds ratio that accounts for the clustering using simple finite-population sampling ideas (41). …”

“…The aggregate odds ratio provides a consistent estimate of the relative risk, albeit at a population-averaged, or marginal, level (41). (This is in contrast to a cluster-specific odds ratio that is, in general, further from the null than the marginal version—see Hayes and Moulton (3); the difference is not of practical concern with rare outcomes.)…”

“…(This is in contrast to a cluster-specific odds ratio that is, in general, further from the null than the marginal version—see Hayes and Moulton (3); the difference is not of practical concern with rare outcomes.) Confidence intervals can either be based on inverting the permutation test or estimated via the approximate variance formula (41). …”

“…At the null, the average of these proportions should be the same in both arms. For testing, the average of these proportions for the intervention clusters can then be compared with the same for control clusters via the t statistic, with inference based on a permutation test again, or on an approximate variance (41). …”

“…The difference in these average proportions of test-positives between intervention and control clusters yields an estimate of the relative risk given that we can substitute the estimated difference in the proportions, d , into the formula $d=\frac{1}{1+true(\frac{r}{2}true)false(1+RRfalse)}-\frac{RR}{RR+true(\frac{r}{2}true)false(1+RRfalse)}$, yielding a quadratic equation for RR. This yields an estimate of RR , along with an appropriately transformed confidence interval (from that for d ) (41). …”