Specifically, we derive a bias-adjusted estimation procedure constructed from a condi- tional inference principle via relevant ancillary statistics from the observed covariates. This estimator is shown to be asymptotically equivalent to an augmentation estimator under the conditional setting. We utilize the data from a clinical trial for evaluating a combination treatment of cardiovascular diseases to illustrate our findings.

]]>**Methods**: We consider cluster randomized trials with staggered enrollment, in each of which the order of enrollment is based on the total number of ties (contacts) from individuals within a cluster to individuals in other clusters. These designs can accommodate connectivity based either on the total number of inter-cluster connections at baseline or on connections only to untreated clusters, and include options analogous both to traditional Parallel and Stepped Wedge designs. We further allow for control clusters to be “held-back” from re-randomization for some period. We investigate the performance of these designs in terms of epidemic control (time to end of epidemic and cumulative incidence) and power to detect vaccine effect by simulating vaccination trials during an SEIR-type epidemic outbreak using a network-structured agent-based model.

**Results**: In our simulations, connectivity-informed designs lead to lower peak infectiousness than comparable traditional study designs and a 20% reduction in cumulative incidence, but have little impact on epidemic length. Power to detect differences in incidence across clusters is reduced in all connectivity-informed designs. However the inclusion of even a brief “holdback” restores most of the power lost in comparison to a traditional Stepped Wedge approach.

**Conclusions**: Incorporating information about cluster connectivity in design of cluster randomized trials can increase their public health impact, especially in acute outbreak settings. Using this information helps control outbreaks – by minimizing the number of cross-cluster infections – with modest cost in power to detect an effective intervention.