Cluster randomized trials (CRTs) are a popular design to study the effect of interventions in infectious disease settings. However, standard analysis of CRTs primarily relies on strong parametric methods, usually mixed-effect models to account for the clustering structure, and focuses on the overall intent-to-treat (ITT) effect to evaluate effectiveness. The article presents two assumption-lean methods to analyze two types of effects in CRTs, ITT effects and network effects among well-known compliance groups. For the ITT effects, we study the overall and the heterogeneous ITT effects among the observed covariates where we do not impose parametric models or asymptotic restrictions on cluster size. For the network effects among compliance groups, we propose a new bound-based method that uses pretreatment covariates, classification algorithms, and a linear program to obtain sharp bounds. A key feature of our method is that the bounds can become narrower as the classification algorithm improves and the method may also be useful for studies of partial identification with instrumental variables. We conclude by reanalyzing a CRT studying the effect of face masks and hand sanitizers on transmission of 2008 interpandemic influenza in Hong Kong.

Fetal sex prognostication has been a common practice in many human societies, yet most of the prognosticative methods do not perform better than chance. Why do these ineffective prognostication practices recur across societies and persist for long periods of time? In this article, we use historical texts of four different genres in traditional China (oracle bone inscriptions, dynastic history, encyclopedia, and local gazetteers) to examine the social and cognitive factors that lead to the overestimation of the predictive accuracy of sex prognostication and place fetal sex prognostication into a more general framework to understand the persistence of ineffective cultural practices. In particular, we present a detailed historical analysis showing that individuals often entertain considerable uncertainty regarding the accuracy of sex prognostication and quantitative data demonstrating a significant bias toward selectively reporting successes in (fictionalized) historical texts. We conclude by discussing how such reporting bias combined with humans’ imperfect information processing may help explain the persistence of ineffective technologies, such as divination, and magic in general.