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In randomized experiments, treatment and control groups should be roughly the same—balanced—in their distributions of pretreatment variables. But how nearly so? Can descriptive comparisons meaningfully be paired with significance tests? If so, should there be several such tests, one for each pretreatment variable, or should there be a single, omnibus test? Could such a test be engineered to give easily computed p-values that are reliable in samples of moderate size, or would simulation be needed for reliable calibration? What new concerns are introduced by random assignment of clusters? Which tests of balance would be optimal? To address these questions, Fisher's randomization inference is applied to the question of balance. Its application suggests the reversal of published conclusions about two studies, one clinical and the other a field experiment in political participation.

A distinctive feature of a clustered observational study is its multilevel or nested data structure arising from the assignment of treatment, in a nonrandom manner, to groups or clusters of units or individuals. Examples are ubiquitous in the health and social sciences including patients in hospitals, employees in firms, and students in schools. What is the optimal matching strategy in a clustered observational study? At first thought, one might start by matching clusters of individuals and then, within matched clusters, continue by matching individuals. But as we discuss in this article, the optimal strategy is the opposite: in typical applications, where the intracluster correlation is not one, it is best to first match individuals and, once all possible combinations of matched individuals are known, then match clusters. In this article, we use dynamic and integer programming to implement this strategy and extend optimal matching methods to hierarchical and multilevel settings. Among other matched designs, our strategy can approximate a paired clustered randomized study by finding the largest sample of matched pairs of treated and control individuals within matched pairs of treated and control clusters that is balanced according to specifications given by the investigator. This strategy directly balances covariates both at the cluster and individual levels and does not require estimating the propensity score, although the propensity score can be balanced as an additional covariate. We illustrate our results with a case study of the comparative effectiveness of public versus private voucher schools in Chile, a question of intense policy debate in the country at the present.

Background Guidance exists to inform the content of statistical analysis plans in clinical trials. Though not explicitly stated, this guidance is generally focused on clinical trials in which the randomization units are individual patients and not groups of patients. There are critical considerations for the analysis of cluster randomized trials, such as accounting for clustering, the risk of imbalances between the arms due to post-randomization recruitment, and the need to use small sample corrections when the number of clusters is small. Methods This paper outlines the protocol for the development of a set of reporting guidelines for the content of statistical analysis plans for cluster randomized trials (including variations such as the stepped wedge cluster randomized trial and other cluster cross-over designs) by extending the minimum reporting analysis requirements as previously defined for individually randomized trials to cluster randomized trials. The guideline will be developed using a consensus-based approach, modifying existing reporting items from the guideline for individually randomized trials and extending to include new items. Discussion The guideline will be developed so it can be used independently of the guideline for individually randomized designs. The consensus guidelines will be published in an open-access journal, including key guidance as well as exploration and elaboration.

Clustered treatment assignment occurs when individuals are grouped into clusters prior to treatment and whole clusters, not individuals, are assigned to treatment or control. In randomized trials, clustered assignments may be required because the treatment must be applied to all children in a classroom, or to all patients at a clinic, or to all radio listeners in the same media market. The most common cluster randomized design pairs 2S clusters into S pairs based on similar pretreatment covariates, then picks one cluster in each pair at random for treatment, the other cluster being assigned to control. Typically, group randomization increases sampling variability and so is less efficient, less powerful, than randomization at the individual level, but it may be unavoidable when it is impractical to treat just a few people within each cluster. Related issues arise in nonrandomized, observational studies of treatment effects, but in this case one must examine the sensitivity of conclusions to bias from nonrandom selection of clusters for treatment. Although clustered assignment increases sampling variability in observational studies, as it does in randomized experiments, it also tends to decrease sensitivity to unmeasured biases, and as the number of cluster pairs increases the latter effect overtakes the former, dominating it when allowance is made for nontrivial biases in treatment assignment. Intuitively, a given magnitude of departure from random assignment can do more harm if it acts on individual students than if it is restricted to act on whole classes, because the bias is unable to pick the strongest individual students for treatment, and this is especially true if a serious effort is made to pair clusters that appeared similar prior to treatment. We examine this issue using an asymptotic measure, the design sensitivity, some inequalities that exploit convexity, simulation, and an application concerned with the flooding of villages in Bangladesh.

This paper presents the results of a European study investigating the extent to which the Dynamic Approach to School Improvement (DASI) can help schools situated in socially disadvantaged areas to improve their effectiveness. At the beginning of the school year 2015–2016, a sample of 72 primary schools in four European countries (Cyprus, England, Greece and Ireland) was randomly allocated into the experimental and control groups. A questionnaire measuring the functioning of school factors related with the school learning environment, school policy for teaching and school evaluation was administered to all teachers of the school sample (n = 762). A battery of mathematics tests and a questionnaire measuring students’ socioeconomic status (SES) were administered to all students of grades 4–6 of the school sample (n = 5560). The experimental group made use of DASI to develop improvement strategies and action plans. Feedback was provided to the control group regarding their students’ achievement and the functioning of school factors in their school. Ιn each country, DASI had an effect on promoting student learning outcomes. For the control group of each country, the total effect of SES on student achievement at the end of the intervention was bigger than the effect of SES at the beginning of the intervention. No increase in the effect of SES was identified in the schools of the experimental group. Implications of findings for establishing a theory-driven and evidence-based approach to improve the quality and the equity dimensions of school effectiveness are discussed and suggestions for future studies are provided.

Voter mobilization experiments are often conducted using individual-level randomization, which can be difficult to implement. A simpler approach is to randomly assign voting precincts, rather than individuals nested within them, to treatment and control groups. Not only is it easier and potentially less expensive to implement, it may allow researchers to study vote preference effects without collecting survey data. This article explores various methodological concerns that researchers should consider when designing and analyzing precinct-level experiments. These concerns are illustrated using data from a precinct-level randomized field experiment conducted in Kansas City, Missouri.

This paper investigates the impact of three different approaches to establishing School Self Evaluation (SSE) mechanisms upon student achievement. Using group randomisation, four groups of schools were created. Different types of support were provided to the first three groups of schools in order to help them establish SSE mechanisms, whereas no SSE mechanism was established in any of the schools of the fourth group. In the first group, school stakeholders were offered the opportunity to develop their own SSE mechanisms and design their own improvement strategies. The second group followed the same process in designing SSE mechanisms as the first, but before introducing this approach support was offered to the stakeholders in order to address and reduce their concerns about SSE. The third group was asked to develop SSE mechanisms and take decisions for their improvement strategies which were in line with the knowledge base of educational effectiveness research. All three experimental groups had better results than the control group, but the impact of the third approach on student achievement was higher than the impact of the other two approaches to SSE. Implications for research on SSE are drawn.

Trials which randomize intact social groups, or clusters, to different interventions are becoming increasingly widespread. Although statistically less efficient than trials which randomize individuals, such designs are often preferred from a practical or ethical point of view, particularly in the evaluation of health care or educational strategies. We discuss selected issues that arise in the conduct of such trials, including the choice of design, ethical implications, sample size estimation and approaches to the analysis. The discussion is closely tied to methodological issues that have arisen in a recent evaluation trial of a new antenatal care programme, as sponsored by the Special Programme of research, Development and Research Training in Human Reproduction of the World Health Organization.

In community‐intervention trials, communities, rather than individuals, are randomized to experimental arms. Generalized linear mixed models offer a flexible parametric framework for the evaluation of community‐intervention trials, incorporating both systematic and random variations at the community and individual levels. We propose here a simple two‐stage inference method for generalized linear mixed models, specifically tailored to the analysis of community‐intervention trials. In the first stage, community‐specific random effects are estimated from individual‐level data, adjusting for the effects of individual‐level covariates. This reduces the model approximately to a linear mixed model with the unit of analysis being community. Because the number of communities is typically small in community‐intervention studies, we apply the small‐sample inference method of Kenward and Roger (1997, Biometrics53, 983–997) to the linear mixed model of second stage. We show by simulation that, under typical settings of community‐intervention studies, the proposed approach improves the inference on the intervention‐effect parameter uniformly over both the linearized mixed‐effect approach and the adaptive Gaussian quadrature approach for generalized linear mixed models. This work is motivated by a series of large randomized trials that test community interventions for promoting cancer preventive lifestyles and behaviors.