In public health research, finite resources often require that decisions be made at the study design stage regarding which individuals to sample for detailed data collection. At the same time, when study units are naturally clustered, as patients are in clinics, it may be preferable to sample clusters rather than the study units, especially when the costs associated with travel between clusters are high. In this setting, aggregated data on the outcome and select covariates are sometimes routinely available through, for example, a country's Health Management Information System. If used wisely, this information can be used to guide decisions regarding which clusters to sample, and potentially obtain gains in efficiency over simple random sampling. In this article, we derive a series of formulas for optimal allocation of resources when a single-stage stratified cluster-based outcome-dependent sampling design is to be used and a marginal mean model is specified to answer the question of interest. Specifically, we consider two settings: (i) when a particular parameter in the mean model is of primary interest; and, (ii) when multiple parameters are of interest. We investigate the finite population performance of the optimal allocation framework through a comprehensive simulation study. Our results show that there are trade-offs that must be considered at the design stage: optimizing for one parameter yields efficiency gains over balanced and simple random sampling, while resulting in losses for the other parameters in the model. Optimizing for all parameters simultaneously yields smaller gains in efficiency, but mitigates the losses for the other parameters in the model.

中文翻译：

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基于分层聚类的结果依赖抽样设计中的最优分配

在公共卫生研究中，有限的资源通常需要在研究设计阶段就对哪些个体进行抽样以收集详细数据做出决定。同时，当研究单元自然聚集时，因为患者在诊所，最好对集群进行抽样而不是对研究单元进行抽样，特别是当与集群之间的旅行相关的成本很高时。在这种情况下，有时可以通过例如一个国家的健康管理信息系统获得关于结果和选择协变量的汇总数据。如果使用得当，此信息可用于指导有关要对哪些集群进行抽样的决策，并有可能比简单的随机抽样获得效率增益。在本文中，当要使用单阶段分层的基于集群的结果依赖抽样设计并指定边际均值模型来回答感兴趣的问题时，我们推导出了一系列资源优化分配公式。具体来说，我们考虑两种设置：（i）当平均模型中的特定参数是主要兴趣时；并且，（ii）当多个参数感兴趣时。我们通过全面的模拟研究研究了最优分配框架的有限人口性能。我们的结果表明，在设计阶段必须考虑权衡取舍：优化一个参数比平衡和简单的随机抽样产生效率增益，同时导致模型中其他参数的损失。同时优化所有参数会产生较小的效率增益，