Department of Statistics, The University of Auckland, Auckland, New Zealand.
Department of Community Health, Institute of Tropical Pathology and Public Health, Federal University of Goiás (UFG), Goiás, Brazil.
PLoS One. 2019 Mar 6;14(3):e0212401. doi: 10.1371/journal.pone.0212401. eCollection 2019.
Multi-stage/level sampling designs have been widely used by survey statisticians as a means of obtaining reliable and efficient estimates at a reasonable implementation cost. This method has been particularly useful in National country-wide surveys to assess the costs of delivering public health programs, which are generally originated in different levels of service management and delivery. Unbiased and efficient estimates of costs are essential to adequately allocate resources and inform policy and planning. In recent years, the global health community has become increasingly interested in estimating the costs of immunization programs. In such programs, part of the cost correspond to vaccines and it is in most countries procured at the central level, while the rest of the costs are incurred in states, municipalities and health facilities, respectively. As such, total program cost is a result of adding these costs, and its variance should account for the relation between the totals at the different levels. An additional challenge is the missing information at the various levels. A variety of methods have been developed to compensate for this missing data. Weighting adjustments are often used to make the estimates consistent with readily-available information. For estimation of total program costs this implies adjusting the estimates at each level to comply with the characteristics of the country. In 2014, A National study to estimate the costs of the Brazilian National Immunization Program was initiated, requested by the Ministry of Health and with the support of international partners. We formulate a quick and useful way to compute the variance and deal with missing values at the various levels. Our approach involves calibrating the weights at each level using additional readily-available information such as the total number of doses administered. Taking the Brazilian immunization costing study as an example, this approach results in substantial gains in both efficiency and precision of the cost estimate.
多阶段/多层次抽样设计已被调查统计学家广泛应用于以合理的实施成本获得可靠和有效的估计。这种方法在全国范围内的调查中特别有用，用于评估公共卫生计划的成本，这些计划通常源自不同层次的服务管理和提供。无偏且有效的成本估计对于充分分配资源以及为政策和规划提供信息至关重要。近年来，全球卫生界越来越有兴趣估计免疫规划的成本。在这些规划中，部分成本与疫苗有关，在大多数国家都是在中央一级采购的，而其余的成本则分别由州、市和卫生机构承担。因此，总规划成本是这些成本相加的结果，其方差应考虑到不同层次之间的关系。一个额外的挑战是各级的缺失信息。已经开发了多种方法来弥补这些缺失数据。权重调整通常用于使估计与现成信息一致。对于总规划成本的估计，这意味着要调整每个级别的估计值，以符合国家的特点。2014 年，应卫生部的要求，并在国际伙伴的支持下，启动了一项估计巴西国家免疫规划成本的国家研究。我们提出了一种快速而有用的方法来计算方差并处理各级别的缺失值。我们的方法涉及使用额外的现成信息（如接种的总剂量数）来校准每个级别的权重。以巴西免疫成本研究为例，这种方法在成本估计的效率和精度方面都有了显著提高。
