In cluster randomized trials (CRTs) of interventions against malaria, mosquito movement between households ultimately leads to contamination between intervention and control arms, unless they are separated by wide buffer zones. This paper proposes a method for adjusting estimates of intervention effectiveness for contamination and for estimating a contamination range between intervention arms, the distance over which contamination measurably biases the estimate of effectiveness. A sigmoid function is fitted to malaria prevalence or incidence data as a function of the distance of households to the intervention boundary, stratified by intervention status and including a random effect for the clustering. The method is evaluated in a simulation study, corresponding to a range of rural settings with varying intervention effectiveness and contamination range, and applied to a CRT of insecticide treated nets in Ghana. The simulations indicate that the method leads to approximately unbiased estimates of effectiveness. Precision decreases with increasing mosquito movement, but the contamination range is much smaller than the maximum distance traveled by mosquitoes. For the method to provide precise and approximately unbiased estimates, at least 50% of the households should be at distances greater than the estimated contamination range from the discordant intervention arm. A sigmoid approach provides an appropriate analysis for a CRT in the presence of contamination. Outcome data from boundary zones should not be discarded but used to provide estimates of the contamination range. This gives an alternative to “fried egg” designs, which use large clusters (increasing costs) and exclude buffer zones to avoid bias.

中文翻译：

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疟疾干预整群随机试验中的污染分析

在针对疟疾的干预措施的集群随机试验 (CRT) 中，家庭之间的蚊子移动最终会导致干预措施和控制措施之间的污染，除非它们被宽阔的缓冲区隔开。本文提出了一种方法，用于调整污染干预有效性的估计值和估计干预组之间的污染范围，即污染对有效性估计的可测量偏差的距离。Sigmoid 函数拟合疟疾流行率或发病率数据，作为家庭到干预边界距离的函数，按干预状态分层，并包括聚类的随机效应。该方法在模拟研究中得到评估，对应于具有不同干预效果和污染范围的一系列农村环境，并应用于加纳的杀虫剂处理过的蚊帐的 CRT。模拟表明该方法导致对有效性的近似无偏估计。精度随着蚊子移动的增加而降低，但污染范围远小于蚊子移动的最大距离。对于提供精确且近似无偏估计的方法，至少 50% 的家庭应与不协调干预组的估计污染范围保持距离。Sigmoid 方法为存在污染的 CRT 提供了适当的分析。来自边界区域的结果数据不应被丢弃，而应用于提供污染范围的估计。