We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity, and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal strategy is to have three group sizes with unequal frequencies. Based on a Chlamydia study in the United States, we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator. We demonstrate that the proposed locally D- and Ds -optimal designs have high efficiencies even when the prespecified values of the parameters are moderately misspecified.

中文翻译：

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最佳的小组测试设计，用于估计具有不确定测试错误的患病率。

我们为小组测试实验构建了最佳设计，其目的是使用不确定性的敏感性和特异性的测试来估计性状的普遍性。使用针对近似设计的最佳设计理论，我们表明，要同时估算患病率，敏感性和特异性的最有效设计，需要三个相同频率的不同群体规模。但是，如果唯一的重点是尽可能准确地估计患病率，则最佳策略是使三个小组人数的频率不相等。基于在美国的衣原体研究，我们比较了竞争设计的性能，并提供了洞察力，以了解未知的灵敏度和测试特异性如何影响患病率估算器的性能。