Petito L C, Jewell N P
Division of Biostatistics, School of Public Health, 101 Haviland Hall, University of California, Berkeley, California 94720,
Biometrika. 2016 Dec;103(4):801-815. doi: 10.1093/biomet/asw043. Epub 2016 Dec 8.
Group testing, introduced by Dorfman (1943), has been used to reduce costs when estimating the prevalence of a binary characteristic based on a screening test of [Formula: see text] groups that include [Formula: see text] independent individuals in total. If the unknown prevalence is low and the screening test suffers from misclassification, it is also possible to obtain more precise prevalence estimates than those obtained from testing all [Formula: see text] samples separately (Tu et al., 1994). In some applications, the individual binary response corresponds to whether an underlying time-to-event variable [Formula: see text] is less than an observed screening time [Formula: see text], a data structure known as current status data. Given sufficient variation in the observed [Formula: see text] values, it is possible to estimate the distribution function [Formula: see text] of [Formula: see text] nonparametrically, at least at some points in its support, using the pool-adjacent-violators algorithm (Ayer et al., 1955). Here, we consider nonparametric estimation of [Formula: see text] based on group-tested current status data for groups of size [Formula: see text] where the group tests positive if and only if any individual's unobserved [Formula: see text] is less than the corresponding observed [Formula: see text]. We investigate the performance of the group-based estimator as compared to the individual test nonparametric maximum likelihood estimator, and show that the former can be more precise in the presence of misclassification for low values of [Formula: see text]. Potential applications include testing for the presence of various diseases in pooled samples where interest focuses on the age-at-incidence distribution rather than overall prevalence. We apply this estimator to the age-at-incidence curve for hepatitis C infection in a sample of U.S. women who gave birth to a child in 2014, where group assignment is done at random and based on maternal age. We discuss connections to other work in the literature, as well as potential extensions.
由多尔夫曼（1943年）提出的分组检测，已被用于在基于对总共包含(n)个独立个体的(m)组进行筛查测试来估计二元特征患病率时降低成本。如果未知患病率较低且筛查测试存在错误分类，那么与对所有(n)个样本分别进行检测相比，也有可能获得更精确的患病率估计值（涂等人，1994年）。在某些应用中，个体二元反应对应于潜在的事件发生时间变量(T)是否小于观察到的筛查时间(t)，这种数据结构被称为当前状态数据。给定观察到的(t)值有足够的变化，就有可能使用合并相邻违反者算法（艾耶等人，1955年）非参数地估计(T)的分布函数(F(t))，至少在其支撑集的某些点上可以做到。在这里，我们考虑基于大小为(k)的分组检测当前状态数据对(F(t))进行非参数估计，其中当且仅当任何个体未观察到的(T)小于相应观察到的(t)时，该组检测为阳性。我们研究了基于分组的估计器与个体测试非参数最大似然估计器相比的性能，并表明在存在错误分类且(t)值较低的情况下，前者可能更精确。潜在应用包括在合并样本中检测各种疾病的存在，其中关注点在于发病年龄分布而非总体患病率。我们将此估计器应用于2014年生育孩子的美国女性样本中丙型肝炎感染的发病年龄曲线，其中分组是随机进行的且基于产妇年龄。我们讨论了与文献中其他工作的联系以及潜在的扩展。
