An important problem in contemporary immunology studies based on single-cell protein expression data is to determine whether cellular expressions are remodeled postinfection by a pathogen. One natural approach for detecting such changes is to use nonparametric two-sample statistical tests. However, in single-cell studies direct application of these tests is often inadequate, because single-cell level expression data from processed uninfected populations often contain attributes of several latent subpopulations with highly heterogeneous characteristics. As a result, viruses often infect these different subpopulations at different rates, in which case the traditional nonparametric two-sample tests for checking similarity in distributions are no longer conservative. In this paper, we propose a new nonparametric method for Testing Remodeling under Heterogeneity (TRUH) that can accurately detect changes in the infected samples compared to possibly heterogeneous uninfected samples. Our testing framework is based on composite nulls and is designed to allow the null model to encompass the possibility that the infected samples, though unaltered by the virus, might be dominantly arising from underrepresented subpopulations in the baseline data. The TRUH statistic, which uses nearest neighbor projections of the infected samples into the baseline uninfected population, is calibrated using a novel bootstrap algorithm. We demonstrate the nonasymptotic performance of the test via simulation experiments and also derive the large sample limit of the test statistic which provides theoretical support toward consistent asymptotic calibration of the test. We use the TRUH statistic for studying remodeling in tonsillar T cells under different types of HIV infection and find that, unlike traditional tests which do not have any heterogeneity correction, TRUH based statistical inference conforms to the biologically validated immunological theories on HIV infection.

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基于最近邻的非参数测试用于异质单细胞蛋白质组学数据中的病毒重塑

基于单细胞蛋白质表达数据的当代免疫学研究中的一个重要问题是确定细胞表达是否在病原体感染后重塑。检测这种变化的一种自然方法是使用非参数的两样本统计检验。但是，在单细胞研究中，直接进行这些检测通常是不够的，因为来自未感染的经过处理的群体的单细胞水平表达数据通常包含具有高度异质性特征的几个潜在亚群的属性。结果，病毒经常以不同的速率感染这些不同的亚群，在这种情况下，用于检查分布相似性的传统非参数两样本检验不再保守。在本文中，我们提出了一种新的非参数方法在异质性下测试重塑（TRUH）可以准确地检测出感染样品与可能是异种未感染样品的变化。我们的测试框架基于复合零值，旨在允许零值模型包含以下可能性：受感染的样本虽然未受到病毒的影响，但可能主要来自基线数据中代表性不足的亚群。TRUH统计量使用新型样本自举算法进行校准，该统计量使用感染样本到基准未感染种群中的最近邻点投影。我们通过仿真实验证明了该测试的非渐近性能，并得出了测试统计量的大样本限制，这为测试的一致渐近校准提供了理论支持。