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An important problem in contemporary immunology studies based on single-cellprotein expression data is to determine whether cellular expressions areremodeled post infection by a pathogen. One natural approach for detecting suchchanges is to use non-parametric two-sample statistical tests. However, insingle-cell studies, direct application of these tests is often inadequatebecause single-cell level expression data from uninfected populations oftencontains attributes of several latent sub-populations with highly heterogeneouscharacteristics. As a result, viruses often infect these differentsub-populations at different rates in which case the traditional nonparametrictwo-sample tests for checking similarity in distributions are no longerconservative. We propose a new nonparametric method for Testing RemodelingUnder Heterogeneity (TRUH) that can accurately detect changes in the infectedsamples compared to possibly heterogeneous uninfected samples. Our testingframework is based on composite nulls and is designed to allow the null modelto encompass the possibility that the infected samples, though unaltered by thevirus, might be dominantly arising from under-represented sub-populations inthe baseline data. The TRUH statistic, which uses nearest neighbor projectionsof the infected samples into the baseline uninfected population, is calibratedusing a novel bootstrap algorithm. We demonstrate the non-asymptoticperformance of the test via simulation experiments and derive the large samplelimit of the test statistic, which provides theoretical support towardsconsistent asymptotic calibration of the test. We use the TRUH statistic forstudying remodeling in tonsillar T cells under different types of HIV infectionand find that unlike traditional tests, TRUH based statistical inferenceconforms to the biologically validated immunological theories on HIV infection.

A Nearest-Neighbor Based Nonparametric Test for Viral Remodeling in Heterogeneous Single-Cell Proteomic Data