A test of homogeneity of distributions when observations are subject to measurement errors.

When the observed data are contaminated with errors, the standard two-sample testing approaches that ignore measurement errors may produce misleading results, including a higher type-I error rate than the nominal level. To tackle this inconsistency, a nonparametric test is proposed for testing equality of two distributions when the observed contaminated data follow the classical additive measurement error model. The proposed test takes into account the presence of errors in the observed data, and the test statistic is defined in terms of the (deconvoluted) characteristic functions of the latent variables. Proposed method is applicable to a wide range of scenarios as no parametric restrictions are imposed either on the distribution of the underlying latent variables or on the distribution of the measurement errors. Asymptotic null distribution of the test statistic is derived, which is given by an integral of a squared Gaussian process with a complicated covariance structure. For data-based calibration of the test, a new nonparametric Bootstrap method is developed under the two-sample measurement error framework and its validity is established. Finite sample performance of the proposed test is investigated through simulation studies, and the results show superior performance of the proposed method than the standard tests that exhibit inconsistent behavior. Finally, the proposed method was applied to real data sets from the National Health and Nutrition Examination Survey. An R package MEtest is available through CRAN.

Quality Control of Quantitative High Throughput Screening Data.

Quantitative high throughput screening (qHTS) experiments can generate 1000s of concentration-response profiles to screen compounds for potentially adverse effects. However, potency estimates for a single compound can vary considerably in study designs incorporating multiple concentration-response profiles for each compound. We introduce an automated quality control procedure based on analysis of variance (ANOVA) to identify and filter out compounds with multiple cluster response patterns and improve potency estimation in qHTS assays. Our approach, called Cluster Analysis by Subgroups using ANOVA (CASANOVA), clusters compound-specific response patterns into statistically supported subgroups. Applying CASANOVA to 43 publicly available qHTS data sets, we found that only about 20% of compounds with response values outside of the noise band have single cluster responses. The error rates for incorrectly separating true clusters and incorrectly clumping disparate clusters were both less than 5% in extensive simulation studies. Simulation studies also showed that the bias and variance of concentration at half-maximal response (AC50 ) estimates were usually within 10-fold when using a weighted average approach for potency estimation. In short, CASANOVA effectively sorts out compounds with "inconsistent" response patterns and produces trustworthy AC50 values.

A Two-Sample Test for Equality of Means in High Dimension.

We develop a test statistic for testing the equality of two population mean vectors in the "large-p-small-n" setting. Such a test must surmount the rank-deficiency of the sample covariance matrix, which breaks down the classic Hotelling T2 test. The proposed procedure, called the generalized component test, avoids full estimation of the covariance matrix by assuming that the p components admit a logical ordering such that the dependence between components is related to their displacement. The test is shown to be competitive with other recently developed methods under ARMA and long-range dependence structures and to achieve superior power for heavy-tailed data. The test does not assume equality of covariance matrices between the two populations, is robust to heteroscedasticity in the component variances, and requires very little computation time, which allows its use in settings with very large p. An analysis of mitochondrial calcium concentration in mouse cardiac muscles over time and of copy number variations in a glioblastoma multiforme data set from The Cancer Genome Atlas are carried out to illustrate the test.