Moment-based multivariate permutation tests for ordinal categorical data

A robust Spearman correlation coefficient permutation test

In this work, we show that Spearman's correlation coefficient test about H 0 : ρ s = 0 found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small. There is common misconception that the tests about ρ s = 0 are robust to deviations from bivariate normality. However, we found under certain scenarios violation of the bivariate normality assumption has severe effects on type I error control for the common tests. To address this issue, we developed a robust permutation test for testing the hypothesis H 0 : ρ s = 0 based on an appropriately studentized statistic. We will show that the test is asymptotically valid in general settings. This was demonstrated by a comprehensive set of simulation studies, where the proposed test exhibits robust type I error control, even when the sample size is small. We also demonstrated the application of this test in two real world examples.

Multivariate permutation tests for two sample testing in presence of nondetects with application to microarray data

Very often, data collected in medical research are characterized by censored observations and/or data with mass on the value zero. This happens for example when some measurements fall below the detection limits of the specific instrument used. This type of left censored observations is called "nondetects". Such a situation of an excessive number of zeros in a data set is also referred to as zero-inflated data. In the present work, we aim at comparing different multivariate permutation procedures in two-sample testing for data with nondetects. The effect of censoring is investigated with regard to the different values that may be attributed to nondetected values, both under the null hypothesis and under alternative. We motivate the problem using data from allergy research.

Iterated combination-based paired permutation tests to determine shape effects of chemotherapy in patients with esophageal cancer

The nonparametric combination of dependent permutation tests method is a useful general tool when a testing problem can be broken down into a set of different k > 1 partial tests. These partial tests, after adjustment of p-values to control for multiplicity, can be marginally analyzed, but jointly considered they can provide information on an overall hypothesis, which might represent the true goal of the testing problem. On the one hand, independence among the partial tests is usually an unrealistic assumption; on the other, even when the underlying dependence relations are known quite often they are difficult to cope with properly. Therefore this combination must be achieved nonparametrically, by implicitly taking into account the dependence structure of tests without explicitly describing it. An important property of the tests based on nonparametric combination methodology, when the number of response variables is high compared to the sample sizes, consists in the finite sample consistency. A practical problem involves choosing the most suitable combining function for each specific testing problem given that the final result can be affected by this crucial choice. The purpose of this article is to present an nonparametric combination solution based on the iterated combination of partial tests, evaluate its power behavior using a Monte Carlo simulation study and apply it to a real medical problem, namely the evaluation of the effects of chemotherapy on the shape of esophageal tumors. R code has been implemented to carry out the analyses.

Order restricted inference for multivariate binary data with application to toxicology

In many applications researchers collect multivariate binary response data under two or more, naturally ordered, experimental conditions. In such situations one is often interested in using all binary outcomes simultaneously to detect an ordering among the experimental conditions. To make such comparisons we develop a general methodology for testing for the multivariate stochastic order between K ≥ 2 multivariate binary distributions. The proposed test uses order restricted estimators which, according to our simulation study, are more efficient than the unrestricted estimators in terms of mean squared error. The power of the proposed test was compared with several alternative tests. These included procedures which combine individual univariate tests for order, such as union intersection tests and a Bonferroni based test. We also compared the proposed test with unrestricted Hotelling's T(2) type test. Our simulations suggest that the proposed method competes well with these alternatives. The gain in power is often substantial. The proposed methodology is illustrated by applying it to a two-year rodent cancer bioassay data obtained from the US National Toxicology Program (NTP). Supplemental materials are available online.