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.