A mixture model approach to the tests of concordance and discordance between two large-scale experiments with two-sample groups

Motivation: Due to advances in experimental technologies, such as microarray, mass spectrometry and nuclear magnetic resonance, it is feasible to obtain large-scale data sets, in which measurements for a large number of features can be simultaneously collected. However, the sample sizes of these data sets are usually small due to their relatively high costs, which leads to the issue of concordance among different data sets collected for the same study: features should have consistent behavior in different data sets. There is a lack of rigorous statistical methods for evaluating this concordance or discordance. Methods: Based on a three-component normal-mixture model, we propose two likelihood ratio tests for evaluating the concordance and discordance between two large-scale data sets with two sample groups. The parameter estimation is achieved through the expectation-maximization (E-M) algorithm. A normal-distributionquantile-based method is used for data transformation. Results: To evaluate the proposed tests, we conducted some simulation studies, which suggested their satisfactory performances. As applications, the proposed tests were applied to three SELDI-MS data sets with replicates. One data set has replicates from different platforms and the other two have replicates from the same platform. We found that data generated by SELDI-MS showed satisfactory concordance between replicates from the same platform but unsatisfactory concordance between replicates from different platforms.