Search

Rank tests are known to be robust to outliers and violation of distributional assumptions. Two major issues besetting microarray data are violation of the normality assumption and contamination by outliers. In this article, we formulate the normal theory simultaneous tests and their aligned rank transformation (ART) analog for detecting differentially expressed genes. These tests are based on the least-squares estimates of the effects when data follow a linear model. Application of the two methods are then demonstrated on a real data set. To evaluate the performance of the aligned rank transform method with the corresponding normal theory method, data were simulated according to the characteristics of a real gene expression data. These simulated data are then used to compare the two methods with respect to their sensitivity to the distributional assumption and to outliers for controlling the family-wise Type I error rate, power, and false discovery rate. It is demonstrated that the ART generally possesses the robustness of validity property even for microarray data with small number of replications. Although these methods can be applied to more general designs, in this article the simulation study is carried out for a dye-swap design since this design is broadly used in cDNA microarray experiments. [ABSTRACT FROM AUTHOR]

A class of simultaneous tests based on the aligned rank transform (ART) statistics is proposed for linear functions of parameters in linear models. The asymptotic distributions are derived. The stability of the finite sample behaviour of the sampling distribution of the ART technique is studied by comparing the simulated upper quantiles of its sampling distribution with those of the multivariatet-distribution. Simulation also shows that the tests based on ART have excellent small sample properties and because of their robustness perform better than the methods based on the least-squares estimates. [ABSTRACT FROM AUTHOR]

Technologies of measuring millions of quantities at once have been rapidly developed and used in biological and biomedical research and other fields in the past decade. Yet a key issue remains unsettled, namely, how to control spurious findings for the ensuing massive number of hypothesis tests. An emerging consensus is to control false discovery rate (FDR), with FDR defined as the expected proportion of true nulls among discoveries, and a discovery the rejection of a null hypothesis. However, the very concept of counting true nulls, implicitly or explicitly, is problematic, for nulls are rarely true in reality. We propose an approach that is philosophically different from the FDR and other approaches. Taking advantage of the massive measurements, we can and should directly evaluate the reproducibility of a discovery by calculating the posterior probability of discovery (PPD) given observed data. A discovery with a great PPD is deemed to be highly reproducible, that is, not spurious. For a subset of hypotheses tested, mean PPD yields the expected rate of discovery (ERD), a measure useful for various applications such as subset enrichment analysis. We present here the rationale, theoretical basis, and an algorithm for computing PPDs and ERDs from data. Their validity, utility, and optimal performance are demonstrated using both simulated and real data. Supplementary material is available online. [ABSTRACT FROM AUTHOR]

In a randomized block design, robust versions based on scale-invariant M-statistics are proposed for single-step multiple comparisons procedures discussed by Tukey (1953) and Dunnett (1955). Although the symmetry of the underlying distribution is needed in the asymptotic theory of Huber's M-estimators, the proposed procedures do not demand the symmetry. It is found that the M-procedures are superior to the classical normal theory procedures except the case that an underlying distribution is normal. [ABSTRACT FROM AUTHOR]