On weighted Hochberg procedures

We consider different ways of constructing weighted Hochberg-typestep-up multiple test procedures including closed proceduresbased on weighted Simes tests and their conservative step-upshort-cuts, and step-up counterparts of two weighted Holm procedures.It is shown that the step-up counterparts have some seriouspitfalls such as lack of familywise error rate control and lackof monotonicity in rejection decisions in terms of p-values.Therefore an exact closed procedure appears to be the best alternative,its only drawback being lack of simple stepwise structure. Aconservative step-up short-cut to the closed procedure may beused instead, but with accompanying loss of power. Simulationsare used to study the familywise error rate and power propertiesof the competing procedures for independent and correlated p-values.Although many of the results of this paper are negative, theyare useful in highlighting the need for caution when procedureswith similar pitfalls may be used.     

Test Procedures in Configural Frequency Analysis (CFA) Controlling the Local and Multiple Level

The test statistics used until now in the CFA have been developed under the assumption of the overall hypothesis of total independence. Therefore, the multiple test procedures based on these statistics are really only different tests of the overall hypothesis. If one likes to test a special cell hypothesis, one should only assume that this hypothesis is true and not the whole overall hypothesis. Such cell tests can then be used as elements of a multiple test procedure. In this paper it is shown that the usual test procedures can be very anticonservative (except of the two-dimensional, and, for some procedures, the three-dimensional case), and corrected test procedures are developed. Furthermore, for the construction of multiple tests controlling the multiple level, modifications of Holm's (1979) procedure are proposed which lead to sharper results than his general procedure and can also be performed very easily.     

A shortcut for multiple testing on the directed acyclic graph of gene ontology

Background

Gene set testing has become an important analysis technique in high throughput microarray and next generation sequencing studies for uncovering patterns of differential expression of various biological processes. Often, the large number of gene sets that are tested simultaneously require some sort of multiplicity correction to account for the multiplicity effect. This work provides a substantial computational improvement to an existing familywise error rate controlling multiplicity approach (the Focus Level method) for gene set testing in high throughput microarray and next generation sequencing studies using Gene Ontology graphs, which we call the Short Focus Level.

Results

The Short Focus Level procedure, which performs a shortcut of the full Focus Level procedure, is achieved by extending the reach of graphical weighted Bonferroni testing to closed testing situations where restricted hypotheses are present, such as in the Gene Ontology graphs. The Short Focus Level multiplicity adjustment can perform the full top-down approach of the original Focus Level procedure, overcoming a significant disadvantage of the otherwise powerful Focus Level multiplicity adjustment. The computational and power differences of the Short Focus Level procedure as compared to the original Focus Level procedure are demonstrated both through simulation and using real data.

Conclusions

The Short Focus Level procedure shows a significant increase in computation speed over the original Focus Level procedure (as much as ∼15,000 times faster). The Short Focus Level should be used in place of the Focus Level procedure whenever the logical assumptions of the Gene Ontology graph structure are appropriate for the study objectives and when either no a priori focus level of interest can be specified or the focus level is selected at a higher level of the graph, where the Focus Level procedure is computationally intractable.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0349-3) contains supplementary material, which is available to authorized users.     

Application of Multiple Test Procedures to the Combination of Multivariate and Univariate Tests with Varying Variable Sets

The positive ascertainment of location differences in a multivariate comparison of two or more groups gives rise to the question for the contribution of the single variables or of subsets of variables to the multivariate difference. In this paper two methods are proposed to accomplish the original multivariate test by tests in variable subsets or in single variables using a closed test procedure and Holm's procedure, respectively. Both control the multiple level of the whole procedure.     

Adjusted regression trend test for a multicenter clinical trial

Studies using a series of increasing doses of a compound, including a zero dose control, are often conducted to study the effect of the compound on the response of interest. For a one-way design, Tukey et al. (1985, Biometrics 41, 295-301) suggested assessing trend by examining the slopes of regression lines under arithmetic, ordinal, and arithmetic-logarithmic dose scalings. They reported the smallest p-value for the three significance tests on the three slopes for safety assessments. Capizzi et al. (1992, Biometrical Journal 34, 275-289) suggested an adjusted trend test, which adjusts the p-value using a trivariate t-distribution, the joint distribution of the three slope estimators. In this paper, we propose an adjusted regression trend test suitable for two-way designs, particularly for multicenter clinical trials. In a step-down fashion, the proposed trend test can be applied to a multicenter clinical trial to compare each dose with the control. This sequential procedure is a closed testing procedure for a trend alternative. Therefore, it adjusts p-values and maintains experimentwise error rate. Simulation results show that the step-down trend test is overall more powerful than a step-down least significant difference test.     

A note on one-sided tests with multiple endpoints

Testing problems with multivariate one-sided alternative hypotheses are common in clinical trials with multiple endpoints. In the case of comparing two treatments, treatment 1 is often preferred if it is superior for at least one of the endpoints and not biologically inferior for the remaining endpoints. Bloch et al. (2001, Biometrics57, 1039-1047) propose an intersection-union test (IUT) for this testing problem, but their test does not utilize the appropriate multivariate one-sided test. In this note we modify their test by an alternative IUT that does utilize the appropriate one-sided test. Empirical and graphical evidence show that the proposed test is more appropriate for this testing problem.     

General solutions to multiple testing problems. Translation of "Sonnemann, E. (1982). Allgemeine Lösungen multipler Test probleme. EDV in Medizin und Biologie 13(4), 120-128"

The introduction of sequentially rejective multiple test procedures (Einot and Gabriel, 1975; Naik, 1975; Holm, 1977; Holm, 1979) has caused considerable progress in the theory of multiple comparisons. Emphasizing the closure of multiple tests we give a survey of the general theory and its recent results in applications. Some new applications are given including a discussion of the connection with the theory of confidence regions.     

A staining procedure for micronucleus test using new methylene blue and acridine orange: specimens that are supravitally stained with possible long-term storage

The micronucleus test has been widely used as an in vivo cytogenetic test. It employs two different kinds of supravital staining methods which use either new methylene blue (N) and Giemsa (G) or acridine orange (AO). We have developed a new staining procedure for the preparation of specimens supravitally stained with possible long-term storage, using both N and AO. This N/AO-staining method involves three steps; (1) combination of the target tissue or target cells with an equivalent volume of 0.5% solution of new methylene blue (N-staining step), (2) immediate smear of the mixture, followed by treatment with methanol for 10 min for fixation and removal of N and drying (referred to as fixed-decolorized specimens), and (3) staining with 0.007% solution of AO for 3 min, followed by washing with Sörensen's buffer (pH 6.8) and covering of specimens before observation (AO-staining step). To examine whether the N/AO-staining method is useful for the micronucleus test, comparisons were made between N-, N/AO-, and AO-stained specimens prepared supravitally from peripheral blood of rats with and without treatment of cyclophosphamide. The results indicate that N/AO-stained specimens can be supravitally observed after long-term storage with the same coloration and comparable frequencies of micronucleated reticulocytes with a positive response as AO-stained specimens, if the staining process is temporarily stopped before AO-staining (as fixed-decolorized specimens), or if the AO-staining step is repeated. The results also showed that separated reticulocyte types are supravitally stained in a similar fashion to N-stained specimens but not to AO-stained specimens, indicative of the preservation of the supravital feature of N-staining. Taken together these results suggest that the N/AO-staining procedure could offer an additional useful staining tool for the micronucleus test.