Resampling-based empirical Bayes multiple testing procedures for controlling generalized tail probability and expected value error rates: focus on the false discovery rate and simulation study

This article proposes resampling-based empirical Bayes multiple testing procedures for controlling a broad class of Type I error rates, defined as generalized tail probability (gTP) error rates, gTP (q,g) = Pr(g (V(n),S(n)) > q), and generalized expected value (gEV) error rates, gEV (g) = E [g (V(n),S(n))], for arbitrary functions g (V(n),S(n)) of the numbers of false positives V(n) and true positives S(n). Of particular interest are error rates based on the proportion g (V(n),S(n)) = V(n) /(V(n) + S(n)) of Type I errors among the rejected hypotheses, such as the false discovery rate (FDR), FDR = E [V(n) /(V(n) + S(n))]. The proposed procedures offer several advantages over existing methods. They provide Type I error control for general data generating distributions, with arbitrary dependence structures among variables. Gains in power are achieved by deriving rejection regions based on guessed sets of true null hypotheses and null test statistics randomly sampled from joint distributions that account for the dependence structure of the data. The Type I error and power properties of an FDR-controlling version of the resampling-based empirical Bayes approach are investigated and compared to those of widely-used FDR-controlling linear step-up procedures in a simulation study. The Type I error and power trade-off achieved by the empirical Bayes procedures under a variety of testing scenarios allows this approach to be competitive with or outperform the Storey and Tibshirani (2003) linear step-up procedure, as an alternative to the classical Benjamini and Hochberg (1995) procedure.     

An investigation on performance of Significance Analysis of Microarray (SAM) for the comparisons of several treatments with one control in the presence of small-variance genes

One of multiple testing problems in drug finding experiments is the comparison of several treatments with one control. In this paper we discuss a particular situation of such an experiment, i.e., a microarray setting, where the many-to-one comparisons need to be addressed for thousands of genes simultaneously. For a gene-specific analysis, Dunnett's single step procedure is considered within gene tests, while the FDR controlling procedures such as Significance Analysis of Microarrays (SAM) and Benjamini and Hochberg (BH) False Discovery Rate (FDR) adjustment are applied to control the error rate across genes. The method is applied to a microarray experiment with four treatment groups (three microarrays in each group) and 16,998 genes. Simulation studies are conducted to investigate the performance of the SAM method and the BH-FDR procedure with regard to controlling the FDR, and to investigate the effect of small-variance genes on the FDR in the SAM procedure.     

FDR control by the BH procedure for two-sided correlated tests with implications to gene expression data analysis

The multiple testing problem attributed to gene expression analysis is challenging not only by its size, but also by possible dependence between the expression levels of different genes resulting from coregulations of the genes. Furthermore, the measurement errors of these expression levels may be dependent as well since they are subjected to several technical factors. Multiple testing of such data faces the challenge of correlated test statistics. In such a case, the control of the False Discovery Rate (FDR) is not straightforward, and thus demands new approaches and solutions that will address multiplicity while accounting for this dependency. This paper investigates the effects of dependency between bormal test statistics on FDR control in two-sided testing, using the linear step-up procedure (BH) of Benjamini and Hochberg (1995). The case of two multiple hypotheses is examined first. A simulation study offers primary insight into the behavior of the FDR subjected to different levels of correlation and distance between null and alternative means. A theoretical analysis follows in order to obtain explicit upper bounds to the FDR. These results are then extended to more than two multiple tests, thereby offering a better perspective on the effect of the proportion of false null hypotheses, as well as the structure of the test statistics correlation matrix. An example from gene expression data analysis is presented.     

Adaptive group sequential designs for clinical trials: combining the advantages of adaptive and of classical group sequential approaches

A general method is presented integrating the concept of adaptive interim analyses into classical group sequential testing. This allows the researcher to represent every group sequential plan as an adaptive trial design and to make design changes during the course of the trial after every interim analysis in the same way as with adaptive designs. The concept of adaptive trial designing is thereby generalized to a large variety of possible sequential plans.     

A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

Methane uptake rates in Japanese forest soils depend on the oxidation ability of topsoil, with a new estimate for global methane uptake in temperate forest

To clarify the reason for the higher CH₄ uptake rate in Japanese forest soils, twenty-seven sites were established for CH₄ flux measurement. The first order rate constant for CH₄ uptake was also determined using soil core incubation at 14 sites. The CH₄ uptake rate had a seasonal fluctuation, high in summer and low in winter, and the rate correlated with soil temperature at 17 sites. The annual CH₄ uptake rates ranged from 2.7 to 24.8 kg CH₄ ha⁻¹ y⁻¹ (the average of these rates was 9.7 or 10.9 kg CH₄ ha⁻¹ y⁻¹, depending on method of calculation), which is somewhat higher than the uptake rates reported in previous literature. The averaged CH₄ uptake rate correlated closely with the CH₄ oxidation rate of the topsoil (0–5 cm) in the study sites. The CH₄ oxidation constant of the topsoil was explained by a multiple regression model using total pore volume of the soil, nitrate content, and C/N ratio (p < 0.05, R ² = 0.684). This result and comparison with literature data suggest that the high CH₄ uptake rate in Japanese forest soils depends on the high porosity probably due to volcanic ash parent materials. According to our review of the literature, the CH₄ uptake rate in temperate forests in Europe is significantly different from that in Asia and North America. A new global CH₄ uptake rate in temperate forests was estimated to be 5.4 Tg y⁻¹ (1 SE is 1.1 Tg y⁻¹) on a continental basis.     

Inference for a RPW‐Type Clinical Trial with Repeated Monitoring for the Treatment of Rheumatoid Arthritis

The present paper describes a controlled clinical trial to investigate the effect of Pulsed Electro‐Magnetic Field for the treatment of sequentially entering patients with Rheumatoid Arthritis. According to the study design, repeated monitorings of the patients are carried out to assess their clinical status. The allocation of the entering patients to either a therapy group or a placebo group is done using a newly designed adaptive allocation rule termed as randomized longitudinal play‐the‐winner rule. A discussion of some inference procedures is followed by the analysis of a real data, which shows a clear preference of the therapy over the placebo. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of the inheritance pattern of a Chinese family with phaeochromocytomas through whole exome sequencing

Phaeochromocytomas (PCCs) and paragangliomas (PGLs) are rare, catecholamine-producing tumors. Most familial PCC/PGLs have been detected to be autosomal dominantly inherited. However, this study was undertaken in a family with PCCs to determine candidate genes in a dominant or recessive inheritance pattern. After excluding mutations in ten PCC/PGL susceptibility genes by Sanger sequencing, we used whole exome sequencing for screening on the four family members to discover novel candidate genes associated with PCCs. Based on the inexistence of non-synonymous mutations or indels in the ten known genes and the structure of this pedigree, 3 damaging loci with dominant inheritance pattern, and 5 damaging loci with recessive homozygous inheritance pattern and 6 damaging genes with compound heterozygous inheritance pattern were narrowed down to indicate the association with PCCs. According to the Gene Ontology (GO) category analysis on the combined results, cell adhesion showed the most significant enrichment.