A robust Bayesian two-sample test for detecting intervals of differential gene expression in microarray time series.

Understanding the regulatory mechanisms that are responsible for an organism's response to environmental change is an important issue in molecular biology. A first and important step towards this goal is to detect genes whose expression levels are affected by altered external conditions. A range of methods to test for differential gene expression, both in static as well as in time-course experiments, have been proposed. While these tests answer the question whether a gene is differentially expressed, they do not explicitly address the question when a gene is differentially expressed, although this information may provide insights into the course and causal structure of regulatory programs. In this article, we propose a two-sample test for identifying intervals of differential gene expression in microarray time series. Our approach is based on Gaussian process regression, can deal with arbitrary numbers of replicates, and is robust with respect to outliers. We apply our algorithm to study the response of Arabidopsis thaliana genes to an infection by a fungal pathogen using a microarray time series dataset covering 30,336 gene probes at 24 observed time points. In classification experiments, our test compares favorably with existing methods and provides additional insights into time-dependent differential expression.

An adaptive algorithm for clustering cumulative probability distribution functions using the Kolmogorov–Smirnov two-sample test

This paper proposes an adaptive algorithm for clustering cumulative probability distribution functions (c.p.d.f.) of a continuous random variable, observed in different populations, into the minimum homogeneous clusters, making no parametric assumptions about the c.p.d.f.’s. The distance function for clustering c.p.d.f.’s that is proposed is based on the Kolmogorov–Smirnov two sample statistic. This test is able to detect differences in position, dispersion or shape of the c.p.d.f.’s. In our context, this statistic allows us to cluster the recorded data with a homogeneity criterion based on the whole distribution of each data set, and to decide whether it is necessary to add more clusters or not. In this sense, the proposed algorithm is adaptive as it automatically increases the number of clusters only as necessary; therefore, there is no need to fix in advance the number of clusters. The output of the algorithm are the common c.p.d.f. of all observed data in the cluster (the centroid) and, for each cluster, the Kolmogorov–Smirnov statistic between the centroid and the most distant c.p.d.f. The proposed algorithm has been used for a large data set of solar global irradiation spectra distributions. The results obtained enable to reduce all the information of more than 270,000 c.p.d.f.’s in only 6 different clusters that correspond to 6 different c.p.d.f.’s.

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Myocardial bridging: depiction rate and morphology at CT coronary angiography--comparison with conventional coronary angiography

PURPOSE: To prospectively assess the depiction rate and morphologic features of myocardial bridging (MB) of coronary arteries with 64-section computed tomographic (CT) coronary angiography in comparison to conventional coronary angiography. MATERIALS AND METHODS: Patients were simultaneously enrolled in a prospective study comparing CT and conventional coronary angiography, for which ethics committee approval and informed consent were obtained. One hundred patients (38 women, 62 men; mean age, 63.8 years +/- 11.6 [standard deviation]) underwent 64-section CT and conventional coronary angiography. Fifty additional patients (19 women, 31 men; mean age, 59.2 years +/- 13.2) who underwent CT only were also included. CT images were analyzed for the direct signs length, depth, and degree of systolic compression, while conventional angiograms were analyzed for the indirect signs step down-step up phenomenon, milking effect, and systolic compression of the tunneled segment. Statistical analysis was performed with Pearson correlation analysis, the Wilcoxon two-sample test, and Fisher exact tests. RESULTS: MB was detected with CT in 26 (26%) of 100 patients and with conventional angiography in 12 patients (12%). Mean tunneled segment length and depth at CT (n = 150) were 24.3 mm +/- 10.0 and 2.6 mm +/- 0.8, respectively. Systolic compression in the 12 patients was 31.3% +/- 11.0 at CT and 28.2% +/- 10.5 at conventional angiography (r = 0.72, P < .001). With CT, a significant correlation was not found between systolic compression and length (r = 0.16, P = .25, n = 150) but was found with depth (r = 0.65, P < .01, n = 150) of the tunneled segment. In 14 patients in whom MB was found at CT but not at conventional angiography, length, depth, and systolic compression were significantly lower than in patients in whom both modalities depicted the anomaly (P < .001, P < .01, and P < .001, respectively). CONCLUSION: The depiction rate of MB is greater with 64-section CT coronary angiography than with conventional coronary angiography. The degree of systolic compression of MB significantly correlates with tunneled segment depth but not length.

A SIMULATION STUDY OF THE SIZE AND POWER OF SOME TWO-SAMPLE TESTS FOR UNEQUALLY CENSORED SURVIVAL DATA (RANK TESTS, LOGRANK, PROPORTIONAL HAZARDS, WILCOXON TESTS, EXPONENTIAL DISTRIBUTION)

Sizes and power of selected two-sample tests of the equality of survival distributions are compared by simulation for small samples from unequally, randomly-censored exponential distributions. The tests investigated include parametric tests (F, Score, Likelihood, Asymptotic), logrank tests (Mantel, Peto-Peto), and Wilcoxon-Type tests (Gehan, Prentice). Equal sized samples, n = 18, 16, 32 with 1000 (size) and 500 (power) simulation trials, are compared for 16 combinations of the censoring proportions 0%, 20%, 40%, and 60%. For n = 8 and 16, the Asymptotic, Peto-Peto, and Wilcoxon tests perform at nominal 5% size expectations, but the F, Score and Mantel tests exceeded 5% size confidence limits for 1/3 of the censoring combinations. For n = 32, all tests showed proper size, with the Peto-Peto test most conservative in the presence of unequal censoring. Powers of all tests are compared for exponential hazard ratios of 1.4 and 2.0. There is little difference in power characteristics of the tests within the classes of tests considered. The Mantel test showed 90% to 95% power efficiency relative to parametric tests. Wilcoxon-type tests have the lowest relative power but are robust to differential censoring patterns. A modified Peto-Peto test shows power comparable to the Mantel test. For n = 32, a specific Weibull-exponential comparison of crossing survival curves suggests that the relative powers of logrank and Wilcoxon-type tests are dependent on the scale parameter of the Weibull distribution. Wilcoxon-type tests appear more powerful than logrank tests in the case of late-crossing and less powerful for early-crossing survival curves. Guidelines for the appropriate selection of two-sample tests are given. ^

Bayesian two-sample tests

In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second class of methods uses Dirichlet process mixtures (DPM) of such conjugate-exponential distributions as flexible nonparametric priors over the unknown distributions.

Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions.

In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Pyramid Multi-resolution Scanning for Two-sample Comparison

Testing for two-sample differences is challenging when the differences are local and only involve a small portion of the data. To solve this problem, we apply a multi- resolution scanning framework that performs dependent local tests on subsets of the sample space. We use a nested dyadic partition of the sample space to get a collection of windows and test for sample differences within each window. We put a joint prior on the states of local hypotheses that allows both vertical and horizontal message passing among the partition tree to reflect the spatial dependency features among windows. This information passing framework is critical to detect local sample differences. We use both the loopy belief propagation algorithm and MCMC to get the posterior null probability on each window. These probabilities are then used to report sample differences based on decision procedures. Simulation studies are conducted to illustrate the performance. Multiple testing adjustment and convergence of the algorithms are also discussed.

The Synthetic Control Chart Based on Two Sample Variances for Monitoring the Covariance Matrix

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Success rate and efficiency of activator treatment

In a retrospective multicentre study, the success rate and efficiency of activator treatment were analysed. All patients from two University clinics (Giessen, Germany and Berne, Switzerland) that fulfilled the selection criteria (Class II division 1 malocclusion, activator treatment, no aplasia, no extraction of permanent teeth, no syndromes, no previous orthodontic treatment except transverse maxillary expansion, full available records) were included in the study. The subject material amounted to 222 patients with a mean age of 10.6 years. Patient records, lateral head films, and dental casts were evaluated. Treatment was classified as successful if the molar relationship improved by at least half to three-fourths cusp width depending on whether or not the leeway space was used during treatment. Group comparisons were carried out using Wilcoxon two-sample and Kruskal-Wallis tests. For discrete data, chi-square analysis was used and Fisher's exact test when the sample size was small. Stepwise logistic regression was also employed. The success rate was 64 per cent in Giessen and 66 per cent in Berne. The only factor that significantly (P < 0.001) influenced treatment success was the level of co-operation. In approximately 27 per cent of the patients at both centres, the post-treatment occlusion was an 'ideal' Class I. In an additional 38 per cent of the patients, marked improvements in occlusal relationships were found. In subjects with Class II division 1 malocclusions, in which orthodontic treatment is performed by means of activators, a marked improvement of the Class II dental arch relationships can be expected in approximately 65 per cent of subjects. Activator treatment is more efficient in the late than in the early mixed dentition.