A single statistic for monitoring the covariance matrix of bivariate processes

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Implementation of an F-statistic all-sky search for continuous gravitational waves in Virgo VSR1 data

We present an implementation of the F-statistic to carry out the first search in data from the Virgo laser interferometric gravitational wave detector for periodic gravitational waves from a priori unknown, isolated rotating neutron stars. We searched a frequency f(0) range from 100 Hz to 1 kHz and the frequency dependent spindown f(1) range from -1.6(f(0)/100 Hz) x 10(-9) Hz s(-1) to zero. A large part of this frequency-spindown space was unexplored by any of the all-sky searches published so far. Our method consisted of a coherent search over two-day periods using the F-statistic, followed by a search for coincidences among the candidates from the two-day segments. We have introduced a number of novel techniques and algorithms that allow the use of the fast Fourier transform (FFT) algorithm in the coherent part of the search resulting in a fifty-fold speed-up in computation of the F-statistic with respect to the algorithm used in the other pipelines. No significant gravitational wave signal was found. The sensitivity of the search was estimated by injecting signals into the data. In the most sensitive parts of the detector band more than 90% of signals would have been detected with dimensionless gravitational-wave amplitude greater than 5 x 10(-24).

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

Assessment of interrater agreement using a binomial-based statistic: K(bin)

This project develops K(bin), a relatively simple, binomial based statistic for assessing interrater agreement in which expected agreement is calculated a priori from the number of raters involved in the study and number of categories on the rating tool. The statistic is logical in interpretation, easily calculated, stable for small sample sizes, and has application over a wide range of possible combinations from the simplest case of two raters using a binomial scale to multiple raters using a multiple level scale.^ Tables of expected agreement values and tables of critical values for K(bin) which include power to detect three levels of the population parameter K for n from 2 to 30 and observed agreement $\ge$.70 calculated at alpha =.05,.025, and.01 are included.^ An example is also included which describes the use of the tables for planning and evaluating an interrater reliability study using the statistic, K(bin). ^

A new combined endpoint using U-statistic in analysis in clinical trials

Common endpoints can be divided into two categories. One is dichotomous endpoints which take only fixed values (most of the time two values). The other is continuous endpoints which can be any real number between two specified values. Choices of primary endpoints are critical in clinical trials. If we only use dichotomous endpoints, the power could be underestimated. If only continuous endpoints are chosen, we may not obtain expected sample size due to occurrence of some significant clinical events. Combined endpoints are used in clinical trials to give additional power. However, current combined endpoints or composite endpoints in cardiovascular disease clinical trials or most clinical trials are endpoints that combine either dichotomous endpoints (total mortality + total hospitalization), or continuous endpoints (risk score). Our present work applied U-statistic to combine one dichotomous endpoint and one continuous endpoint, which has three different assessments and to calculate the sample size and test the hypothesis to see if there is any treatment effect. It is especially useful when some patients cannot provide the most precise measurement due to medical contraindication or some personal reasons. Results show that this method has greater power then the analysis using continuous endpoints alone. ^

A simulation study using the hybrid statistic and the meta-analysis t-test for data with matched and unmatched subjects in the interim analysis of clinical trials

An interim analysis is usually applied in later phase II or phase III trials to find convincing evidence of a significant treatment difference that may lead to trial termination at an earlier point than planned at the beginning. This can result in the saving of patient resources and shortening of drug development and approval time. In addition, ethics and economics are also the reasons to stop a trial earlier. In clinical trials of eyes, ears, knees, arms, kidneys, lungs, and other clustered treatments, data may include distribution-free random variables with matched and unmatched subjects in one study. It is important to properly include both subjects in the interim and the final analyses so that the maximum efficiency of statistical and clinical inferences can be obtained at different stages of the trials. So far, no publication has applied a statistical method for distribution-free data with matched and unmatched subjects in the interim analysis of clinical trials. In this simulation study, the hybrid statistic was used to estimate the empirical powers and the empirical type I errors among the simulated datasets with different sample sizes, different effect sizes, different correlation coefficients for matched pairs, and different data distributions, respectively, in the interim and final analysis with 4 different group sequential methods. Empirical powers and empirical type I errors were also compared to those estimated by using the meta-analysis t-test among the same simulated datasets. Results from this simulation study show that, compared to the meta-analysis t-test commonly used for data with normally distributed observations, the hybrid statistic has a greater power for data observed from normally, log-normally, and multinomially distributed random variables with matched and unmatched subjects and with outliers. Powers rose with the increase in sample size, effect size, and correlation coefficient for the matched pairs. In addition, lower type I errors were observed estimated by using the hybrid statistic, which indicates that this test is also conservative for data with outliers in the interim analysis of clinical trials.^

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Metadata und statistic analysis of archael and bacterial sequences originating from sediments of the Håkon Mosby mud volcano (Z1-Z3, all habitats)

DNA extraction was carried out as described on the MICROBIS project pages (http://icomm.mbl.edu/microbis ) using a commercially available extraction kit. We amplified the hypervariable regions V4-V6 of archaeal and bacterial 16S rRNA genes using PCR and several sets of forward and reverse primers (http://vamps.mbl.edu/resources/primers.php). Massively parallel tag sequencing of the PCR products was carried out on a 454 Life Sciences GS FLX sequencer at Marine Biological Laboratory, Woods Hole, MA, following the same experimental conditions for all samples. Sequence reads were submitted to a rigorous quality control procedure based on mothur v30 (doi:10.1128/AEM.01541-09) including denoising of the flow grams using an algorithm based on PyroNoise (doi:10.1038/nmeth.1361), removal of PCR errors and a chimera check using uchime (doi:10.1093/bioinformatics/btr381). The reads were taxonomically assigned according to the SILVA taxonomy (SSURef v119, 07-2014; doi:10.1093/nar/gks1219) implemented in mothur and clustered at 98% ribosomal RNA gene V4-V6 sequence identity. V4-V6 amplicon sequence abundance tables were standardized to account for unequal sampling effort using 1000 (Archaea) and 2300 (Bacteria) randomly chosen sequences without replacement using mothur and then used to calculate inverse Simpson diversity indices and Chao1 richness (doi:10.2307/4615964). Bray-Curtis dissimilarities (doi:10.2307/1942268) between all samples were calculated and used for 2-dimensional non metric multidimensional scaling (NMDS) ordinations with 20 random starts (doi:10.1007/BF02289694). Stress values below 0.2 indicated that the multidimensional dataset was well represented by the 2D ordination. NMDS ordinations were compared and tested using Procrustes correlation analysis (doi:10.1007/BF02291478). All analyses were carried out with the R statistical environment and the packages vegan (available at: http://cran.r-project.org/package=vegan), labdsv (available at: http://cran.r-project.org/package=labdsv), as well as with custom R scripts. Operational taxonomic units at 98% sequence identity (OTU0.03) that occurred only once in the whole dataset were termed absolute single sequence OTUs (SSOabs; doi:10.1038/ismej.2011.132). OTU0.03 sequences that occurred only once in at least one sample, but may occur more often in other samples were termed relative single sequence OTUs (SSOrel). SSOrel are particularly interesting for community ecology, since they comprise rare organisms that might become abundant when conditions change.16S rRNA amplicons and metagenomic reads have been stored in the sequence read archive under SRA project accession number SRP042162.