A random effects model for multivariate failure time data from multicenter clinical trials

A random effects model for analyzing multivariate failure time data is proposed. The work is motivated by the need for assessing the mean treatment effect in a multicenter clinical trial study, assuming that the centers are a random sample from an underlying population. An estimating equation for the mean hazard ratio parameter is proposed. The proposed estimator is shown to be consistent and asymptotically normally distributed. A variance estimator, based on large sample theory, is proposed. Simulation results indicate that the proposed estimator performs well in finite samples. The proposed variance estimator effectively corrects the bias of the naive variance estimator, which assumes independence of individuals within a group. The methodology is illustrated with a clinical trial data set from the Studies of Left Ventricular Dysfunction. This shows that the variability of the treatment effect is higher than found by means of simpler models.     

Estimates of DNA and protein sequence divergence: an examination of some assumptions

Some of the assumptions underlying estimates of DNA and protein sequence divergence are examined. A solution for the variance of these estimates that allows for different mutation rates and different population sizes in each species and for an arbitrary structure in the initial population is obtained. It is shown that these conditions do not strongly affect estimates of divergence. In general, they cause the variance of divergence to be smaller than a binomial variance. Thus, the binomial variance that is usually assumed for these estimates is safely conservative. It is shown that variability in the mutation rate among sites can have an effect as large as or larger than variability in the mutation rate among bases. Variability in the mutation rate among bases and among sites causes the number of substitutions between two sequences to be underestimated. Protein and DNA sequences from several species are collected to estimate the variability in mutation rates among sites. When many homologous sequences are known, standard methods to estimate this variability can be used. The estimates of this variability show that this factor is important when considering the spectrum of spontaneous mutations and is strongly reflected in the divergence of sequences. Smaller variability is found for the third position of codons than for the first and second codon positions. This may be because of less selective constraints on this position or because the third position has been saturated with mutations for the sequences examined.      

Effects on phenotypic variability of directional selection arising through genetic differences in residual variability

In standard models of quantitative traits, genotypes are assumed to differ in mean but not variance of the trait. Here we consider directional selection for a quantitative trait for which genotypes also confer differences in variability, viewed either as differences in residual phenotypic variance when individual loci are concerned or as differences in environmental variability when the whole genome is considered. At an individual locus with additive effects, the selective value of the increasing allele is given by ia/sigma + 1/2 ixb/sigma2, where i is the selection intensity, x is the standardized truncation point, sigma2 is the phenotypic variance, and a/sigma and b/sigma2 are the standardized differences in mean and variance respectively between genotypes at the locus. Assuming additive effects on mean and variance across loci, the response to selection on phenotype in mean is isigma2(Am)/sigma + 1/2 ixcov(Amv)/sigma2 and in variance is icov(Amv)/sigma + 1/2 ixsigma2(Av)/sigma2, where sigma2(Am) is the (usual) additive genetic variance of effects of genes on the mean, sigma2(Av) is the corresponding additive genetic variance of their effects on the variance, and cov(Amv) is the additive genetic covariance of their effects. Changes in variance also have to be corrected for any changes due to gene frequency change and for the Bulmer effect, and relevant formulae are given. It is shown that effects on variance are likely to be greatest when selection is intense and when selection is on individual phenotype or within family deviation rather than on family mean performance. The evidence for and implications of such variability in variance are discussed.     

Analysis of variance components in gene expression data

MOTIVATION: A microarray experiment is a multi-step process, and each step is a potential source of variation. There are two major sources of variation: biological variation and technical variation. This study presents a variance-components approach to investigating animal-to-animal, between-array, within-array and day-to-day variations for two data sets. The first data set involved estimation of technical variances for pooled control and pooled treated RNA samples. The variance components included between-array, and two nested within-array variances: between-section (the upper- and lower-sections of the array are replicates) and within-section (two adjacent spots of the same gene are printed within each section). The second experiment was conducted on four different weeks. Each week there were reference and test samples with a dye-flip replicate in two hybridization days. The variance components included week-to-week, animal-to-animal and between-array and within-array variances. RESULTS: We applied the linear mixed-effects model to quantify different sources of variation. In the first data set, we found that the between-array variance is greater than the between-section variance, which, in turn, is greater than the within-section variance. In the second data set, for the reference samples, the week-to-week variance is larger than the between-array variance, which, in turn, is slightly larger than the within-array variance. For the test samples, the week-to-week variance has the largest variation. The animal-to-animal variance is slightly larger than the between-array and within-array variances. However, in a gene-by-gene analysis, the animal-to-animal variance is smaller than the between-array variance in four out of five housekeeping genes. In summary, the largest variation observed is the week-to-week effect. Another important source of variability is the animal-to-animal variation. Finally, we describe the use of variance-component estimates to determine optimal numbers of animals, arrays per animal and sections per array in planning microarray experiments.     

Linear and generalized linear models for the detection of QTL effects on within-subject variability

Quantitative trait loci (QTLs) may affect not only the mean of a trait but also its variability. A special aspect is the variability between multiple measured traits of genotyped animals, such as the within-litter variance of piglet birth weights. The sample variance of repeated measurements is assigned as an observation for every genotyped individual. It is shown that the conditional distribution of the non-normally distributed trait can be approximated by a gamma distribution. To detect QTL effects in the daughter design, a generalized linear model with the identity link function is applied. Suitable test statistics are constructed to test the null hypothesis H(0): No QTL with effect on the within-litter variance is segregating versus H(A): There is a QTL with effect on the variability of birth weight within litter. Furthermore, estimates of the QTL effect and the QTL position are introduced and discussed. The efficiency of the presented tests is compared with a test based on weighted regression. The error probability of the first type as well as the power of QTL detection are discussed and compared for the different tests.     

Evolution of the environmental component of the phenotypic variance: stabilizing selection in changing environments and the cost of homogeneity

Quantitative traits show abundant genetic, environmental, and phenotypic variance, yet if they are subject to stabilizing selection for an optimal phenotype, both the genetic and environmental components are expected to decline. The mechanisms that determine the level and maintenance of phenotypic variance are not yet fully understood. While there has been extensive study of mechanisms maintaining genetic variability, it has generally been assumed that environmental variance is not dependent on the genotype and therefore not subject to change. However, accumulating data suggest that the environmental variance is under some degree of genetic control. In this study, it is assumed accordingly that both the genotypic value (i.e., mean phenotypic value) and the variance of phenotypic value given genotypic value depend on the genotype. Two models are investigated as potentially able to explain the protected maintenance of environmental variance of quantitative traits under stabilizing selection. One is varying environment among generations, such that both the optimal phenotype and the strength of the stabilizing selection vary between generations. The other is the cost of homogeneity, which is based on an assumption of an engineering cost of minimizing variability in development. It is shown that a small homogeneity cost is enough to maintain the observed levels of environmental variance, whereas a large amount of temporal variation in the optimal phenotype and the strength of selection would be necessary.     

Relative quantification: characterization of bias, variability and fold changes in mass spectrometry data from iTRAQ-labeled peptides

Shotgun proteomics via mass spectrometry (MS) is a powerful technology for biomarker discovery that has the potential to lead to noninvasive disease screening mechanisms. Successful application of MS-based proteomics technologies for biomarker discovery requires accurate expectations of bias, reproducibility, variance, and the true detectable differences in platforms chosen for analyses. Characterization of the variability inherent in MS assays is vital and should affect interpretation of measurements of observed differences in biological samples. Here we describe observed biases, variance structure, and the ability to detect known differences in spike-in data sets for which true relative abundance among defined samples were known and were subsequently measured with the iTRAQ technology on two MS platforms. Global biases were observed within these data sets. Measured variability was a function of mean abundance. Fold changes were biased toward the null and variance of a fold change was a function of protein mass and abundance. The information presented herein will be valuable for experimental design and analysis of the resulting data.     

Short-term microbial and physico-chemical variability in low-temperature hydrothermal fluids near 5°S on the Mid-Atlantic Ridge

This study examines the representativeness of low-temperature hydrothermal fluid samples with respect to their chemical and microbiological characteristics. Within this scope, we investigated short-term temporal chemical and microbial variability of the hydrothermal fluids. For this purpose we collected three fluid samples consecutively from the same spot at the Clueless field near 5°S on the southern Mid-Atlantic Ridge over a period of 50 min. During sampling, the temperature was monitored online. We measured fluid chemical parameters, characterized microbial community compositions and used statistical analyses to determine significant differences between the samples. Overall, the three fluid samples are more closely related to each other than to any other tested habitat. Therefore, on a broad scale, the three collected fluid samples can be regarded as habitat representatives. However, small differences are apparent between all samples. One of the Clueless samples even displayed significant differences ( P -value < 0.01) to the other two Clueless samples. Our data suggest that the observed variations in fluid chemical and microbial compositions are not reflecting sampling artefacts but are related to short-term fluid variability due to dynamic subseafloor fluid mixing. Recorded temporal changes in fact reflect spatial heterogeneity found in the subsurface as the fluid flows through distinctive pathways. While conservative elements (Cl, Si, Na and K) indicate variable degrees of fluid-seawater mixing, reactive components, including Fe(II), O₂ and H₂S, show that chemical and microbial reactions within the mixing zone further modify the emanating fluids on short-time scales. Fluids entrain microorganisms, which modify the chemical microenvironment within the subsurface biotopes. This is the first study focusing on short-term microbial variability linked to chemical changes in hydrothermal fluids.     

Preliminary validation of an activation assay for ex vivo activated T cells utilized in cancer immunotherapy

An in vitro assay that measures the activation level of ex vivo activated (EVA) T cells currently being used in the adoptive immunotherapy of metastatic renal cell carcinoma has been developed. This assay is based on the ability of activated, but not resting. T cells to proliferate in response to the protein kinase C activator, phorbol myristate (PMA). To utilize this assay for in-process monitoring and control, we have begun an initial validation of the overall reproducibility of this assay. The proliferation of activated T cells in response to PMA, as measured by the mean cpm values of (3)H-thymidine incorporated, was demonstrated to have intra-assay coefficients of variation (cv's) for individual analysts that were typically less than 10% and rarely exceeded 20%. Activated T cells could be frozen and stored for at least 6 weeks with little or no deterioration in their ability to proliferate in response to PMA. Using these cells, inter-assay cv's that were typically less than 15% were obtained by individual analysts, and overall cv's of 10% to 25% were obtained for different samples assayed by different analysts at different times. This level of variability is very reasonable for a cellular assay. Furhter validation of this assay will address the issues of sensitivity, linearity and selectivity. To date, this assay has been used to analyze over 90 patient EVA cell samples and has revealed a broad range of proliferative responses to PMA. Taken together, these results suggest that this assay may be useful in defining the potency of the activated T cell used therapeutically.     

The variability in numbers of perch Perca fluviatilis L. caught in traps

The variability in the catch of perch traps set in Windermere over the period 1955–70 has been analysed. Altogether 2690 catches in four series have been treated by analyses of variance after a logarithmic transformation. A representative value of the between traps variance from all sources of variation has been used to estimate the reliability of the mean catches based on different numbers of traps. It is shown that many traps are needed to obtain consistent results.     

Variation in physical and chemical characteristics of common bean (Phaseolus vulgaris L.) grain along a domestication gradient

The objective of this study was to compare six samples of Mexican wild common bean (Phaseolus vulgaris L.) against three landraces and three improved cultivars with respect to physical and chemical attributes, and the culinary quality potential of their grain. A completely randomized experimental design was used to characterize the twelve genotypes. Data were analyzed by analysis of variance and pair-wise comparison of the treatment means by the Tukey test. In addition, correlation and principal-component analysis (PCA) were carried out using twelve characteristics of raw and four of cooked wild and domesticated grains. The results show a larger variability of the physical and chemical characteristics in wild than in domesticated beans. The PCA confirmed that grain gigantism was the main physical characteristic resulting of domestication, whereas the protein and tryptophan contents tended to be higher in wild than domesticated genotypes. Some wild samples from Chihuahua and Durango, Mexico, showed to be a genetic resource to improve food quality, because of their richness in minerals, protein, lysine, tryptophan, and dietary fibers.     

Legionella pneumophila in Thermal Spa – Methodological Aspects of Sampling and Analysis

The aim of the study was to check the occurrence of Legionella pneumophila in thermal water and to compare different analytical methods of its determination and/or quantification used in different laboratories. The research has shown that there are noticeable differences between results from culture method, qPCR, and FISH. Significant influence on the results has got analysts qualification, samples preparation, and equipment parameters. Very important is also the homogeneousness of the samples. qPCR or FISH method can be used as a preliminary, quick study, for identification of Legionella in water samples but the results obtained should be confirmed by culture method.     

Accounting for variability in sample size estimation with applications to nonadherence and estimation of variance and effect size

We consider sample size calculations for testing differences in means between two samples and allowing for different variances in the two groups. Typically, the power functions depend on the sample size and a set of parameters assumed known, and the sample size needed to obtain a prespecified power is calculated. Here, we account for two sources of variability: we allow the sample size in the power function to be a stochastic variable, and we consider estimating the parameters from preliminary data. An example of the first source of variability is nonadherence (noncompliance). We assume that the proportion of subjects who will adhere to their treatment regimen is not known before the study, but that the proportion is a stochastic variable with a known distribution. Under this assumption, we develop simple closed form sample size calculations based on asymptotic normality. The second source of variability is in parameter estimates that are estimated from prior data. For example, we account for variability in estimating the variance of the normal response from existing data which are assumed to have the same variance as the study for which we are calculating the sample size. We show that we can account for the variability of the variance estimate by simply using a slightly larger nominal power in the usual sample size calculation, which we call the calibrated power. We show that the calculation of the calibrated power depends only on the sample size of the existing data, and we give a table of calibrated power by sample size. Further, we consider the calculation of the sample size in the rarer situation where we account for the variability in estimating the standardized effect size from some existing data. This latter situation, as well as several of the previous ones, is motivated by sample size calculations for a Phase II trial of a malaria vaccine candidate.     

Assessing intrasample variation: analysis of Rapa Nui (Easter Island) museum cranial collections example

Osteological studies both old and new have utilized various Polynesian cranial samples, individually or in combination, to assess the racial composition of prehistoric Polynesians as a group, with regards to other Pacific populations, or to represent the Polynesian peoples as a whole in various multivariate analyses of worldwide populations. However, few of these studies have assessed the degree of intrasample variation produced when data derived from skeletal samples from different Polynesian islands (populations) are pooled to represent "Polynesians" as a whole. A similar argument can be made when data derived from various museum skeletal samples of the same Polynesian population are pooled to produce a larger sample representing that particular Polynesian population (Murrill [1968] Cranial and postcranial skeletal remains from Easter Island; Minneapolis: University of Minnesota Press; Stefan [2002] Am. J. Phys. Anthropol. [Suppl.] 34:147). This study examined Easter Island crania curated at various museums in North America, South America, and Europe to assess whether significant differences exist among the museum collections of Rapa Nui (Easter Island) skeletal material. A NORM statistical program (Schafer and Olsen [1997] NORM, version 1.01; University Park: Pennsylvania State University) for multiple imputation of incomplete multivariate datasets was utilized to estimate missing data. A variance comparison method, which utilizes variance/covariance matrices derived from "hypothesis" and "baseline/reference" samples (Key and Jantz [1990] Hum. Evol. 5:457-469; Key and Jantz [1990] Am. J. Phys. Anthropol. 82:53-59) was used to compare the Rapa Nui museum samples. This method is designed to test whether variability in a "hypothesis" museum sample exceeds "normal within-group variability" represented by the "baseline/reference" sample. The method was applied to six Rapa Nui museum samples (AANMW, MNHN-KB, MNHN-NAE, NHM, MH, and AMNH). The results indicate that the museum "hypothesis," male and female samples, exhibited little intrasample variability from the "baseline/reference" sample (MAPSE), though the samples were collected at different times and by different individuals. These results show the ability of multiple imputation and variance comparison methodologies to predict missing variables while maintaining the inherent variance/covariance structure and to discriminate sample variation in artificially assembled samples.     

The variability of the catch from gill nets set for pike Esox lucius L.

The variability of the catch of pike Esox lucius L. from gill nets in Windermere over the period 1961–71 has been analysed. Altogether 2952 catches have been treated by analysis of variance after an appropriate transformation. A representative value of the residual between catch variance has been used to estimate the reliability of the means of catches based on different numbers of net settings. It is shown that many settings of gill nets are required to get a reliable mean catch.     

Laboratory evaluation of oil spill bioremediation products in salt and freshwater systems

Ten oil spill bioremediation products were tested in the laboratory for their ability to enhance biodegradation of weathered Alaskan North Slope crude oil in both freshwater and saltwater media. The products included nutrients to stimulate inoculated microorganisms, nutrients plus an oil-degrading inoculum, nutrients plus compounds intended to stimulate oil-degrading activity, or other compounds intended to enhance microbial activity. The product tests were undertaken to evaluate significant modifications in the existing official United States Environmental Protection Agency (EPA) protocol used for qualifying commercial bioremediation agents for use in oil spills. The EPA protocol was modified to include defined formulas for the exposure waters (freshwater, saltwater), a positive control using a known inoculum and nutrients, two negative controls (one sterile, the other inoculated but nutrient-limited), and simplified oil chemical analysis. Three analysts conducted the product test independently in each type of exposure water in round-robin fashion. Statistical tests were performed on analyst variability, reproducibility, and repeatability, and the performance of the various products was quantified in both exposure media. Analysis of variance showed that the analyst error at each time-point was highly significant (P values ranged from 0.0001 to 0.008, depending on water type and oil fraction). In the saltwater tests, six products demonstrated various degrees of biodegradative activity against the alkane fraction of the crude oil and three degraded the aromatic hydrocarbons by >10%. In the freshwater tests, eight products caused >20% loss of alkane hydrocarbons, of which five degraded the alkanes by >50%. Only four products were able to degrade polycyclic aromatic hydrocarbons (PAHs) by >20%, one of which caused 88% removal. However, when the variability of the analysts was taken into consideration, only one of the ten products was found to yield significant percent removals of the PAH fraction and only in freshwater. Viable microorganism population analysis (most-probable-number method) was also performed on every sample by each operator to measure the changes in aromatic and alkane hydrocarbon-degrading organism numbers. In general, little evidence of significant growth of either alkane- or PAH-degraders occurred among any of the ten products in either the saltwater or freshwater testing.     

Guanine Nucleotide Exchange Factor OSG-1 Confers Functional Aging via Dysregulated Rho Signaling in Caenorhabditis elegans Neurons

Genetic studies usually focus on quantifying and understanding the existence of genetic control on expected phenotypic outcomes. However, there is compelling evidence suggesting the existence of genetic control at the level of environmental variability, with some genotypes exhibiting more stable and others more volatile performance. Understanding the mechanisms responsible for environmental variability not only informs medical questions but is relevant in evolution and in agricultural science. In this work fully sequenced inbred lines of Drosophila melanogaster were analyzed to study the nature of genetic control of environmental variance for two quantitative traits: starvation resistance (SR) and startle response (SL). The evidence for genetic control of environmental variance is compelling for both traits. Sequence information is incorporated in random regression models to study the underlying genetic signals, which are shown to be different in the two traits. Genomic variance in sexual dimorphism was found for SR but not for SL. Indeed, the proportion of variance captured by sequence information and the contribution to this variance from four chromosome segments differ between sexes in SR but not in SL. The number of studies of environmental variation, particularly in humans, is limited. The availability of full sequence information and modern computationally intensive statistical methods provides opportunities for rigorous analyses of environmental variability.     

The inheritance of morphological variation in Pileolaria pseudomilitaris (Polychaeta: Spirorbidae)

The genetic control of morphological variation (expressed as heritability) was examined by means of laboratory culture in Pileolaria pseudomilitaris. Fourteen of 22 traits examined were shown to have an appreciable genetic component, after an analysis of variance among groups of full siblings. The range of variability for several traits is as large within a single sibling group as the difference between described species in the family.
Comparisons among samples of P. pseudomilitaris from two habitats revealed no consistent morphological dillerences. A similar comparison between P. pseudomilitaris and its nearest congener, I', potswaldi , indicated significant differences for 15 of 22 traits, although ranges overlapped for all bin two of these.