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PubMed2003

Identifying differentially expressed genes using false discovery rate controlling procedures.

MOTIVATION: DNA microarrays have recently been used for the purpose of monitoring expression levels of thousands of genes simultaneously and identifying those genes that are differentially expressed. The probability that a false identification (type I error) is committed can increase sharply when the number of tested genes gets large. Correlation between the test statistics attributed to gene co-regulation and dependency in the measurement errors of the gene expression levels further complicates the problem. In this paper we address this very large multiplicity problem by adopting the false discovery rate (FDR) controlling approach. In order to address the dependency problem, we present three resampling-based FDR controlling procedures, that account for the test statistics distribution, and compare their performance to that of the naïve application of the linear step-up procedure in Benjamini and Hochberg (1995). The procedures are studied using simulated microarray data, and their performance is examined relative to their ease of implementation. RESULTS: Comparative simulation analysis shows that all four FDR controlling procedures control the FDR at the desired level, and retain substantially more power then the family-wise error rate controlling procedures. In terms of power, using resampling of the marginal distribution of each test statistics substantially improves the performance over the naïve one. The highest power is achieved, at the expense of a more sophisticated algorithm, by the resampling-based procedures that resample the joint distribution of the test statistics and estimate the level of FDR control. AVAILABILITY: An R program that adjusts p-values using FDR controlling procedures is freely available over the Internet at www.math.tau.ac.il/~ybenja.

Algorithms↗
PubMed1999

[Performance assessment of mammographic diagnostic systems: evolution of methods and their application to a digital image study].

INTRODUCTION: "Receiver Operating Characteristic" (ROC) curves are one of the most efficient analysis tools for the complete evaluation of a diagnostic system performance. However this method is limited in visualizing and locating abnormal structures, such as clusters of microcalcifications on mammographic images. Other more refined and complex techniques have also been suggested, where particular statistical hypotheses are assumed, namely the "Free-response ROC" (FROC), the "Alternative FROC" (AFROC) and the "Free-response Forced Error" (FFE) analyses. We studied the theoretical bases of these different methods and their experimental applications to assess the correctness of the hypothetical statistical distributions. MATERIAL AND METHODS: We considered two statistical hypotheses: first, that the false-positive response distribution follows the Poissonian statistics; second, that "signal" and "noise" distributions have a Gaussian trend with different means and variances. Thus, we applied the different methods to the responses given by 8 observers (5 radiologists and 3 medical physicists) who independently evaluated 3 digital mammographic samples. Every sample consisted of 39 images, with 1-15 clusters each (total: 100 clusters). The samples were obtained from 39 images available in an Internet database (sample 1); 2 different digital filters were applied to each image (samples 2 and 3). To collects responses, we provided for two phases: first, every observer visualized and located the clusters at a given confidence level; second, when a false-positive response was given, spontaneously or after forcing, the responses were ordered by decreasing conspicuity. Finally, data were analyzed with a "home-made" software by applying the FROC and AFROC analyses to the data collected in phase 1 and the FFE analysis to those collected in phase 2. RESULTS: We considered the area under the AFROC curve as the most important parameter: the values obtained with the 3 types of analysis are well in agreement within their uncertainties. In particular, the FROC-AFROC agreement did not exceed 5.9% (10 of 14 cases within 2.5%), while the FFE analysis had higher standard deviations associated with the area value (about 10%). The interpolated curves from both FROC and AFROC data were very similar. The three methods had various advantages: the FFE is very simple to calculate and makes the most of the information given by the observer; FROC and AFROC can provide true-positive and false-positive responses on the same image, which permits to optimize the evaluation of a diagnostic system performance. The statistical tools used in the simplest methods are usually integrated with the completeness characteristics of the location of multiple signals on mammograms. CONCLUSIONS: In theory, every method is necessary because it provides additional information to validate the statistical hypotheses under investigation. In fact, when the methods are used to evaluate and compare several diagnostic systems, the results of the three techniques are equivalent. Therefore, choosing a specific technique depends on both available resources and response type all the hypothetical statistical distributions in our study proved correct.

Mammography↗
PubMed2006

Extended bidirectional reflectance distribution function for polarized light scattering from subsurface defects under a smooth surface.

By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions.

Journal Article↗
PubMed2002

On the distribution of fast-phase intervals in optokinetic and vestibular nystagmus.

Histograms of fast-phase intervals in human optokinetic and vestibular nystagmus were generated, and fitted to statistical distributions used in previous studies. The distributions did not depend on stimulation type (optokinetic or vestibular). An inverse Gaussian or a gamma distribution fitted the data better than did a reciprocal Gaussian distribution, but none fitted the data especially well. In some cases, however, the interpretation of these distributions is more physiologically satisfactory than in others. Recommendations are made on which class of models is preferred, and the experiments needed to support the particular models. Our results call into question the validity of previous studies that fit statistical distributions to data sets of a size comparable to ours.

Adult↗
PubMed2003

Estimating the probability of recontamination via the air using Monte Carlo simulations.

Recontamination of food products can cause foodborne illnesses or spoilage of foods. It is therefore useful to quantify this recontamination so that it can be incorporated in microbiological risk assessments (MRA). This paper describes a first attempt to quantify one of the recontamination routes: via the air. Data on the number of airborne microorganisms were collected from literature and industries. The settling velocities of different microorganisms were calculated for different products by combining the data on aerial concentrations with sedimentation counts assuming that settling is under the influence of gravity only. Air movement is not explicitly considered in this study. Statistical analyses were performed to clarify the effect of different products and seasons on the number of airborne microorganisms and the settling velocity. For both bacteria and moulds, three significantly different product categories with regard to the level of airborne organisms were identified. The statistical distribution in these categories was described by a lognormal distribution. The settling velocity did not depend on the product, the season of sampling or the type of microorganism, and had a geometrical mean value of 2.7 mm/s. The statistical distribution of the settling velocity was described by a lognormal distribution as well. The probability of recontamination via the air was estimated by the product of the number of bacteria in the air, the settling velocity, and the exposed area and time of the product. For three example products, the contamination level as a result of airborne recontamination was estimated using Monte Carlo simulations. What-if scenarios were used to exemplify determination of design criteria to control a specified contamination level.

Air Microbiology↗
PubMed2002

Infant sensitivity to distributional information can affect phonetic discrimination.

For nearly two decades it has been known that infants' perception of speech sounds is affected by native language input during the first year of life. However, definitive evidence of a mechanism to explain these developmental changes in speech perception has remained elusive. The present study provides the first evidence for such a mechanism, showing that the statistical distribution of phonetic variation in the speech signal influences whether 6- and 8-month-old infants discriminate a pair of speech sounds. We familiarized infants with speech sounds from a phonetic continuum, exhibiting either a bimodal or unimodal frequency distribution. During the test phase, only infants in the bimodal condition discriminated tokens from the endpoints of the continuum. These results demonstrate that infants are sensitive to the statistical distribution of speech sounds in the input language, and that this sensitivity influences speech perception.

Attention↗
PubMed1993

Applications and statistics for multiple high-scoring segments in molecular sequences.

Score-based measures of molecular-sequence features provide versatile aids for the study of proteins and DNA. They are used by many sequence data base search programs, as well as for identifying distinctive properties of single sequences. For any such measure, it is important to know what can be expected to occur purely by chance. The statistical distribution of high-scoring segments has been described elsewhere. However, molecular sequences will frequently yield several high-scoring segments for which some combined assessment is in order. This paper describes the statistical distribution for the sum of the scores of multiple high-scoring segments and illustrates its application to the identification of possible transmembrane segments and the evaluation of sequence similarity.

Amino Acid Sequence↗
PubMed1995

Comparison between the phi distribution of the amino acids in the protein database and NMR data indicates that amino acids have various phi propensities in the random coil conformation.

It has been indicated that amino acids have various intrinsic phi and psi propensities, as demonstrated from the comparison between experimental secondary structure propensities and their relative statistical distribution in the protein database for the appropriate region of the Ramachandran plot. However, this does not eliminate the possibility that these experimental propensities are the result of context effects due to the secondary structure environment of the mutated position. To demonstrate that there are at least real intrinsic phi propensities, independent of context effects, we have used two different nuclear magnetic resonance parameters related to the phi dihedral angle (J3 alpha HN coupling constants and the chemical shift of the C alpha H proton), determined in random-coil tetra- and pentapeptides, and/or in proteins. Comparison of the experimentally determined values for these parameters with the theoretical ones determined from the analysis by different empirical and theoretical equations of the phi dihedral angle statistical distribution of the amino acids in the protein database, supports the idea that each amino acid has, at least, different phi intrinsic propensities. Consideration of all conformations, or only coil conformations, in the protein database produces similar results. The reasonable correlation between these experimental and theoretical data and the hydrogen-exchange data in random-coil peptides suggests that maximisation of hydrophobic surface-buried and hydrogen-bond formation with the solvent could be responsible for these different random-coil conformational preferences. Analysis of the intrinsic propensities for beta-strand, alpha-helix and polyproline II dihedral angles of the 20 amino acids in coil conformations, indicates that the side-chain of the amino acids is mainly determining the relative preferences for the phi angle.

Amino Acids↗
PubMed1988

Exposure to agricultural treatment residues: some simple statistical considerations based on monitoring data for ethoxyquin on apples.

The data examined here concern ethoxyquin levels, mainly measured in apple samples from the retail market. In this study about three hundred measurements, carried out on apples in Northern-Central Italy and recently published, are examined, with the purpose of defining the main characteristics of value statistical distribution and variability and to optimize sampling criteria. The analysis did not indicate the presence of significantly high levels or consequently significantly high risks; nevertheless, it pointed out some important aspects in data collection and evaluation. First, it appeared that the statistical distribution of data is typically nonsymmetrical, non-Gaussian, and characterized by a tail extending toward the high values. The logarithmic transformation of data appeared useful in order to obtain a Gaussian distribution. As a rule, the data variability appeared to be high. The frequency and distribution of values above the analytical threshold resulted in significant change, both in time and in space. The percentage of positive values (above the analytical threshold) appeared to vary up to a factor of 2-3, as analogously did their geometric mean.(ABSTRACT TRUNCATED AT 250 WORDS)

Environmental Monitoring↗
PubMed2001

Information tools for exploratory data analysis in population pharmacokinetics.

For a group of individuals, population pharmacokinetic studies describe the interindividual variability through a statistical distribution. These studies conducted during the drug development serve as a useful marker of the safety of the drug, provide information that might be decisive for future experiments and, in a clinical context, help establish guidelines for optimal use in each patient. As complementary tools to the existing statistical and graphical techniques for population pharmacokinetic data analysis, indexes derived from information theory were used to select the most appropriate modelfor the statistical distribution, to detect atypical individuals, and to screen influential covariates. The rationale for using these indexes is shown using simulated and real data.

Humans↗
PubMed1983

Artificial neural nets: dependence of the EEG amplitude's probability distribution on statistical parameters.

The statistical laws governing the output of a population of unitary generators are not explicit with regard to the effect of population size and properties of the individual generators on the summed activity. Experimental work was therefore undertaken with artificial nerve nets, the activity of which simulates with a high degree of realism individual nerve cells and the electroencephalogram. It was found that the summed activity is not affected by the statistical properties of single generators even in nets of only 200-1000 elements. On the other hand, the output of the net is highly sensitive to the level of connectivity between individual generators. When connectivity is low, the summed output is distributed in normal (Gaussian) fashion. The output of the net becomes less and less Gaussian with increase in coupling between the generators.

Animals↗
PubMed1992

Quantification of biological variability.

Pharmacokinetic models are usually developed to describe the kinetic behaviour of the chemical compounds in an average human body. There are however many situations were the effects of variations in a given pharmacokinetic parameter would be of interest. For example, in biological monitoring, the variability of biological data is a critical parameter when relating air and biological measures of an individual exposure. This paper reviews two possible approaches for the simulation of such variability in occupational pharmacokinetics. In the first, a simple one-compartment model is used together with statistical distributions for the intake and elimination of the compounds involved. Based on realistic distributions, this simple model is applied to the comparison of biological and air monitoring to estimate workers' exposure. The second involves a seven-compartment physiologically based pharmacokinetic model, which includes provision of the means to input satistical distributions for some of the parameters: exposures, physical workload, body height, body weight, liver function and renal function. It makes it possible to predict the pharmacokinetic response of groups of workers, who differ in their exposures and in their physiological parameters. Realistic statistical distributions are then used to describe biological monitoring variability. The advantages and disadvantages of both the simple pharmacokinetic model and the physiological model are discussed in the context of predicting and understanding variability in occupational situations. Other potential developments are also considered.

Environmental Monitoring↗
PubMed1990

Human choriogonadotropin (hCG): comparisons between determinations of intact hCG, free hCG beta-subunit, and "total" hCG + beta in serum during the first half of high-risk pregnancy.

We have studied the concentrations of intact human choriogonadotropin (hCG) and the free hCG beta-subunit in blood samples from singleton pregnancies at risk for habitual or threatened abortion. The samples were obtained weekly between the 6th and 12th weeks and in the 14th and 16th weeks of gestational age. The concentrations of intact hCG, of the free hCG beta-subunit, and of "total" hCG (i.e., intact hCG and the free hCG beta-subunit: hCG + beta) were measured in serum by specific immunoassays. The distributional statistics (the 5th, 50th, and 95th percentiles) of "total" hCG + beta and of intact hCG showed very similar patterns, whereas the response curves for the free hCG beta-subunit showed very much lower serum concentrations. From these data we also estimated distributional statistics of the percent molar ratios of free hCG beta-subunit to intact hCG. We conclude that (a) the relatively small proportion of free hCG beta-subunit in serum during the first half of singleton pregnancy is far too low to interfere with the applied "total" hCG assay, as compared with the serum values obtained for intact hCG, and (b) the percent molar ratios of free hCG beta-subunit to intact hCG, or to "total" hCG + beta, never exceeded 1.0% throughout the period of pregnancy studied.

Abortion, Threatened↗
PubMed2005

How effective for fold recognition is a potential of mean force that includes relative orientations between contacting residues in proteins?

We estimate the statistical distribution of relative orientations between contacting residues from a database of protein structures and evaluate the potential of mean force for relative orientations between contacting residues. Polar angles and Euler angles are used to specify two degrees of directional freedom and three degrees of rotational freedom for the orientation of one residue relative to another in contacting residues, respectively. A local coordinate system affixed to each residue based only on main chain atoms is defined for fold recognition. The number of contacting residue pairs in the database will severely limit the resolution of the statistical distribution of relative orientations, if it is estimated by dividing space into cells and counting samples observed in each cell. To overcome such problems and to evaluate the fully anisotropic distributions of relative orientations as a function of polar and Euler angles, we choose a method in which the observed distribution is represented as a sum of delta functions each of which represents the observed orientation of a contacting residue, and is evaluated as a series expansion of spherical harmonics functions. The sample size limits the frequencies of modes whose expansion coefficients can be reliably estimated. High frequency modes are statistically less reliable than low frequency modes. Each expansion coefficient is separately corrected for the sample size according to suggestions from a Bayesian statistical analysis. As a result, many expansion terms can be utilized to evaluate orientational distributions. Also, unlike other orientational potentials, the uniform distribution is used for a reference distribution in evaluating a potential of mean force for each type of contacting residue pair from its orientational distribution, so that residue-residue orientations can be fully evaluated. It is shown by using decoy sets that the discrimination power of the orientational potential in fold recognition increases by taking account of the Euler angle dependencies and becomes comparable to that of a simple contact potential, and that the total energy potential taken as a simple sum of contact, orientation, and (phi,psi) potentials performs well to identify the native folds.

Journal Article↗
PubMed1999

Incubation period of Creutzfeldt-Jakob disease in human growth hormone recipients in France.

OBJECTIVE: To estimate the statistical distribution of the incubation period of Creutzfeldt-Jakob disease (CJD) in human growth hormone (hGH) recipients in France. BACKGROUND: Published papers suggest that the median incubation period of hGH-related CJD is approximately 15 years, but there are as yet no statistical data that support this assertion. METHODS: Of the 1,361 hGH recipients who were included in this study, 55 had developed CJD at the time of the study. Individual data on hGH treatment history were available. Different mathematical models were used to estimate the statistical distribution of the incubation period. One main feature of the models was to take into account the occurrence of future CJD cases. RESULTS: Models showed that the mean incubation period was 9 to 10 years, and the 95th percentile of the distribution was 15 to 16 years. Data and models indicated that the incubation period was significantly shorter in homozygotes at codon 129 of the prion protein gene than in heterozygotes. CONCLUSIONS: The short mean incubation period of CJD in French hGH recipients may be due to high infectivity in hormone lots. Estimates of the 95th percentile indicate that the number of hGH-related CJD cases may continue to increase in the coming years.

Creutzfeldt-Jakob Syndrome↗
PubMed1982

CD and 1H-n.m.r. studies on the side-chain conformation of tyrosine derivatives and tyrosine residues in di- and tripeptides.

Tyrosine, tyrosine peptides and derivatives, in total 11 species, were selected as models for the study of optical properties (1Lb band of phenolic group) and side-chain arrangement (rotamers around C alpha-C beta bond) of tyrosine as a function of chemical structure and pH effects. Circular dichroism spectra between 240 and 320 nm and n.m.r. spectra were recorded for the different ionization states. Results are discussed in terms of charge effects from N- and C-terminal groups and local conformation influence on 1Lb band of the phenolic chromophore and on distribution of rotamer populations in side-chain of tyrosine. Fractions of rotamer populations were estimated from alpha-beta proton-proton coupling constants and, in the cases of tyrosine and N-acetyl-tyrosine, from 15N-beta nitrogen-proton coupling constants, which allow the stereospecific assignment of the beta and beta' protons. The rotamer populations of tyrosine, averaged from all the data of the samples In solution, were then compared with their statistical distribution in th solid state. Interestingly, agreement is excellent when we refer to crystal of tyrosine, tyrosine derivatives or small peptides (31 samples) and poor in the case of proteins. This leads to a discussion on both the validity of using statistical distributions of rotamers in proteins as reference for rotamer preferences inside small peptides in solution and the choice of the appropriate Jg and Jt values in Pachler's approach. The possible existence of a correlation between ellipticity and rotamer populations for such samples is examined.

Circular Dichroism↗
PubMed2006

Solid-state NMR analysis of a peptide (Gly-Pro-Gly-Gly-Ala)6-Gly derived from a flagelliform silk sequence of Nephila clavipes.

Solid-state NMR is especially useful when the structures of peptides and proteins should be analyzed by taking into account the structural distribution, that is, the distribution of the torsion angle of the individual residue. In this study, two-dimensional spin-diffusion solid-state NMR spectra of 13C-double-labeled model peptides (GPGGA)6G of flagelliform silk were observed for studying the local structure in the solid state. The spin-diffusion NMR spectra calculated by assuming the torsion angles of the beta-spiral structure exclusively could not reproduce the observed spectra. In contrast, the spectra calculated by taking into account the statistical distribution of the torsion angles of the individual central residues in the sequences Ala-Gly-Pro, Gly-Pro-Gly, Pro-Gly-Gly, Gly-Gly-Ala, and Gly-Ala-Gly from PDB data could reproduce the observed spectra well. This indicates that the statistical distribution of the torsion angles should be considered for the structural model of (GPGGA)6G similar to the case of the model peptide of elastin.

Animals↗