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PubMed2001

Statistical estimation of cluster boundaries in gene expression profile data.

MOTIVATION: Gene expression profile data are rapidly accumulating due to advances in microarray techniques. The abundant data are analyzed by clustering procedures to extract the useful information about the genes inherent in the data. In the clustering analyses, the systematic determination of the boundaries of gene clusters, instead of by visual inspection and biological knowledge, still remains challenging. RESULTS: We propose a statistical procedure to estimate the number of clusters in the hierarchical clustering of the expression profiles. Following the hierarchical clustering, the statistical property of the profiles at the node in the dendrogram is evaluated by a statistics-based value: the variance inflation factor in the multiple regression analysis. The evaluation leads to an automatic determination of the cluster boundaries without any additional analyses and any biological knowledge of the measured genes. The performance of the present procedure is demonstrated on the profiles of 2467 yeast genes, with very promising results. AVAILABILITY: A set of programs will be electronically sent upon request. CONTACT: horimoto@post.saga-med.ac.jp; toh@beri.co.jp

Analysis of Variance↗
PubMed2002

Statistical analysis of a small set of time-ordered gene expression data using linear splines.

MOTIVATION: Recently, the temporal response of genes to changes in their environment has been investigated using cDNA microarray technology by measuring the gene expression levels at a small number of time points. Conventional techniques for time series analysis are not suitable for such a short series of time-ordered data. The analysis of gene expression data has therefore usually been limited to a fold-change analysis, instead of a systematic statistical approach. METHODS: We use the maximum likelihood method together with Akaike's Information Criterion to fit linear splines to a small set of time-ordered gene expression data in order to infer statistically meaningful information from the measurements. The significance of measured gene expression data is assessed using Student's t-test. RESULTS: Previous gene expression measurements of the cyanobacterium Synechocystis sp. PCC6803 were reanalyzed using linear splines. The temporal response was identified of many genes that had been missed by a fold-change analysis. Based on our statistical analysis, we found that about four gene expression measurements or more are needed at each time point.

Algorithms↗
PubMed2002

A conditional density error model for the statistical analysis of microarray data.

MOTIVATION: In many microarray experiments, relatively few intra- and inter-array replicate measurements are made due to significant cost limitations and sample availability. Compounding this problem is a lack of robust statistical methods for analyzing gene expression data with limited experimental replicates. As a result, the interpretation of the results of these experiments are difficult with little understanding of the probability of type I and type II errors. RESULTS: The variability in a series of replicate microarray measurements was modelled using a combination of parametric and non-parametric methods. A 3-dimensional surface was created for the conditional distribution of the variability given the mean signal intensity in both the Cy3 and Cy5 channels. The results were used as the basis for developing statistical methods for analyzing gene expression data with limited experimental replicates. AVAILABILITY: The statistical analysis scripts are available upon request.

Computer Simulation↗
PubMed2003

Statistical evaluation of the Predictive Toxicology Challenge 2000-2001.

MOTIVATION: The development of in silico models to predict chemical carcinogenesis from molecular structure would help greatly to prevent environmentally caused cancers. The Predictive Toxicology Challenge (PTC) competition was organized to test the state-of-the-art in applying machine learning to form such predictive models. RESULTS: Fourteen machine learning groups generated 111 models. The use of Receiver Operating Characteristic (ROC) space allowed the models to be uniformly compared regardless of the error cost function. We developed a statistical method to test if a model performs significantly better than random in ROC space. Using this test as criteria five models performed better than random guessing at a significance level p of 0.05 (not corrected for multiple testing). Statistically the best predictor was the Viniti model for female mice, with p value below 0.002. The toxicologically most interesting models were Leuven2 for male mice, and Kwansei for female rats. These models performed well in the statistical analysis and they are in the middle of ROC space, i.e. distant from extreme cost assumptions. These predictive models were also independently judged by domain experts to be among the three most interesting, and are believed to include a small but significant amount of empirically learned toxicological knowledge. AVAILABILITY: PTC details and data can be found at: http://www.predictive-toxicology.org/ptc/.

Algorithms↗
PubMed2003

Comparison of statistical methods for classification of ovarian cancer using mass spectrometry data.

MOTIVATION: Novel methods, both molecular and statistical, are urgently needed to take advantage of recent advances in biotechnology and the human genome project for disease diagnosis and prognosis. Mass spectrometry (MS) holds great promise for biomarker identification and genome-wide protein profiling. It has been demonstrated in the literature that biomarkers can be identified to distinguish normal individuals from cancer patients using MS data. Such progress is especially exciting for the detection of early-stage ovarian cancer patients. Although various statistical methods have been utilized to identify biomarkers from MS data, there has been no systematic comparison among these approaches in their relative ability to analyze MS data. RESULTS: We compare the performance of several classes of statistical methods for the classification of cancer based on MS spectra. These methods include: linear discriminant analysis, quadratic discriminant analysis, k-nearest neighbor classifier, bagging and boosting classification trees, support vector machine, and random forest (RF). The methods are applied to ovarian cancer and control serum samples from the National Ovarian Cancer Early Detection Program clinic at Northwestern University Hospital. We found that RF outperforms other methods in the analysis of MS data.

Algorithms↗
PubMed2004

Comparison of Li-Wong and loglinear mixed models for the statistical analysis of oligonucleotide arrays.

MOTIVATION: Li and Wong have described some useful statistical models for probe-level, oligonucleotide array data based on a multiplicative parametrization. In earlier work, we proposed similar analysis-of-variance-style mixed models fit on a log scale. With only subtle differences in the specification of their mean and stochastic error components, a question arises as to whether these models could lead to varying conclusions in practical application. RESULTS: In this paper, we provide an empirical comparison of the two models using a real data set, and find the models perform quite similarly across most genes, but with some interesting and important distinctions. We also present results from a simulation study designed to assess inferential properties of the models, and propose a modified test statistic for the Li-Wong model that provides an improvement in Type 1 error control. Advantages of both methods include the ability to directly assess and account for key sources of variability in the chip data and a means to automate statistical quality control.

Algorithms↗
PubMed2005

Statistics of local multiple alignments.

SUMMARY: BLAST statistics have been shown to be extremely useful for searching for significant similarity hits, for amino acid and nucleotide sequences. Although these statistics are well understood for pairwise comparisons, there has been little success developing statistical scores for multiple alignments. In particular, there is no score for multiple alignment that is well founded and treated as a standard. We extend the BLAST theory to multiple alignments. Following some simple assumptions, we present and justify a significance score for multiple segments of a local multiple alignment. We demonstrate its usefulness in distinguishing high and moderate quality multiple alignments from low quality ones, with supporting experiments on orthologous vertebrate promoter sequences.

Algorithms↗
PubMed2005

A model-based scan statistic for identifying extreme chromosomal regions of gene expression in human tumors.

MOTIVATION: The analysis of gene expression data in its chromosomal context has been a recent development in cancer research. However, currently available methods fail to account for variation in the distance between genes, gene density and genomic features (e.g. GC content) in identifying increased or decreased chromosomal regions of gene expression. RESULTS: We have developed a model-based scan statistic that accounts for these aspects of the complex landscape of the human genome in the identification of extreme chromosomal regions of gene expression. This method may be applied to gene expression data regardless of the microarray platform used to generate it. To demonstrate the accuracy and utility of this method, we applied it to a breast cancer gene expression dataset and tested its ability to predict regions containing medium-to-high level DNA amplification (DNA ratio values >2). A classifier was developed from the scan statistic results that had a 10-fold cross-validated classification rate of 93% and a positive predictive value of 88%. This result strongly suggests that the model-based scan statistic and the expression characteristics of an increased chromosomal region of gene expression can be used to accurately predict chromosomal regions containing amplified genes. AVAILABILITY: Functions in the R-language are available from the author upon request. CONTACT: fcouples@umich.edu.

Base Composition↗
PubMed2005

Convergent Island Statistics: a fast method for determining local alignment score significance.

MOTIVATION: Background distribution statistics for profile-based sequence alignment algorithms cannot be calculated analytically, and hence such algorithms must resort to measuring the significance of an alignment score by assessing its location among a distribution of background alignment scores. The Gumbel parameters that describe this background distribution are usually pre-computed for a limited number of scoring systems, gap schemes, and sequence lengths and compositions. The use of such look-ups is known to introduce errors, which compromise the significance assessment of a remote homology relationship. One solution is to estimate the background distribution for each pair of interest by generating a large number of sequence shuffles and use the distribution of their scores to approximate the parameters of the underlying extreme value distribution. This is computationally very expensive, as a large number of shuffles are needed to precisely estimate the score statistics. RESULTS: Convergent Island Statistics (CIS) is a computationally efficient solution to the problem of calculating the Gumbel distribution parameters for an arbitrary pair of sequences and an arbitrary set of gap and scoring schemes. The basic idea behind our method is to recognize the lack of similarity for any pair of sequences early in the shuffling process and thus save on the search time. The method is particularly useful in the context of profile-profile alignment algorithms where the normalization of alignment scores has traditionally been a challenging task. CONTACT: aleksandar@eidogen.com SUPPLEMENTARY INFORMATION: http://www.eidogen-sertanty.com/Documents/convergent_island_stats_sup.pdf.

Algorithms↗
PubMed2005

Statistical analysis of antigen receptor spectratype data.

MOTIVATION: The effectiveness of vertebrate adaptive immunity depends crucially on the establishment and maintenance of extreme diversity in the antigen receptor repertoire. Spectratype analysis is a method used in clinical and basic immunological settings in which antigen receptor length diversity is assessed as a surrogate for functional diversity. The purpose of this paper is to describe the systematic derivation and application of statistical methods for the analysis of spectratype data. RESULTS: The basic probability model used for spectratype analysis is the multinomial model with n, the total number of counts, indeterminate. We derive the appropriate statistics and statistical procedures for testing hypotheses regarding differences in antigen receptor distributions and variable repertoire diversity in different treatment groups. We then apply these methods to spectratype data obtained from several healthy donors to examine the differences between normal CD4+ and CD8+ T cell repertoires, and to data from a thymus transplant patient to examine the development of repertoire diversity following the transplant.

Algorithms↗
PubMed2005

Robust accurate identification of peptides (RAId): deciphering MS2 data using a structured library search with de novo based statistics.

MOTIVATION: The key to MS -based proteomics is peptide sequencing. The major challenge in peptide sequencing, whether library search or de novo, is to better infer statistical significance and better attain noise reduction. Since the noise in a spectrum depends on experimental conditions, the instrument used and many other factors, it cannot be predicted even if the peptide sequence is known. The characteristics of the noise can only be uncovered once a spectrum is given. We wish to overcome such issues. RESULTS: We designed RAId to identify peptides from their associated tandem mass spectrometry data. RAId performs a novel de novo sequencing followed by a search in a peptide library that we created. Through de novo sequencing, we establish the spectrum-specific background score statistics for the library search. When the database search fails to return significant hits, the top-ranking de novo sequences become potential candidates for new peptides that are not yet in the database. The use of spectrum-specific background statistics seems to enable RAId to perform well even when the spectral quality is marginal. Other important features of RAId include its potential in de novo sequencing alone and the ease of incorporating post-translational modifications.

Algorithms↗
PubMed2006

Software for dynamic analysis of tracer-based metabolomic data: estimation of metabolic fluxes and their statistical analysis.

MOTIVATION: Metabolic flux analysis of biochemical reaction networks using isotope tracers requires software tools that can analyze the dynamics of isotopic isomer (isotopomer) accumulation in metabolites and reveal the underlying kinetic mechanisms of metabolism regulation. Since existing tools are restricted by the isotopic steady state and remain disconnected from the underlying kinetic mechanisms, we have recently developed a novel approach for the analysis of tracer-based metabolomic data that meets these requirements. The present contribution describes the last step of this development: implementation of (i) the algorithms for the determination of the kinetic parameters and respective metabolic fluxes consistent with the experimental data and (ii) statistical analysis of both fluxes and parameters, thereby lending it a practical application. RESULTS: The C++ applications package for dynamic isotopomer distribution data analysis was supplemented by (i) five distinct methods for resolving a large system of differential equations; (ii) the 'simulated annealing' algorithm adopted to estimate the set of parameters and metabolic fluxes, which corresponds to the global minimum of the difference between the computed and measured isotopomer distributions; and (iii) the algorithms for statistical analysis of the estimated parameters and fluxes, which use the covariance matrix evaluation, as well as Monte Carlo simulations. An example of using this tool for the analysis of (13)C distribution in the metabolites of glucose degradation pathways has demonstrated the evaluation of optimal set of parameters and fluxes consistent with the experimental pattern, their range and statistical significance, and also the advantages of using dynamic rather than the usual steady-state method of analysis. AVAILABILITY: Software is available free from http://www.bq.ub.es/bioqint/selivanov.htm

Algorithms↗
PubMed1989

Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.

The relationship between the two estimates of genetic variation at the DNA level, namely the number of segregating sites and the average number of nucleotide differences estimated from pairwise comparison, is investigated. It is found that the correlation between these two estimates is large when the sample size is small, and decreases slowly as the sample size increases. Using the relationship obtained, a statistical method for testing the neutral mutation hypothesis is developed. This method needs only the data of DNA polymorphism, namely the genetic variation within population at the DNA level. A simple method of computer simulation, that was used in order to obtain the distribution of a new statistic developed, is also presented. Applying this statistical method to the five regions of DNA sequences in Drosophila melanogaster, it is found that large insertion/deletion (greater than 100 bp) is deleterious. It is suggested that the natural selection against large insertion/deletion is so weak that a large amount of variation is maintained in a population.

Animals↗
PubMed1996

New statistical tests of neutrality for DNA samples from a population.

The purpose of this paper is to develop statistical tests of the neutral model of evolution against a class of alternative models with the common characteristic of having an excess of mutations that occurred a long time ago or a reduction of recent mutations compared to the neutral model. This class of population genetics models include models for structured populations, models with decreasing effective population size and models of selection and mutation balance. Four statistical tests were proposed in this paper for DNA samples from a population. Two of these tests, one new and another a modification of an existing test, are based on EWENS' sampling formula, and the other two new tests make use of the frequencies of mutations of various classes. Using simulated samples and regression analyses, the critical values of these tests can be computed from regression equations. This approach for computing the critical values of a test was found to be appropriate and quite effective. We examined the powers of these four tests using simulated samples from structured populations, populations with linearly decreasing sizes and models of selection and mutation balance and found that they are more powerful than existing statistical tests of the neutral model of evolution.

Biological Evolution↗
PubMed2001

A statistical framework for quantitative trait mapping.

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.

Algorithms↗
PubMed2003

A general statistical framework for mapping quantitative trait loci in nonmodel systems: issue for characterizing linkage phases.

Because of uncertainty about linkage phases of founders, linkage mapping in nonmodel, outcrossing systems using molecular markers presents one of the major statistical challenges in genetic research. In this article, we devise a statistical method for mapping QTL affecting a complex trait by incorporating all possible QTL-marker linkage phases within a mapping framework. The advantage of this model is the simultaneous estimation of linkage phases and QTL location and effect parameters. These estimates are obtained through maximum-likelihood methods implemented with the EM algorithm. Extensive simulation studies are performed to investigate the statistical properties of our model. In a case study from a forest tree, this model has successfully identified a significant QTL affecting wood density. Also, the probability of the linkage phase between this QTL and its flanking markers is estimated. The implications of our model and its extension to more general circumstances are discussed.

Chromosome Mapping↗
PubMed1989

An 'electronic' extramural course in epidemiology and medical statistics.

This article describes an extramural university course in epidemiology and medical statistics taught using a computer conferencing system, microcomputers and data communications. Computer conferencing was shown to be a powerful, yet quite easily mastered, vehicle for distance education. It allows health personnel unable to attend regular classes due to geographical or time constraints, to take part in an interactive learning environment at low cost. This overcomes part of the intellectual and social isolation associated with traditional correspondence courses. Teaching of epidemiology and medical statistics is well suited to computer conferencing, even if the asynchronicity of the medium makes discussion of the most complex statistical concepts a little cumbersome. Computer conferencing may also prove to be a useful tool for teaching other medical and health related subjects.

Computer Communication Networks↗
PubMed1985

Statistical analysis of molecular genetic data.

Recent advances in molecular biology have made it possible for geneticists to collect data at the DNA sequence level, and so make observations on genes directly, instead of on characters affected by genes. This new nature of genetic data is posing new problems of statistical analyses, as is shown in this paper. After an explanation of the methodology of recombinant DNA studies, separate consideration is given to the statistical analyses of restriction-map and complete-sequence data. The initial observations from restriction-enzyme studies are of the number and sizes of the fragments produced by digesting a DNA region with the enzymes, and it is necessary to infer the location of the breakage points. Model-based analyses are then necessary to infer characteristics of the DNA sequence from the frequency of these break points. An important application of such restriction maps is the detection of human disease genes, with the most notable success to date being the chromosomal allocation of the gene for Huntington's chorea. Complete sequence data present conflicting problems of scale. The amount of information collected per individual is so large that analyses must always be done on a computer, but the number of individuals studied in a population is too low to allow the magnitudes of between- and within-population variation to be assessed. Statistical problems also include the detection and testing of sequence patterns and the comparison of sequences. Any analyses are going to have to incorporate the observed high levels of association between adjacent sequence members. While national data bases now contain about three million sequence elements, very little is known about the error rate in the generation or recording of these sequences.

DNA↗