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PubMed2005

Whole-body dosimetry for targeted radionuclide therapy using spectral analysis.

The whole-body dose (WBD) is routinely calculated for targeted radionuclide therapy (TRT). The aim of this work was to investigate the feasibility of using spectral analysis (SA) for the automatic delineation of decay phases, and consequently, the calculation of the WBD given a whole-body (WB) time-activity curve (TAC). SA characterizes the TAC as an arbitrary sum of exponential functions determined by fitting the data with a non-negative least-squares (NNLS) algorithm. The cumulated activity (CA) is calculated analytically as the integral of the fitted curve while the number of phases describing the kinetics of the radiopharmaceutical and the half-lives of the phases can be determined from the spectrum. The uncertainty associated with the estimation of the WBD can be obtained using bootstrap techniques. SA was applied to WB TACs from (186)Re-HEDP and (131)I-mIBG therapies. The results were compared to results obtained using a semiempirical method and showed good agreement in the calculated WBDs. Bootstrapping with resampling on a subset of patients from the two therapies showed much larger coefficient-ofvariation (CV) for the (186)Re-HEDP TACs than for the (131)I-mIBG therapies. We concluded that SA provides a fast, accurate, and reproducible method to obtain WBDs and accurate estimates of the parameters describing the radiotracer kinetics. The method could be extended to other dosimetric applications.

Algorithms↗

PubMed1997

Biochemical markers as additional measurements in dietary validity studies: application of the method of triads with examples from the European Prospective Investigation into Cancer and Nutrition.

The validity coefficient of dietary questionnaire measurements can be estimated from a triangular comparison between questionnaire, reference, and biochemical marker measurements with the method of triads. The method assumes that the measurements are linearly related to true intake and have independent random errors. We applied the method of triads to examples from the European Prospective Investigation into Cancer and Nutrition. In some examples, Heywood cases occurred, ie, the estimated validity coefficients were > 1 or the validity coefficients were not estimable. Such results are caused by random sampling fluctuations or violation of the model assumptions. One possible violation is a positive correlation between the random errors of questionnaire and reference measurements. We used a bootstrap method to estimate CIs for the validity coefficients. Validity studies with several hundred subjects, more accurate biochemical indicators of dietary intake, or both, are needed to estimate validity coefficients precisely and avoid complications with the bootstrap method.

Biomarkers↗

PubMed2000

Neural network schemes for detecting rare events in human genomic DNA.

MOTIVATION: Many problems in molecular biology as well as other areas involve detection of rare events in unbalanced data. We develop two sample stratification schemes in conjunction with neural networks for rare event detection in such databases. Sample stratification is a technique for making each class in a sample have equal influence on decision making. The first scheme proposed stratifies a sample by adding up the weighted sum of the derivatives during the backward pass of training. The second scheme proposed uses a technique of modified bootstrap aggregating. After training neural networks with multiple sets of bootstrapped examples of the rare event classes and subsampled examples of common event classes, multiple voting for classification is performed. RESULTS: These two schemes make rare event classes have a better chance of being included in the sample used for training neural networks and thus improve the classification accuracy for rare event detection. The experimental performance of the two schemes using two sets of human DNA sequences as well as another set of Gaussian data indicates that proposed schemes have the potential of significantly improving accuracy of neural networks to recognize rare events.

Algorithms↗

PubMed2001

CONSEL: for assessing the confidence of phylogenetic tree selection.

UNLABELLED: CONSEL is a program to assess the confidence of the tree selection by giving the p-values for the trees. The main thrust of the program is to calculate the p-value of the Approximately Unbiased (AU) test using the multi-scale bootstrap technique. This p-value is less biased than the other conventional p-values such as the Bootstrap Probability (BP), the Kishino-Hasegawa (KH) test, the Shimodaira-Hasegawa (SH) test, and the Weighted Shimodaira-Hasegawa (WSH) test. CONSEL calculates all these p-values from the output of the phylogeny program packages such as Molphy, PAML, and PAUP*. Furthermore, CONSEL is applicable to a wide class of problems where the BPs are available. AVAILABILITY: The programs are written in C language. The source code for Unix and the executable binary for DOS are found at http://www.ism.ac.jp/~shimo/ CONTACT: shimo@ism.ac.jp

Likelihood Functions↗

PubMed2002

Automated ortholog inference from phylogenetic trees and calculation of orthology reliability.

MOTIVATION: Orthologous proteins in different species are likely to have similar biochemical function and biological role. When annotating a newly sequenced genome by sequence homology, the most precise and reliable functional information can thus be derived from orthologs in other species. A standard method of finding orthologs is to compare the sequence tree with the species tree. However, since the topology of phylogenetic tree is not always reliable one might get incorrect assignments. RESULTS: Here we present a novel method that resolves this problem by analyzing a set of bootstrap trees instead of the optimal tree. The frequency of orthology assignments in the bootstrap trees can be interpreted as a support value for the possible orthology of the sequences. Our method is efficient enough to analyze data in the scale of whole genomes. It is implemented in Java and calculates orthology support levels for all pairwise combinations of homologous sequences of two species. The method was tested on simulated datasets and on real data of homologous proteins.

Algorithms↗

PubMed1992

MacT: Apple Macintosh programs for constructing phylogenetic trees.

MacT is a set of programs for the Apple Macintosh to construct and evaluate unrooted trees derived from amino acid sequences using a distance matrix method. Programs are designed on a 'one program--one task' basis for (i) determining the branching order in trees consisting of four or five species and calculating various statistical measures, (ii) calculating statistical measures for all possible topologies of unrooted trees and (iii) generating and evaluating trees derived from bootstrapped samples. With four auxiliary programs unrooted trees can be built for maximal 26 species, and the robustness of topologies be tested by bootstrapping.

Algorithms↗

PubMed2004

Is cross-validation valid for small-sample microarray classification?

MOTIVATION: Microarray classification typically possesses two striking attributes: (1) classifier design and error estimation are based on remarkably small samples and (2) cross-validation error estimation is employed in the majority of the papers. Thus, it is necessary to have a quantifiable understanding of the behavior of cross-validation in the context of very small samples. RESULTS: An extensive simulation study has been performed comparing cross-validation, resubstitution and bootstrap estimation for three popular classification rules-linear discriminant analysis, 3-nearest-neighbor and decision trees (CART)-using both synthetic and real breast-cancer patient data. Comparison is via the distribution of differences between the estimated and true errors. Various statistics for the deviation distribution have been computed: mean (for estimator bias), variance (for estimator precision), root-mean square error (for composition of bias and variance) and quartile ranges, including outlier behavior. In general, while cross-validation error estimation is much less biased than resubstitution, it displays excessive variance, which makes individual estimates unreliable for small samples. Bootstrap methods provide improved performance relative to variance, but at a high computational cost and often with increased bias (albeit, much less than with resubstitution).

Algorithms↗

PubMed2005

DNA assembly with gaps (Dawg): simulating sequence evolution.

MOTIVATION: Relationships amongst taxa are inferred from biological data using phylogenetic methods and procedures. Very few known phylogenies exist against which to test the accuracy of our inferences. Therefore, in the absence of biological data, simulated data must be used to test the accuracy of methods which produce these inferences. Researchers have limited or non-existent options for simulations useful for studying the impact of insertions, deletions, and alignments on phylogenetic accuracy. RESULTS: To satisfy this gap I have developed a new algorithm of indel formation and incorporated it into a new, flexible, and portable application for sequence simulation. The application, called Dawg, simulates phylogenetic evolution of DNA sequences in continuous time using the robust general time reversible model with gamma and invariant rate heterogeneity and a novel length-dependent model of indel formation. On completion, Dawg produces the true alignment of the simulated sequences. Unlike other applications, Dawg allows indel lengths to be explicitly distributed via a biologically realistic power law. Many options are available to allow users to customize their simulations and results. Because simulating with indels would be problematic if biologically realistic parameters could not be estimated, a script is provided with Dawg that can estimate the parameters of indel formation from sequence data. Dawg was applied to the sequences of four chloroplast trnK introns. It was used to parametrically bootstrap an estimation of the rate of indel formation for the phylogeny. Because Dawg can assist in parametric bootstrapping of sequence data it is useful beyond phylogenetics, such as studying alignment algorithms or parameters of molecular evolution. AVAILABILITY: Dawg 1.0.0 can be obtained at the following websites: http://www.genetics.uga.edu/sw/ or http://scit.us/dawg/. The package includes source code, example files, a brief manual and helper scripts. Binary distributions are available for Windows and Macintosh OS X. A development page for Dawg exists at http://scit.us/dawg/, with links to a Subversion repository, mailing lists and updated versions.

Base Sequence↗

PubMed2005

Differential and trajectory methods for time course gene expression data.

MOTIVATION: The issue of high dimensionality in microarray data has been, and remains, a hot topic in statistical and computational analysis. Efficient gene filtering and differentiation approaches can reduce the dimensions of data, help to remove redundant genes and noises, and highlight the most relevant genes that are major players in the development of certain diseases or the effect of drug treatment. The purpose of this study is to investigate the efficiency of parametric (including Bayesian and non-Bayesian, linear and non-linear), non-parametric and semi-parametric gene filtering methods through the application of time course microarray data from multiple sclerosis patients being treated with interferon-beta-1a. The analysis of variance with bootstrapping (parametric), class dispersion (semi-parametric) and Pareto (non-parametric) with permutation methods are presented and compared for filtering and finding differentially expressed genes. The Bayesian linear correlated model, the Bayesian non-linear model the and non-Bayesian mixed effects model with bootstrap were also developed to characterize the differential expression patterns. Furthermore, trajectory-clustering approaches were developed in order to investigate the dynamic patterns and inter-dependency of drug treatment effects on gene expression. RESULTS: Results show that the presented methods performed significant differently but all were adequate in capturing a small number of the potentially relevant genes to the disease. The parametric method, such as the mixed model and two Bayesian approaches proved to be more conservative. This may because these methods are based on overall variation in expression across all time points. The semi-parametric (class dispersion) and non-parametric (Pareto) methods were appropriate in capturing variation in expression from time point to time point, thereby making them more suitable for investigating significant monotonic changes and trajectories of changes in gene expressions in time course microarray data. Also, the non-linear Bayesian model proved to be less conservative than linear Bayesian correlated growth models to filter out the redundant genes, although the linear model showed better fit than non-linear model (smaller DIC). We also report the trajectories of significant genes-since we have been able to isolate trajectories of genes whose regulations appear to be inter-dependent.

Computer Simulation↗

PubMed2002

Parametric and semiparametric approaches to testing for seasonal trend in serial count data.

We present two tests for seasonal trend in monthly incidence data. The first approach uses a penalized likelihood to choose the number of harmonic terms to include in a parametric harmonic model (which includes time trends and autogression as well as seasonal harmonic terms) and then tests for seasonality using a parametric bootstrap test. The second approach uses a semiparametric regression model to test for seasonal trend. In the semiparametric model, the seasonal pattern is modeled nonparametrically, parametric terms are included for autoregressive effects and a linear time trend, and a parametric bootstrap test is used to test for seasonality. For both procedures, a null distribution is generated under a null Poisson model with time trends and autoregression parameters. We apply the methods to skin melanoma incidence rates collected by the surveillance, epidemiology, and end results (SEER) program of the National Cancer Institute, and perform simulation studies to evaluate the type I error rate and power for the two procedures. These simulations suggest that both procedures are alpha-level procedures. In addition, the harmonic model/bootstrap test had similar or larger power than the semiparametric model/bootstrap test for a wide range of alternatives, and the harmonic model/bootstrap test is much easier to implement. Thus, we recommend the harmonic model/bootstrap test for the analysis of seasonal incidence data.

Journal Article↗

PubMed2003

Estimating haplotype frequencies and standard errors for multiple single nucleotide polymorphisms.

Estimating haplotype frequencies becomes increasingly important in the mapping of complex disease genes, as millions of single nucleotide polymorphisms (SNPs) are being identified and genotyped. When genotypes at multiple SNP loci are gathered from unrelated individuals, haplotype frequencies can be accurately estimated using expectation-maximization (EM) algorithms (Excoffier and Slatkin, 1995; Hawley and Kidd, 1995; Long et al., 1995), with standard errors estimated using bootstraps. However, because the number of possible haplotypes increases exponentially with the number of SNPs, handling data with a large number of SNPs poses a computational challenge for the EM methods and for other haplotype inference methods. To solve this problem, Niu and colleagues, in their Bayesian haplotype inference paper (Niu et al., 2002), introduced a computational algorithm called progressive ligation (PL). But their Bayesian method has a limitation on the number of subjects (no more than 100 subjects in the current implementation of the method). In this paper, we propose a new method in which we use the same likelihood formulation as in Excoffier and Slatkin's EM algorithm and apply the estimating equation idea and the PL computational algorithm with some modifications. Our proposed method can handle data sets with large number of SNPs as well as large numbers of subjects. Simultaneously, our method estimates standard errors efficiently, using the sandwich-estimate from the estimating equation, rather than the bootstrap method. Additionally, our method admits missing data and produces valid estimates of parameters and their standard errors under the assumption that the missing genotypes are missing at random in the sense defined by Rubin (1976).

Algorithms↗

PubMed2005

Nonparametric confidence intervals for the one- and two-sample problems.

Confidence intervals for the mean of one sample and the difference in means of two independent samples based on the ordinary-t statistic suffer deficiencies when samples come from skewed families. In this article we evaluate several existing techniques and propose new methods to improve coverage accuracy. The methods examined include the ordinary-t, the bootstrap-t, the biased-corrected acceleration and three new intervals based on transformation of the t-statistic. Our study shows that our new transformation intervals and the bootstrap-t intervals give best coverage accuracy for a variety of skewed distributions, and that our new transformation intervals have shorter interval lengths.

Computer Simulation↗

PubMed2006

Multiple comparisons distortions of parameter estimates.

In experiments involving many variables, investigators typically use multiple comparisons procedures to determine differences that are unlikely to be the result of chance. However, investigators rarely consider how the magnitude of the greatest observed effect sizes may have been subject to bias resulting from multiple testing. These questions of bias become important to the extent investigators focus on the magnitude of the observed effects. As an example, such bias can lead to problems in attempting to validate results, if a biased effect size is used to power a follow-up study. An associated important consequence is that confidence intervals constructed using standard distributions may be badly biased. A bootstrap approach is used to estimate and adjust for the bias in the effect sizes of those variables showing strongest differences. This bias is not always present; some principles showing what factors may lead to greater bias are given and a proof of the convergence of the bootstrap distribution is provided.

Bias↗

PubMed2026

Phylogenomic subsampling and upsampling for efficient evolutionary analyses of big data.

Long runtimes, high memory demands, and reliance on high-performance computing impede phylogenomic analyses. We review a scalable phylogenomic subsampling with upsampling (PSU) framework to address this challenge, which reduces runtime and memory requirements by orders of magnitude. In PSU, small subsamples of sites from a concatenated alignment are analyzed, which are expanded by upsampling before inference, and the resulting inferences are aggregated to obtain evolutionary estimates. PSU harnesses the fact that the computational cost of maximum likelihood analysis is strongly influenced by the number of distinct site patterns in the concatenated alignment, whereas statistical power depends primarily on the amount of evolutionary information represented by the total number of sites and substitutions. By reducing the former while restoring the latter through upsampling, PSU can approximate many full-alignment analyses at substantially lower computational cost. Analysis of simulated and empirical datasets shows that PSU can accurately estimate bootstrap support values, select the optimal substitution model, test evolutionary hypotheses, and infer branch lengths, divergence times, and associated uncertainty measures. PSU also provides distributions of inferred clade support across independent subsamples, enabling detection of conflicting phylogenetic signals that may remain hidden in conventional bootstrap analysis of concatenated alignments. Automated tuning of subsample size, the number of subsamples, and the number of upsampling replicates make PSU practical. We suggest that PSU is a general approach for scalable phylogenomic inference using a broad range of statistical methods. By enabling analyses of genome-scale alignments on commodity hardware, PSU broadens research access and reduces environmental and infrastructural costs of big-data phylogenomics.

Phylogeny↗

PubMed2004

Genome-scale phylogeny and the detection of systematic biases.

Phylogenetic inference from sequences can be misled by both sampling (stochastic) error and systematic error (nonhistorical signals where reality differs from our simplified models). A recent study of eight yeast species using 106 concatenated genes from complete genomes showed that even small internal edges of a tree received 100% bootstrap support. This effective negation of stochastic error from large data sets is important, but longer sequences exacerbate the potential for biases (systematic error) to be positively misleading. Indeed, when we analyzed the same data set using minimum evolution optimality criteria, an alternative tree received 100% bootstrap support. We identified a compositional bias as responsible for this inconsistency and showed that it is reduced effectively by coding the nucleotides as purines and pyrimidines (RY-coding), reinforcing the original tree. Thus, a comprehensive exploration of potential systematic biases is still required, even though genome-scale data sets greatly reduce sampling error.

Genome, Fungal↗

PubMed2004

Male-biased mutation rate and divergence in autosomal, z-linked and w-linked introns of chicken and Turkey.

To investigate mutation-rate variation between autosomes and sex chromosomes in the avian genome, we have analyzed divergence between chicken (Gallus gallus) and turkey (Meleagris galopavo) sequences from 33 autosomal, 28 Z-linked, and 14 W-linked introns with a total ungapped alignment length of approximately 43,000 bp. There are pronounced differences in the mean divergence among autosomes and sex chromosomes (autosomes [A] = 10.08%, Z chromosome = 10.99%, and W chromosome = 5.74%), and we use these data to estimate the male-to-female mutation-rate ratio (alpha(m)) from Z/A, Z/W, and A/W comparisons at 1.71, 2.37, and 2.52, respectively. Because the alpha(m) estimates of the three comparisons do not differ significantly, we find no statistical support for a specific reduction in the Z chromosome mutation rate (Z reduction estimated at 4.89%, P = 0.286). The idea of mutation-rate reduction in the sex chromosome hemizygous in one sex (i.e., X in mammals, Z in birds) has been suggested on the basis of theory on adaptive mutation-rate evolution. If it exists in birds, the effect would, thus, seem to be weak; a preliminary power analysis suggests that it is significantly less than 18%. Because divergence may vary within chromosomal classes as a result of variation in mutation and/or selection, we developed a novel double-bootstrapping method, bootstrapping both by introns and sites from concatenated alignments, to estimate confidence intervals for chromosomal class rates and for alpha(m). The narrowest interval for the alpha(m) estimate is 1.88 to 2.97 from the Z/W comparison. We also estimated alpha(m) using maximum likelihood on data from all three chromosome classes; this method yielded alpha(m) = 2.47 and approximate 95% confidence intervals of 2.27 to 2.68. Our data are broadly consistent with the idea that mutation-rate differences between chromosomal classes can be explained by the male mutation bias alone.

Animals↗

PubMed2004

Molecular claims of Gondwanan age for Australian agamid lizards are untenable.

A recent mtDNA study proposes a surprisingly deep (approximately 150 MYA) divergence between SE Asian and Australasian agamid lizards, consistent with ancient Gondwanan vicariance rather than dispersal across the Indonesian Archipelago. However, the analysis contains a fundamental error: use of rates of molecular evolution inferred from uncorrected sequence divergence to put a time frame on a tree with branch lengths greatly elongated by complex likelihood and rate-smoothing models. Furthermore, this date implies that basal splits within agamids occurred implausibly early, at least 300 MYA (100 Myr before the first fossil lizards and coincident with the earliest fossil reptiles). Analyses of the mtDNA data using more appropriate methods and new information from nuclear (c-mos) sequences suggest a much more recent divergence between SE Asian and Australian agamids (around 30 MYA). Using two fossil boundary dates, bootstrapping the c-mos data gives a 95% confidence interval for this divergence time that is sufficiently recent (14-41 MYA) to exclude an ancient Gondwanan vicariance and is more consistent with Miocene over-water dispersal. As with the mtDNA, the c-mos data implies implausibly old basal divergences among agamids if a Gondwanan age is assumed for the Australasian clade. The analyses also highlight how methods for creating ultrametric trees (especially nonparametric rate smoothing) can greatly modify branch lengths and, thus, always require internal calibrations. The errors associated with inferred dates in the previous study (inferred through parametric bootstrapping) were also unjustifiably low, as this method only considers stochasticity in the substitution model and ignores much larger sources of uncertainty, such as variation in character sampling, tree topology, and calibration accuracy.

Animals↗

PubMed2005

Identifying the basal angiosperm node in chloroplast genome phylogenies: sampling one's way out of the Felsenstein zone.

While there has been strong support for Amborella and Nymphaeales (water lilies) as branching from basal-most nodes in the angiosperm phylogeny, this hypothesis has recently been challenged by phylogenetic analyses of 61 protein-coding genes extracted from the chloroplast genome sequences of Amborella, Nymphaea, and 12 other available land plant chloroplast genomes. These character-rich analyses placed the monocots, represented by three grasses (Poaceae), as sister to all other extant angiosperm lineages. We have extracted protein-coding regions from draft sequences for six additional chloroplast genomes to test whether this surprising result could be an artifact of long-branch attraction due to limited taxon sampling. The added taxa include three monocots (Acorus, Yucca, and Typha), a water lily (Nuphar), a ranunculid (Ranunculus), and a gymnosperm (Ginkgo). Phylogenetic analyses of the expanded DNA and protein data sets together with microstructural characters (indels) provided unambiguous support for Amborella and the Nymphaeales as branching from the basal-most nodes in the angiosperm phylogeny. However, their relative positions proved to be dependent on the method of analysis, with parsimony favoring Amborella as sister to all other angiosperms and maximum likelihood (ML) and neighbor-joining methods favoring an Amborella + Nymphaeales clade as sister. The ML phylogeny supported the later hypothesis, but the likelihood for the former hypothesis was not significantly different. Parametric bootstrap analysis, single-gene phylogenies, estimated divergence dates, and conflicting indel characters all help to illuminate the nature of the conflict in resolution of the most basal nodes in the angiosperm phylogeny. Molecular dating analyses provided median age estimates of 161 MYA for the most recent common ancestor (MRCA) of all extant angiosperms and 145 MYA for the MRCA of monocots, magnoliids, and eudicots. Whereas long sequences reduce variance in branch lengths and molecular dating estimates, the impact of improved taxon sampling on the rooting of the angiosperm phylogeny together with the results of parametric bootstrap analyses demonstrate how long-branch attraction might mislead genome-scale phylogenetic analyses.

Chloroplasts↗