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Results for “Models, Statistical”

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PubMed1998

Strategies for estimating behavioural frequency in survey interviews.

When people answer survey questions of the form "During the past month, how many times did you...?" their responses provide valuable data for researchers and policy makers. Yet the way respondents produce their answers to these "behavioural frequency questions" is not well understood. This article demonstrates that survey respondents can use an array of distinct estimation strategies, depending on what information is available in their memories. The kind of event information that people use is related to factors such as the regularity of occurrence, similarity of one episode to the next, and frequency. In a study conducted as a telephone survey, respondents' verbal reports and response-time patterns indicate that they usually answer behavioural frequency questions by either retrieving and counting episodes, retrieving or estimating rates of occurrence, or converting a general impression of frequency into a numerical quantity. The third strategy should be of particular concern to survey researchers because respondents provide a quantitative estimate without any relevant numerical knowledge. The set of strategies and the factors that influence their use are integrated into a statistical model that could help survey practitioners to improve data quality and memory researchers to broaden their perspective.

Behavior↗

PubMed2003

Optimal and efficient crossover designs under different assumptions about the carryover effects.

In certain studies it is desirable or necessary that a subject, such as a patient in a medical trial, receive a treatment in each period. This facilitates a within-subject comparison of the treatments. Designs for studies of this type are called crossover designs or repeated measurements designs. If there are s subjects in p periods, the design should specify which of the t treatments is assigned to subject j in period i, i = 1,... ,p,j = 1,..., s. Equivalently we may think of a design as assigning each subject to one of the t(p) possible treatment sequences. The choice of a design will clearly depend on the values of p, s, and t, to which we will refer as the design parameters. But for any set of design parameters, we will typically still have many design choices. To distinguish between different designs for the same design parameters, we will compare the designs under criteria that are related to the objective of the study. Often the objective is a comparison of the treatments, and we would choose a design that, in some sense, provides good estimates of the treatment differences. For these criteria, a design that is optimal under one statistical model may not be optimal under another. It is therefore also of interest to identify designs that are efficient (relative to an optimal design) for more than one model. The main difference in the models that we will consider is in how the possible first-order carryover effects are modeled. This is a controversial issue, and it is by no means our intent to resolve this here. But a design that is efficient under a variety of plausible models is preferable to one that performs well under one model but poorly under another. Our main focus will be on two models. One of these models has been considered extensively in the literature, while the other is relatively new. For selected design parameters, we will compare selected designs under these models.

Clinical Trials as Topic↗

PubMed1999

A spline-regularized minimal residual algorithm for iterative attenuation correction in SPECT.

In SPECT, regularization is necessary to avoid divergence of the iterative algorithms used for non uniform attenuation compensation. In this paper, we propose a spline-based regularization method for the minimal residual algorithm. First, the acquisition noise is filtered using a statistical model involving spline smoothing so that the filtered projections belong to a Sobolev space with specific continuity and derivability properties. Then, during the iterative reconstruction procedure, the continuity of the inverse Radon transform between Sobolev spaces is used to design a spline-regularized filtered backprojection method, by which the known regularity properties of the projections determine those of the corresponding reconstructed slices. This ensures that the activity distributions estimated at each iteration present regularity properties, which avoids computational noise amplification, thus stabilizing the iterative process. Analytical and Monte Carlo simulations are used to show that the proposed spline-regularized minimal residual algorithm converges to a satisfactory stable solution in terms of restored activity and homogeneity, using at most 25 iterations, whereas the non regularized version of the algorithm diverges. Choosing the number of iterations is therefore no longer a critical issue for this reconstruction procedure.

Algorithms↗

PubMed2004

LOR-OSEM: statistical PET reconstruction from raw line-of-response histograms.

Iterative statistical reconstruction methods are becoming the standard in positron emission tomography (PET). Conventional maximum-likelihood expectation-maximization (MLEM) and ordered-subsets (OSEM) algorithms act on data which have been pre-processed into corrected, evenly-spaced histograms; however, such pre-processing corrupts the Poisson statistics. Recent advances have incorporated attenuation, scatter and randoms compensation into the iterative reconstruction. The objective of this work was to incorporate the remaining pre-processing steps, including arc correction, to reconstruct directly from raw unevenly-spaced line-of-response (LOR) histograms. This exactly preserves Poisson statistics and full spatial information in a manner closely related to listmode ML, making full use of the ML statistical model. The LOR-OSEM algorithm was implemented using a rotation-based projector which maps directly to the unevenly-spaced LOR grid. Simulation and phantom experiments were performed to characterize resolution, contrast and noise properties for 2D PET. LOR-OSEM provided a beneficial noise-resolution tradeoff, outperforming AW-OSEM by about the same margin that AW-OSEM outperformed pre-corrected OSEM. The relationship between LOR-ML and listmode ML algorithms was explored, and implementation differences are discussed. LOR-OSEM is a viable alternative to AW-OSEM for histogram-based reconstruction with improved spatial resolution and noise properties.

Algorithms↗

PubMed2005

Effects of averaging over motion and the resulting systematic errors in radiation therapy.

The potential for systematic errors in radiotherapy of a breathing patient is considered using the statistical model of Bortfeld et al (2002 Phys. Med. Biol. 47 2203-20). It is shown that although averaging over 30 fractions does result in a narrow Gaussian distribution of errors, as predicted by the central limit theorem, the fact that one or a few samples of the breathing patient's motion distribution are used for treatment planning (in contrast to the many treatment fractions that are likely to be delivered) may result in a much larger error with a systematic component. The error distribution may be particularly large if a scan at breath-hold is used for planning.

Humans↗

PubMedDate not supplied

A discriminative framework for detecting remote protein homologies.

A new method for detecting remote protein homologies is introduced and shown to perform well in classifying protein domains by SCOP superfamily. The method is a variant of support vector machines using a new kernel function. The kernel function is derived from a generative statistical model for a protein family, in this case a hidden Markov model. This general approach of combining generative models like HMMs with discriminative methods such as support vector machines may have applications in other areas of biosequence analysis as well.

Biometry↗

PubMed2000

Optimal amnesic probabilistic automata or how to learn and classify proteins in linear time and space.

Statistical modeling of sequences is a central paradigm of machine learning that finds multiple uses in computational molecular biology and many other domains. The probabilistic automata typically built in these contexts are subtended by uniform, fixed-memory Markov models. In practice, such automata tend to be unnecessarily bulky and computationally imposing both during their synthesis and use. Recently, D. Ron, Y. Singer, and N. Tishby built much more compact, tree-shaped variants of probabilistic automata under the assumption of an underlying Markov process of variable memory length. These variants, called Probabilistic Suffix Trees (PSTs) were subsequently adapted by G. Bejerano and G. Yona and applied successfully to learning and prediction of protein families. The process of learning the automaton from a given training set S of sequences requires theta(Ln2) worst-case time, where n is the total length of the sequences in S and L is the length of a longest substring of S to be considered for a candidate state in the automaton. Once the automaton is built, predicting the likelihood of a query sequence of m characters may cost time theta(m2) in the worst case. The main contribution of this paper is to introduce automata equivalent to PSTs but having the following properties: Learning the automaton, for any L, takes O (n) time. Prediction of a string of m symbols by the automaton takes O (m) time. Along the way, the paper presents an evolving learning scheme and addresses notions of empirical probability and related efficient computation, which is a by-product possibly of more general interest.

Algorithms↗

PubMed2005

Toric ideals of phylogenetic invariants.

Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants of a model are the polynomials which vanish on the variety. Several widely used models for biological sequences have transition matrices that can be diagonalized by means of the Fourier transform of an Abelian group. Their phylogenetic invariants form a toric ideal in the Fourier coordinates. We determine generators and Gröbner bases for these toric ideals. For the Jukes-Cantor and Kimura models on a binary tree, our Gröbner bases consist of certain explicitly constructed polynomials of degree at most four.

Computational Biology↗

PubMedDate not supplied

Checking homogeneity of motifs' distribution in heterogenous sequences.

Studying the distribution of a motif along sequences may help in the understanding of its biological function, or to detect regions of interest. A statistical model is needed to assess the significance of the observed distribution. We propose a heterogenous compound Poisson process to model the possibility of overlap between occurrences and some heterogeneity of the sequence known a priori. The estimation procedure of the parameters is described and tests of homogenous sub-models are proposed. We also consider the detection of rich regions using either cumulated distances or moving intervals, via a homogenization technique. Illustrations of the method are given with applications to bacterial genomes.

Algorithms↗

PubMed2005

Finding approximate tandem repeats in genomic sequences.

An efficient algorithm is presented for detecting approximate tandem repeats in genomic sequences. The algorithm is based on a flexible statistical model which allows a wide range of definitions of approximate tandem repeats. The ideas and methods underlying the algorithm are described and its effectiveness on genomic data is demonstrated.

Algorithms↗

PubMed2005

Effect of inherent variability of inhalation products on impactor mass balance limits.

When measuring the aerodynamic particle size distribution of pulmonary drug products, the commonly used instrument is a cascade impactor. For this type of analysis, a mass balance (MB) criterion, 85-115% of label claim, has been recommended by the U.S. Food and Drug Administration (FDA) to be included in the drug product specification. Using statistical model simulations, the effect of inherent product variability on the risk to fail the proposed criteria has been assessed and compared to the corresponding risk to fail the delivered dose uniformity (DDU) test. The results clearly show that the MB criterion is at odds with typical variability of orally inhaled products and seriously contributes to the risk that a typical batch would be rejected due to natural variability of the delivered dose of the product. The MB criterion is generally more difficult to comply with compared to the corresponding delivered dose uniformity (DDU) test, indicating that the proposed FDA MB specification overrules the DDU criteria as being that controlling the DDU.

Administration, Inhalation↗

PubMed2004

Genome-scale gene function prediction using multiple sources of high-throughput data in yeast Saccharomyces cerevisiae.

Characterizing gene function is one of the major challenging tasks in the post-genomic era. To address this challenge, we have developed GeneFAS (Gene Function Annotation System), a new integrated probabilistic method for cellular function prediction by combining information from protein-protein interactions, protein complexes, microarray gene expression profiles, and annotations of known proteins through an integrative statistical model. Our approach is based on a novel assessment for the relationship between (1) the interaction/correlation of two proteins' high-throughput data and (2) their functional relationship in terms of their Gene Ontology (GO) hierarchy. We have developed a Web server for the predictions. We have applied our method to yeast Saccharomyces cerevisiae and predicted functions for 1548 out of 2472 unannotated proteins.

Automation↗

PubMed2002

Is residual confounding a reasonable explanation for the apparent protective effects of beta-carotene found in epidemiologic studies of lung cancer in smokers?

The results of three randomized trials of beta-carotene supplementation for the prevention of lung cancer among smokers are in contradiction to a large body of epidemiologic evidence for the reduction of risk of lung cancer among smokers with higher intake and/or higher serum levels of beta-carotene. Complicating this issue are widely noted negative associations between tobacco use and intake or serum levels of beta-carotene. Although observational studies attempt to control for reported smoking histories, the accuracy of self-reported smoking is uncertain; correlations as low as 0.5 between reported and true smoking exposure are not inconsistent with studies of biomarkers of cigarette exposure. The authors developed a simple statistical model for random errors in reported smoking (relative to true tobacco exposure) and assumed a modest (inverse) relation between true tobacco exposure and serum beta-carotene. Calculations from this model, combined with a model for lung cancer contemplated by Doll and Peto (J Epidemiol Community Health 1978;78:303-13), suggest that biases in assessment of smoking exposure between smokers with low versus high beta-carotene intake may plausibly explain much or all of the observed protective effect of high beta-carotene levels. Appropriate cohort studies of lung cancer in smokers, utilizing biomarkers of smoking, are needed and are presently ongoing.

Antioxidants↗

PubMed2003

Sample size needed to detect gene-gene interactions using association designs.

It is likely that many complex diseases result from interactions among several genes, as well as environmental factors. The presence of such interactions poses challenges to investigators in identifying susceptibility genes, understanding biologic pathways, and predicting and controlling disease risks. Recently, Gauderman (Am J Epidemiol 2002;155:478-84) reported results from the first systematic analysis of the statistical power needed to detect gene-gene interactions in association studies. However, Gauderman used different statistical models to model disease risks for different study designs, and he assumed a very low disease prevalence to make different models more comparable. In this article, assuming a logistic model for disease risk for different study designs, the authors investigate the power of population-based and family-based association designs to detect gene-gene interactions for common diseases. The results indicate that population-based designs are more powerful than family-based designs for detecting gene-gene interactions when disease prevalence in the study population is moderate.

Genetic Predisposition to Disease↗

PubMed2002

Comparison of microarray designs for class comparison and class discovery.

MOTIVATION: Two-color microarray experiments in which an aliquot derived from a common RNA sample is placed on each array are called reference designs. Traditionally, microarray experiments have used reference designs, but designs without a reference have recently been proposed as alternatives. RESULTS: We develop a statistical model that distinguishes the different levels of variation typically present in cancer data, including biological variation among RNA samples, experimental error and variation attributable to phenotype. Within the context of this model, we examine the reference design and two designs which do not use a reference, the balanced block design and the loop design, focusing particularly on efficiency of estimates and the performance of cluster analysis. We calculate the relative efficiency of designs when there are a fixed number of arrays available, and when there are a fixed number of samples available. Monte Carlo simulation is used to compare the designs when the objective is class discovery based on cluster analysis of the samples. The number of discrepancies between the estimated clusters and the true clusters were significantly smaller for the reference design than for the loop design. The efficiency of the reference design relative to the loop and block designs depends on the relation between inter- and intra-sample variance. These results suggest that if cluster analysis is a major goal of the experiment, then a reference design is preferable. If identification of differentially expressed genes is the main concern, then design selection may involve a consideration of several factors.

Algorithms↗

PubMed2002

Why are complementary DNA strands symmetric?

MOTIVATION: Over sufficiently long windows, complementary strands of DNA tend to have the same base composition. A few reports have indicated that this first-order parity rule extends at higher orders to oligonucleotide composition, at least in some organisms or taxa. However, the scientific literature falls short of providing a comprehensive study of reverse-complement symmetry at multiple orders and across the kingdom of life. It also lacks a characterization of this symmetry and a convincing explanation or clarification of its origin. RESULTS: We develop methods to measure and characterize symmetry at multiple orders, and analyze a wide set of genomes, encompassing single- and double-stranded RNA and DNA viruses, bacteria, archae, mitochondria, and eukaryota. We quantify symmetry at orders 1 to 9 for contiguous sequences and pools of coding and non-coding upstream regions, compare the observed symmetry levels to those predicted by simple statistical models, and factor out the effect of lower-order distributions. We establish the universality and variability range of first-order strand symmetry, as well as of its higher-order extensions, and demonstrate the existence of genuine high-order symmetric constraints. We show that ubiquitous reverse-complement symmetry does not result from a single cause, such as point mutation or recombination, but rather emerges from the combined effects of a wide spectrum of mechanisms operating at multiple orders and length scales.

Base Composition↗

PubMed2002

Discovering statistically significant biclusters in gene expression data.

In gene expression data, a bicluster is a subset of the genes exhibiting consistent patterns over a subset of the conditions. We propose a new method to detect significant biclusters in large expression datasets. Our approach is graph theoretic coupled with statistical modelling of the data. Under plausible assumptions, our algorithm is polynomial and is guaranteed to find the most significant biclusters. We tested our method on a collection of yeast expression profiles and on a human cancer dataset. Cross validation results show high specificity in assigning function to genes based on their biclusters, and we are able to annotate in this way 196 uncharacterized yeast genes. We also demonstrate how the biclusters lead to detecting new concrete biological associations. In cancer data we are able to detect and relate finer tissue types than was previously possible. We also show that the method outperforms the biclustering algorithm of Cheng and Church (2000).

Algorithms↗

PubMed2003

Quantitative quality control in microarray experiments and the application in data filtering, normalization and false positive rate prediction.

Data preprocessing including proper normalization and adequate quality control before complex data mining is crucial for studies using the cDNA microarray technology. We have developed a simple procedure that integrates data filtering and normalization with quantitative quality control of microarray experiments. Previously we have shown that data variability in a microarray experiment can be very well captured by a quality score q(com) that is defined for every spot, and the ratio distribution depends on q(com). Utilizing this knowledge, our data-filtering scheme allows the investigator to decide on the filtering stringency according to desired data variability, and our normalization procedure corrects the q(com)-dependent dye biases in terms of both the location and the spread of the ratio distribution. In addition, we propose a statistical model for false positive rate determination based on the design and the quality of a microarray experiment. The model predicts that a lower limit of 0.5 for the replicate concordance rate is needed in order to be certain of true positives. Our work demonstrates the importance and advantages of having a quantitative quality control scheme for microarrays.

Algorithms↗