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PubMed2002

Describing data: statistical and graphical methods.

An important step in any analysis is to describe the data by using descriptive and graphic methods. The author provides an approach to the most commonly used numeric and graphic methods for describing data. Methods are presented for summarizing data numerically, including presentation of data in tables and calculation of statistics for central tendency, variability, and distribution. Methods are also presented for displaying data graphically, including line graphs, bar graphs, histograms, and frequency polygons. The description and graphing of study data result in better analysis and presentation of data.

Brain Neoplasms↗
PubMed1998

"Biphasic" fevers often consist of more than two phases.

This paper disproves the common belief that all doses of lipopolysaccharide (LPS) that are commonly referred to as biphasic fever inducing (>/=2 microg/kg) cause truly biphasic responses. A catheter was implanted into the right jugular vein of several strains of adult male rats, and the animals were habituated to the experimental conditions. At an ambient temperature of 30.0 degrees C, loosely restrained animals were injected with a 10 microg/kg dose of LPS (various preparations), and their colonic (Tc) and tail skin temperatures were monitored (from >/=1 h before to >/=7 h after the injection). The results are presented as time graphs and phase-plane plots; in the latter case the rate of change of Tc is plotted against Tc. In experiment 1 the intravenous injection of LPS (from Escherichia coli 0111:B4, phenol extract) into the rats (Bkl:Wistar) induced a triphasic febrile response, as is obvious from time graphs of Tc (3 peaks), time graphs of effector activity (3 waves of tail skin vasoconstriction), and phase-plane plots (3 complete loops); the injection of saline (control) induced no Tc changes. We analyzed whether the triphasic pattern was due to some peculiarities of the experimental design, i.e., the pyrogen preparation used (experiment 2) or the rat strain tested (experiment 3) or whether this pattern reflects a more general law. In experiment 2 we used the same (phenol) preparation of different LPS (from Shigella flexneri 1A and Salmonella typhosa) and a different preparation (TCA extract) of the same LPS (E. coli). Regardless of the LPS used, rats of the Bkl:Wistar strain responded to the 10 microg/kg dose with the triphasic fever. In experiment 3, rats of other strains [Bkl:Sprague-Dawley and Sim:(LE)fBR(Black-hooded)] were tested. Again, all animals responded to the 10 microg/kg dose of E. coli LPS (phenol extract) with the triphasic fever. Because all fevers caused by four different LPS preparations in three rat strains were triphasic, the triphasic pattern is likely to constitute an intrinsic characteristic of the febrile response.

Activity Cycles↗
PubMedDate not supplied

Intraspinal masses: efficacy of plain spine radiography.

Plain spine radiographs from 31 patients with pathologically proven intraspinal tumors were analyzed retrospectively by an experienced pediatric radiologist unfamiliar with the cases in order to evaluate the applicability and reliability of the radiographic signs commonly used for diagnosis. Interpediculate distances (IPDs) were graphed onto standard curves to assess whether graphic analysis aided in diagnosis. In this group of patients, no single radiographic criterion permitted better than 40% true-positive diagnosis. False-positive diagnoses were made in 0-10% of cases, depending on the sign employed. Use of multiple roentgen signs in conjunction achieved 55% true-positive and 3% false-positive diagnoses, while use of graphed IPDs alone achieved 57% true-positive and 11% false-positive diagnoses. Addition of graphed IPDs to visual inspection of the radiographs led to detection of 6 tumors (19%) not otherwise appreciated, but tripled the false-positive rate from 3 to 10%.

Adolescent↗
PubMed2004

Linear response algorithms for approximate inference in graphical models.

Belief propagation (BP) on cyclic graphs is an efficient algorithm for computing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. However, it does not prescribe a way to compute joint distributions over pairs of distant nodes in the graph. In this article, we propose two new algorithms for approximating these pairwise probabilities, based on the linear response theorem. The first is a propagation algorithm that is shown to converge if BP converges to a stable fixed point. The second algorithm is based on matrix inversion. Applying these ideas to gaussian random fields, we derive a propagation algorithm for computing the inverse of a matrix.

Algorithms↗
PubMed1999

Visualizing evolutionary activity of genotypes.

We introduce a method for visualizing evolutionary activity of genotypes. Following a proposal of Bedau and Packard [11], we define a genotype's evolutionary activity in terms of the history of its concentration in the evolving population. To visualize this evolutionary activity we graph the distribution of evolutionary activity in the population of genotypes as a function of time. Adaptively significant genotypes trace a salient line or "wave" in these graphs. The quality of these waves indicates a variety of neutral variation, and random genetic drift. We apply this method in an evolutionary model of self-replicating assembly language programs competing for room in a two-dimensional space. Comparison with fitness graphs and with a nonadaptive analogue of this model shows how this method highlights adaptively significant events.

Biological Evolution↗
PubMedDate not supplied

Intussusception incidence relative to rotavirus vaccine use in Honolulu.

Rotavirus vaccine was in use during the period August 1998 to October 1999. Epidemics of intussusception during this period were allegedly due to rotavirus vaccine, which prompted the vaccine to be withdrawn. Hawaii's geographic location between Asia and the mainland United States may subject it to infectious disease epidemic periods midway between occurrence in Asia and occurrence in the mainland United States. In contrast, immunization recommendations are temporally identical across all 50 states. The purpose of this study was to determine whether an epidemic of intussusception was experienced in Honolulu during the period of rotavirus vaccine use. This is a retrospective study of data obtained from inpatient and emergency department discharge diagnosis codes of intussusception for children up to 36 months of age. The incidence data were plotted by time periods to identify possible epidemic periods. The data are graphed. The arrows on the graphs indicate the period of time that rotavirus vaccine was in use. These graphs are most consistent with an increase in the cases of intussusception during the period July 2000 to December 2000, and a possible decline of intussusception during the rotavirus vaccine period. These incidence data are inconsistent with a temporal association between rotavirus vaccine and an epidemic of intussusception in Honolulu.

Child, Preschool↗
PubMedDate not supplied

Effect of framing as gain versus loss on understanding and hypothetical treatment choices: survival and mortality curves.

BACKGROUND: Presentation of information using survival or mortality (i.e., incidence) curves offers a potentially powerful method of communication because such curves provide information about risk over time in a relatively simple graphic format. However, the effect of framing as survival versus mortality on understanding and treatment choice is not known. METHODS: In this study, 451 individuals awaiting jury duty at the Philadelphia City Courthouse were randomized to receive 1 of 3 questionnaires: (1) survival curves, (2) mortality curves, or (3) both survival and mortality curves. Each questionnaire included a brief description of a hypothetical treatment decision, survival curve graphs and/or mortality curve graphs presenting the outcome of the treatment, and questions measuring understanding of the information contained in the graphs and preference for undergoing treatment. After completing a brief practice exercise, participants were asked to answer questions assessing their ability to interpret single points on a curve and the difference between curves, and then to decide whether they would choose to undergo preventive surgery for 3 different scenarios in which the benefit of surgery varied. RESULTS: Participants who received only survival curves or who received both survival and mortality curves were significantly more accurate in answering questions about the information than participants who received only mortality curves (P < 0.05). For 2 of the 3 treatment presentations, participants who received only mortality curves were significantly less likely to prefer preventive surgery than participants who received survival curves only or both survival and mortality curves (P < 0.05). The effect of framing on understanding was greatest among participants with less than a college education and among non-Caucasian participants. CONCLUSION: Framing graphic risk information as chance of death over time results in lower levels of understanding and less interest in preventive surgery than framing as chance of survival over time.

Adolescent↗
PubMedDate not supplied

The effect of physician's explanations on patients' treatment preferences: five-year survival data.

OBJECTIVE: To evaluate the influence of physicians' explanations on patients' choices. SETTING: A university-based Department of Veterans Affairs Medical Center. PARTICIPANTS: 136 patients seen in a continuity-care general medicine clinic. MEASUREMENTS AND RESULTS: Patients were randomized to two groups [Limited Explanation (LE) and Extensive Explanation (EE)] and asked to choose between two alternative treatments (differing in short-term vs long-term survival benefits) for an unidentified medical condition, based on the information given in the explanations. LE consisted of a brief orientation to graphs summarizing the treatment results, while EE consisted of a detailed verbal description of the graphs. Significantly (p < 0.001) more patients receiving EE changed their preferences across the three pairs of five-year survival curves, compared with patients receiving LE. Of the patients receiving EE, 57% reported either medium-term (year 0-to-intercept or intercept-to-year 5) data or the average life expectancy for the five-year period contained in the curves (ALE-5) as most influencing their decision making; whereas 78% of patients receiving LE reported only endpoint (year 0 or year 5) data as most influencing their preferences. CONCLUSIONS: The patients' treatment preferences for long-term vs short-term survival benefits were influenced by the amounts of verbal explanation provided to them about five-year survival graphs summarizing treatment results. The patients appeared to minimize the importance of medium-range data when those data were not specifically pointed out to them.

Female↗
PubMedDate not supplied

A sampling algorithm for segregation analysis.

Methods for detecting Quantitative Trait Loci (QTL) without markers have generally used iterative peeling algorithms for determining genotype probabilities. These algorithms have considerable shortcomings in complex pedigrees. A Monte Carlo Markov chain (MCMC) method which samples the pedigree of the whole population jointly is described. Simultaneous sampling of the pedigree was achieved by sampling descent graphs using the Metropolis-Hastings algorithm. A descent graph describes the inheritance state of each allele and provides pedigrees guaranteed to be consistent with Mendelian sampling. Sampling descent graphs overcomes most, if not all, of the limitations incurred by iterative peeling algorithms. The algorithm was able to find the QTL in most of the simulated populations. However, when the QTL was not modeled or found then its effect was ascribed to the polygenic component. No QTL were detected when they were not simulated.

Algorithms↗
PubMed2006

Construction of phylogenetic trees by kernel-based comparative analysis of metabolic networks.

BACKGROUND: To infer the tree of life requires knowledge of the common characteristics of each species descended from a common ancestor as the measuring criteria and a method to calculate the distance between the resulting values of each measure. Conventional phylogenetic analysis based on genomic sequences provides information about the genetic relationships between different organisms. In contrast, comparative analysis of metabolic pathways in different organisms can yield insights into their functional relationships under different physiological conditions. However, evaluating the similarities or differences between metabolic networks is a computationally challenging problem, and systematic methods of doing this are desirable. Here we introduce a graph-kernel method for computing the similarity between metabolic networks in polynomial time, and use it to profile metabolic pathways and to construct phylogenetic trees. RESULTS: To compare the structures of metabolic networks in organisms, we adopted the exponential graph kernel, which is a kernel-based approach with a labeled graph that includes a label matrix and an adjacency matrix. To construct the phylogenetic trees, we used an unweighted pair-group method with arithmetic mean, i.e., a hierarchical clustering algorithm. We applied the kernel-based network profiling method in a comparative analysis of nine carbohydrate metabolic networks from 81 biological species encompassing Archaea, Eukaryota, and Eubacteria. The resulting phylogenetic hierarchies generally support the tripartite scheme of three domains rather than the two domains of prokaryotes and eukaryotes. CONCLUSION: By combining the kernel machines with metabolic information, the method infers the context of biosphere development that covers physiological events required for adaptation by genetic reconstruction. The results show that one may obtain a global view of the tree of life by comparing the metabolic pathway structures using meta-level information rather than sequence information. This method may yield further information about biological evolution, such as the history of horizontal transfer of each gene, by studying the detailed structure of the phylogenetic tree constructed by the kernel-based method.

Archaeal Proteins↗
PubMed2006

Correlated fragile site expression allows the identification of candidate fragile genes involved in immunity and associated with carcinogenesis.

BACKGROUND: Common fragile sites (cfs) are specific regions in the human genome that are particularly prone to genomic instability under conditions of replicative stress. Several investigations support the view that common fragile sites play a role in carcinogenesis. We discuss a genome-wide approach based on graph theory and Gene Ontology vocabulary for the functional characterization of common fragile sites and for the identification of genes that contribute to tumour cell biology. RESULTS: Common fragile sites were assembled in a network based on a simple measure of correlation among common fragile site patterns of expression. By applying robust measurements to capture in quantitative terms the non triviality of the network, we identified several topological features clearly indicating departure from the Erdos-Renyi random graph model. The most important outcome was the presence of an unexpected large connected component far below the percolation threshold. Most of the best characterized common fragile sites belonged to this connected component. By filtering this connected component with Gene Ontology, statistically significant shared functional features were detected. Common fragile sites were found to be enriched for genes associated to the immune response and to mechanisms involved in tumour progression such as extracellular space remodeling and angiogenesis. Moreover we showed how the internal organization of the graph in communities and even in very simple subgraphs can be a starting point for the identification of new factors of instability at common fragile sites. CONCLUSION: We developed a computational method addressing the fundamental issue of studying the functional content of common fragile sites. Our analysis integrated two different approaches. First, data on common fragile site expression were analyzed in a complex networks framework. Second, outcomes of the network statistical description served as sources for the functional annotation of genes at common fragile sites by means of the Gene Ontology vocabulary. Our results support the hypothesis that fragile sites serve a function; we propose that fragility is linked to a coordinated regulation of fragile genes expression.

Cells, Cultured↗
PubMed2006

A methodology for the structural and functional analysis of signaling and regulatory networks.

BACKGROUND: Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks. RESULTS: We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior. We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli. CONCLUSION: The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T-cell signaling model, makes them a promising tool.

Animals↗
PubMed2001

Identifying patient preferences for communicating risk estimates: a descriptive pilot study.

BACKGROUND: Patients increasingly seek more active involvement in health care decisions, but little is known about how to communicate complex risk information to patients. The objective of this study was to elicit patient preferences for the presentation and framing of complex risk information. METHOD: To accomplish this, eight focus group discussions and 15 one-on-one interviews were conducted, where women were presented with risk data in a variety of different graphical formats, metrics, and time horizons. Risk data were based on a hypothetical woman's risk for coronary heart disease, hip fracture, and breast cancer, with and without hormone replacement therapy. Participants' preferences were assessed using likert scales, ranking, and abstractions of focus group discussions. RESULTS: Forty peri- and postmenopausal women were recruited through hospital fliers (n = 25) and a community health fair (n = 15). Mean age was 51 years, 50% were non-Caucasian, and all had completed high school. Bar graphs were preferred by 83% of participants over line graphs, thermometer graphs, 100 representative faces, and survival curves. Lifetime risk estimates were preferred over 10 or 20-year horizons, and absolute risks were preferred over relative risks and number needed to treat. CONCLUSION: Although there are many different formats for presenting and framing risk information, simple bar charts depicting absolute lifetime risk were rated and ranked highest overall for patient preferences for format.

Communication↗
PubMed1990

A simple procedure for determining spatial and transient variations of cooling rate within a specimen during cryopreservation. Part 2: Graphical solutions.

The ability to analyse the cooling rate history and its spatial distribution is useful in predicting the response of a biological specimen to a specific cryopreservation protocol. Although analytical and numerical methods exist for performing rigorous analyses of these thermal processes, their practical use requires considerable time and/or mathematical sophistication. In Part 1 of this paper a theoretical basis was presented for the development of a graphical analysis procedure for determining cooling rate that is quick and straightforward to apply. In this paper derived graphs are presented, from which the instantaneous cooling rate may be determined for specimens of a wide range of physical shapes. These dimensions graphs have been derived for determination of cooling rate as a function of time, position, the system's physical properties and the thermal boundary conditions. Numerical examples are presented for analysing the cooling of biological specimens for specific preservation protocols, illustrating solution both by computation using the tabulated constants from tables in the first paper and by reading directly from the graphed solutions.

Cryopreservation↗
PubMed2025

MaxComp: Predicting single-cell chromatin compartments from 3D chromosome structures.

The genome is organized into distinct chromatin compartments with at least two main classes, a transcriptionally active A and an inactive B compartment, broadly corresponding to euchromatin and heterochromatin. Chromatin regions within the same compartment preferentially interact with each other over regions in the opposite compartment. A/B compartments are traditionally identified from ensemble Hi-C contact frequency matrices using principal component analysis of their covariance matrices. However, defining compartments at the single-cell level from sparse single-cell Hi-C data is challenging, especially since homologous copies are often not resolved. To address this, we present MaxComp, an unsupervised method, for inferring single-cell A/B compartments based on 3D geometric considerations in single-cell chromosome structures-derived either from multiplexed FISH-omics imaging or 3D structure models derived from Hi-C data. By representing each 3D chromosome structure as an undirected graph with edge-weights encoding structural information, MaxComp reformulates compartment prediction as a variant of the Max-cut problem, solved using semidefinite graph programming (SPD) to optimally partition the graph into two structural compartments. Our results show that the population average of MaxComp single-cell compartment annotations closely matches those derived from ensemble Hi-C principal component analysis, demonstrating that compartmentalization can be recovered from geometric principles alone, using only the 3D coordinates and nuclear microenvironment of chromatin regions. Our approach reveals widespread cell-to-cell variability in compartment organization, with substantial heterogeneity across genomic loci. When applied to multiplexed FISH imaging data, MaxComp also uncovers relationships between compartment annotations and transcriptional activity at the single-cell level. In summary, MaxComp offers a new framework for understanding chromatin compartmentalization in single cells, connecting 3D genome architecture, and transcriptional activity with the cell-to-cell variations of chromatin compartments.

Chromatin↗
PubMed1994

Measurement of lifetime alcohol consumption.

The reliability and validity of a retrospective, self-report measure, the Concordia Lifetime Drinking Questionnaire (CLDQ), were assessed with a group of 72 elderly Canadian men. The CLDQ includes quantity and frequency questions on current beverage-specific alcohol use and a series of questions about the start of alcohol use. The innovative features of the CLDQ include requiring subjects to collaborate with the interviewer in drawing a graph that represents their lifetime drinking patterns and encouraging more accurate recall by the use of salient events in the subject's life history. Drinking was assessed on two occasions approximately 33 months apart. Forty-six wives responded to questions about their husband's drinking. The reliability coefficient for lifetime drinking was .78. A comparison of the two graphs every fifth year from 1945 to 1985 yielded significant correlations that ranged from .65 to .87. Validity was tested by comparing each wife's rating of her husband's drinking at present and at time of marriage with similar points on the husband's graphs; the correlations were .87 and .72, respectively. Moderate correlations were obtained between the MAST and the CLDQ. The CLDQ was judged to be a reliable and valid measure of lifetime drinking, appropriate for use with the elderly. The longitudinal lifetime drinking patterns appeared similar to those found in cross-sectional studies.

Aged↗
PubMed2005

The emergence of scaling in sequence-based physical models of protein evolution.

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other systems has previously been explained using network growth models that, although motivated by biological processes, do not explicitly consider the underlying physics or biology. In this work we explore a sequence-based model for the evolution protein structures and demonstrate that this model is able to recapitulate the scale-free nature observed in graphs of real protein structures. We find that this model also reproduces other statistical feature of the protein domain graph. This represents, to our knowledge, the first such microscopic, physics-based evolutionary model for a scale-free network of biological importance and as such has strong implications for our understanding of the evolution of protein structures and of other biological networks.

Algorithms↗
PubMed2001

Determination of beryllium and selenium in human urine and of selenium in human serum by graphite-furnace atomic absorption spectrophotometry.

For human urine beryllium (Be), each sample (500 microl) was diluted (1+1) with Nash reagent (containing 0.2% (v/v) acetylacetone and 2.0 M ammonium acetate buffer at pH 6.0) and then a 20-microl volume of Triton X-100 (0.4%, v/v) aqueous solution was added. An aliquot (10 microl) of the diluted urine mixture was introduced into a graphite cuvette and was atomized according to a temperature program. The method detection limit (MDL, 3sigma) for Be was 0.37 microg/l in the undiluted urine sample and the calibration graph was linear up to 65.0 microg/l. Calibration graphs were prepared by the standard addition method. Accuracies of 98.6-102% were obtained when testing standard reference material (SRM 2670) freeze dried human urine samples. Precision (relative standard deviation, RSD) for urine Be was < or = 2.3% (withinrun, n = 5) and was < or = 3.0% (between-run, n = 3). For human urine and serum selenium (Se), samples (100 microl) were diluted with HNO3 (0.2%, v/v) to make a (1+1) dilution for urine analysis or a (1+4) dilution for serum analysis. An additional aliquot (10 microl) of Triton X-100 (0.1%, v/v) was added to each 200 microl of (1+1) diluted urine (or 20 microl of the Triton X-100 was added to each 500 microl of (1+4) diluted serum) sample. After the diluted sample mixture (10 microl) was introduced into a graphite cuvette, the corresponding chemical modifier (10 microl, containing Ni2+ + Pd + NH4NO3 in HNO3 (0.2%, v/v)) was added to it and the mixture was atomized. The MDL (3sigma) for Se in urine and in serum was 4.4 and 21.4 microg/l in undiluted sample, respectively, and the calibration graphs were linear up to 150 and 400 microg/l. Accuracies of urine Se were 98.9 - 99.4% by testing SRM 2670 (NIST) urine standards with RSD (between-run, n = 3) within 2.9%; and that of serum Se was 97.2% when testing a certified second-generation human serum (No. 29, #664) with RSD (between-run, n = 3) of 1.4%. The proposed method can be applied easily, directly, and accurately to the measurement of Be and Se in real samples (including six urine Se and four serum Se from patients of Blackfoot Disease in Taiwan).

Beryllium↗