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PubMed1994

Examination of International Normalised Ratio (INR) imprecision by comparison of exact and approximate formulas. Intermountain Laboratory Data Project.

AIM: To evaluate the accuracy of the approximate linear formula of International Normalised Ratio (INR) imprecision by formal mathematical analysis. METHODS: Using probability theory, an exact formula for the coefficient of variation (CV) of the INR was derived. The CV from the approximate formula was compared with the CV from the exact formula for INR determinations between 1.0 and 10.0 with International Sensitivity Indices (ISIs) between 1.0 and 3.0 and prothrombin time ratio CVs between 1.0 and 10.0%. RESULTS: When the ISI equals 1.0, the approximate formula and the exact formula are equal. When the ISI is more than 1.0, the approximate formula overestimates the exact CV, but by less than one hundredth of the exact CV in the parameter ranges studied. The approximate formula is most accurate when laboratories achieve excellent prothrombin time measurement precision and use sensitive thromboplastins. CONCLUSIONS: The approximate formula provides a simple means for estimating the imprecision of the INR and is sufficiently accurate to warrant its use in clinical laboratories.

Humans↗
PubMed1991

Diffusion models for chemotaxis: a statistical analysis of noninteractive unicellular movement.

A program is developed for applying stochastic differential equations to models for chemotaxis. First a few of the experimental and theoretical models for chemotaxis both for swimming bacteria and for cells migrating along a substrate are reviewed. In physical and biological models of deterministic systems, finite difference equations are often replaced by a limiting differential equation in order to take advantage of the ease in the use of calculus. A similar but more intricate methodology is developed here for stochastic models for chemotaxis. This exposition is possible because recent work in probability theory gives ease in the use of the stochastic calculus for diffusions and broad applicability in the convergence of stochastic difference equations to a stochastic differential equation. Stochastic differential equations suggest useful data for the model and provide statistical tests. We begin with phenomenological considerations as we analyze a one-dimensional model proposed by Boyarsky, Noble, and Peterson in their study of human granulocytes. In this context, a theoretical model consists in identifying which diffusion best approximates a model for cell movement based upon theoretical considerations of cell physiology. Such a diffusion approximation theorem is presented along with discussion of the relationship between autocovariance and persistence. Both the stochastic calculus and the diffusion approximation theorem are described in one dimension. Finally, these tools are extended to multidimensional models and applied to a three-dimensional experimental setup of spherical symmetry.

Chemotaxis↗
PubMed2001

The optimal measure of allelic association.

Allelic association between pairs of loci is derived in terms of the association probability rho as a function of recombination theta, effective population size N, linear systematic pressure v, and time t, predicting both rho(rt), the decrease of association from founders and rho(ct), the increase by genetic drift, with rho(t) = rho(rt) + rho(ct). These results conform to the Malecot equation, with time replaced by distance on the genetic map, or on the physical map if recombination in the region is uniform. Earlier evidence suggested that rho is less sensitive to variations in marker allele frequencies than alternative metrics for which there is no probability theory. This robustness is confirmed for six alternatives in eight samples. In none of these 48 tests was the residual variance as small as for rho. Overall, efficiency was less than 80% for all alternatives, and less than 30% for two of them. Efficiency of alternatives did not increase when information was estimated simultaneously. The swept radius within which substantial values of rho are conserved lies between 385 and 893 kb, but deviation of parameters between measures is enormously significant. The large effort now being devoted to allelic association has little value unless the rho metric with the strongest theoretical basis and least sensitivity to marker allele frequencies is used for mapping of marker association and localization of disease loci.

Alleles↗
PubMed1999

Mean free energy topology for nucleotide sequences of varying composition based on secondary structure calculations.

The mean free energy generated from the secondary structure of RNA sequences of varying length and composition has been studied by way of probability theory. The expected boundaries or maximal and minimal values of a given distribution are explored and a method for estimating error as a function of the number of shuffled sequences is also examined. For typical nucleotide sequences found in biologically active organisms, the mean free energy, free energy distributions and errors appear to be scalable in terms of a fixed set of algorithm-dependent parameters and the nucleotide composition of the particular sequence under evaluation. In addition, a general semi-analytical formula for predicting the mean free energy is proposed which, at least to first-order approximation, can be used to rapidly predict the mean free energy of any sequence length and composition of RNA. The general methodology appears to be algorithm independent. The results are expected to provide a reference point for certain types of analysis related to structure of RNA or DNA sequences and to assist in measuring the somewhat related matter of complexity in algorithm development. Some related applications are discussed.

Algorithms↗
PubMed1971

Production of artificial "case histories" by using a small computer.

This paper describes a method of producing artificial "case histories" by using probability theory and clinical data from a series of 600 patients with acute abdominal pain. A series of 12 such cases were distributed to clinicians, medical students, medical secretaries and technicians, and members of the general public. For each "case" most clinicians concurred with the intended diagnosis. So did the medical secretaries and technicians; indeed this group were more confident of their chosen diagnoses than were the clinicians.It is suggested that clinicians are concerned to a large extent with the consequences of a diagnosis as well as its accuracy, and are motivated to some degree by a fear of the consequences of failure. They may be justified in adopting this policy, for when "errors" in diagnosis are harshly penalized the clinicians were infinitely more effective than any of the other groups.

Abdomen↗
PubMed1981

Stereological methods in cell biology: where are we--where are we going?

The current state of the art in morphometric cell biology is reviewed by looking at the developmental state of stereological methods, and at the approaches used to arrive at quantitative structure-function correlation. Stereological methods have reached a fairly advanced level of sophistication since mathematical stereology has been developed as a branch of geometric probability theory. The application of these methods in cell biology lags behind, both quantitatively and qualitatively. Among the strategies used in exploiting stereological methods in cell biology the physiological approach (where a change is induced experimentally and its effect on the cells is followed by biochemical and morphometric methods) ranks highest and is still valid. More analytical approaches, such as combining stereology and biochemistry in cell fraction studies, are fraught with difficulties. In considering future developments of stereological methods, the emphasis will have to be 1) on developing procedures for eliminating biases such as section thickness or resolution effects, and 2) on increasing the efficiency of the methods by better sampling rules and improved instrumentation. The future trends in morphometric cell biology might best be served by exploiting the potentials of histochemistry and stereology by combining them with a view to 1) establishing procedures for cell-specific sampling and 2) developing methods towards "molecular morphometry" on the basis of immunocytochemical labeling.

Animals↗
PubMedDate not supplied

Precautionary approaches to the appraisal of risk: a case study of a genetically modified crop.

There are strong scientific reasons for holding the broader scope of precautionary approaches to be more consistent with the scientific foundations of rational choice and probability theory than are conventional narrow risk-assessment techniques. The imperatives both of science and precaution can be seen to pull in the same direction. The regulatory appraisal of risk should become more systematic and broader in scope. In particular, a set of criteria can be developed concerning the need for greater humility, completeness, transparency, and participation in regulatory appraisal, with specific attention to the comparison of different options (including mixtures of options), the consideration of benefits and justifications, and the systematic "mapping" of the ways in which different framing assumptions lead to different pictures of performance. A case study of a pilot exercise applying a multi-criteria mapping method to the regulatory appraisal of a genetically modified crop is reported. The results are more complete than orthodox risk assessment, in that they embody consideration of an unlimited array of issues and include consideration of a wide range of different strategic alternatives to the use of GM technologies. It is concluded that conventional regulatory appraisal might be adapted to better address the imperatives of both science and precaution.

Consumer Product Safety↗
PubMed2001

Localization error analysis for stereo X-ray image guidance with probability method.

The mean value and standard deviation of localization error for the stereo imaging systems are derived based on probability theory. Compared with the maximum error analysis method used in our previous study, the new approach yields more informative and precise results as the guidance for X-ray imaging system design and protocol optimization. The prototype for our current study is a CCD based monoplane digital stereo X-ray imaging system. The imaging model consists of two X-ray sources and one detector plane. With perspective geometry, the least-square solution is derived to reconstruct 3-dimensional object points, such as a biopsy needle tip, from a pair of 2-dimensional digital radiographs. Under the conditions of our specific prototype, the measurement errors of interested points in the radiographs are modeled as random variables with Gaussian distribution. Such variables account for finite image system noise and positioning errors. Then, the 3D localization error, in terms of mean value and standard deviation, is formulated using measurement error, feature point location, and separation between the two X-ray sources and distance from source to detector. Both theoretical analysis and numerical simulation are performed. The mean value and standard deviation of the localization error are first evaluated using numerical simulation under practical imaging conditions. Then, the error estimates are given in simply analytic forms. Simulation and theoretical results are in excellent agreement. The results show that our prototype X-ray stereological imaging system is accurate and reliable to locate feature points in 3D for medical intervention. Imaging protocols can be effectively optimized through the 3D localization error analysis using the approximate formulas proposed in this study.

Algorithms↗
PubMed1996

A systematic analysis of average molecular weights and gelation conditions for branched immune complexes: the interaction between a multivalent antigen with distinct epitopes and many different types of bivalent antibodies.

A systematic model, based on standard equilibrium expressions and probability theory, is presented to calculate average molecular weights and gelation conditions for the immune system consisting of a single type of antigens with three (or more) different epitopes and three (or more) types of bivalent antibodies. Molecular weights Mn, Mw, Mz, and any other higher average molecular weights of formed branched antigen-antibody complexes in such an immune system are calculated directly without determining the whole distribution. The conditions for the formation of gel complexes also can be determined by this model.

Antibodies, Bispecific↗
PubMed2000

Contact-Angle Hysteresis Caused by a Random Distribution of Weak Heterogeneities on a Solid Surface.

A model according to which contact-angle hysteresis arises as the result of a random distribution of irregularities on the solid surface is investigated on the basis of probability theory. An estimate is obtained of the mathematical expectation of the number of stable equilibria when the effective angle between the liquid-gas surface and the solid surface with which the liquid is in contact deviates from the value, say theta(0), which would obtain if the solid surface were uniform, i.e., free from irregularities. It is found that when the effective contact angle deviates from theta(0) by less than a critical value, then the expected number of stable equilibria increases exponentially with the length of the contact line; therefore such a contact angle can occur under static conditions. But if the deviation of the contact angle from theta(0) exceeds the critical value, then the expected number of stable equilibria decreases exponentially with the length of the contact line, so a stable equilibrium is not possible for a macroscopic length of the contact line. The method is applicable only if the random deviations of the spreading power (defined as the solid-gas surface tension minus the sum of the liquid-gas and liquid-solid surface tensions) from its average are sufficiently small. It is found that the critical deviation of the contact angle from theta(0) is, apart from a slowly varying logarithmic factor, proportional to H(2)rho(s), where H is a measure of the amplitude of the surface irregularities and rho(s) is the surface density (i.e., number per unit area) of the irregularities. This qualitative feature agrees with the results previously obtained by several other authors, and, moreover, there is a surprisingly close agreement of the proportionality factor with the results of some earlier work in which the method of statistical analysis was much less elaborate than here. The effect of the logarithmic factor is to make the critical deviation of the contact angle increase more slowly than the first power of H(2)rho(s), and this is also in qualitative agreement with some earlier work. Copyright 2000 Academic Press.

Journal Article↗
PubMed1975

[Quantitative study of autoradiographic marking in the rat nervous system. II. Final characteristics of the adult animal brain: interpretation rules and concept of cortical chronoarchitecture].

In this work a statistical study is made of the final outcome of the quantification of the nerve cell labelling in the adult, after prenatal injection of tritiated thymidine. This outcome is presented in the form of histograms which are the superposition of elementary Poisson distributions. A theoretical model, based on Probability theory, has been developed explaining the experimental outcome. Studying the final histograms of a defined region, according to this model, we can find out the number and the importance of the constitutive cell generations (chronology). From the graphic study of the percentage of labelled cells and that of the average of grains, the characteristics of the stratification of the neuronic populations/architectony) can be defined. All these notions have been gathered into a new concept: chronoarchitectony. This concept has also been applied to the neocortex. The results show that there is a strong interpenetration of the different cell generations in a given layer. The cortical neuronic production is a continuous phenomenon and there is no correspondence with the discontinuity of the cortical layers.

Animals↗
PubMed1990

Laboratory screening method for selection of healthy volunteers.

The aim of laboratory screening in Phase I is to exclude subjects with subclinical illness, who might be at increased risk in the study, and who might also adversely influence interpretation of the results. A new method for laboratory screening, based on Bayesian probability theory, is proposed, which consists of: 1. Drawing up a list of diseases to be excluded. 2. Defining for each disease, the maximum acceptable risk that an included subject could be affected by it. 3. Identifying one test for each disease. 4. Using a contingency table to calculate the specificity of the test and integrating the estimated prevalence of the disease from epidemiological data. 5. Applying the percentage obtained by the calculation of specificity to the previously determined distribution of values in the volunteer population to identify the threshold value for inclusion. Use of this deductive method in screening volunteers for Phase I trials affords increased security of selection, while reducing the number of non-pertinent exclusions because of laboratory findings.

Bayes Theorem↗
PubMed2002

Depth profiles and resolution limits in accelerator-based solid state analysis.

A ubiquitous problem in solid state analysis is the determination of the elemental composition of a sample as a function of the depth. The determination of the depth profiles from ion-beam experiments is an ill-posed inversion problem due to ion-beam and detector-induced energy spreads as well as energy-loss straggling and small-angle scattering effects. The inversion problem is solved in the framework of Bayesian probability theory, which provides a method for quantifying and combining uncertain data and uncertain additional information. By deconvolving the apparatus transfer function and modeling the scattering events in the sample we reconstructed depth profiles of (13)C in tetrahedral amorphous carbon (ta-C) and depth profiles in (12)C/(13)C marker probes. An enhancement of the energy resolution by a factor of 6 was obtained.

Journal Article↗
PubMed1979

Cellular senescence and the analysis of generation time distributions.

Generation time analysis by time lapse cinematography is an important method for investigating cellular senescence in culture, but its interpretation is complicated by several types of bias and artifact, including small sample size, cut-off bias, changes in global growth rate, and phase of the population growth cycle. When these factors are considered, interpretation of the data base used by previous investigators changes considerably, and does not reveal any differences in growth behavior between middle and late passage WI-38 cells. Nor does it support the transition probability theory either of cell cycle transit or of culture senescence.

Cell Cycle↗
PubMed2005

Bayesian networks: computer-assisted diagnosis support in radiology.

Medical knowledge is growing at an explosive rate. While the availability of pertinent data has the potential to make the task of diagnosis more accurate, it is also increasingly overwhelming for physicians to assimilate. Using artificial intelligence techniques, a computer can process large amounts of data to help physicians manage the growing body of medical knowledge and thereby make better decisions. Computer-assisted diagnosis support is of particular interest to the diagnostic imaging community because radiologists must integrate huge amounts of data in order to diagnose disease. Bayesian networks, among the most promising artificial intelligence techniques available, enable computers to store knowledge and estimate the probability of outcomes based on probability theory. The article describes what a Bayesian network is and how it works using a system in mammography for illustration. A comparison of Bayesian networks with other types of artificial intelligence methods, specifically neural networks and case-based reasoning, clarifies the unique features and the potential of these systems to aid radiologists in the decisions they make every day.

Bayes Theorem↗
PubMed2004

Computer tools to assist the monitoring of outcomes in surgery.

OBJECTIVE: In recent years, there has been increasing use of analytical and graphical methods to assist the monitoring of outcomes in adult cardiac surgery. In this paper, we present extensions to the basic VLAD methodology that add flexibility and assist in its interpretation. METHODS: Using techniques from probability theory, we have devised graphical tools whereby deviations from expected outcomes can be monitored to see how likely they are to have occurred by chance. The methods are based upon pre-operative assessments of risk and use exact analytical techniques. RESULTS: These tools allow deviations from expected outcomes to be readily assessed and compared with the distribution of chance outcomes. Appropriate colour coding allows interpretation in terms of a temperature gradient. CONCLUSIONS: Exact analysis methods based on the use of pre-operative risk assessment provide a useful means for assisting the interpretation of VLAD charts. Such analysis has the advantage that it is applicable even for relatively short series of operations. Also, it takes specific account of the heterogeneity of case mix when quantifying the variability that is expected. By displaying the overall history of outcomes in a visually intuitive manner, it complements the more formal tools for detecting isolated good and bad runs that are available.

Cardiovascular Surgical Procedures↗
PubMed2005

Forensic interpretation of Y-chromosomal DNA mixtures.

The mathematical concept previously introduced for the forensic interpretation of DNA mixtures using non-associated genetic markers has been adapted to the assessment of haplotypes. Such calculus is required, for example, when Y-chromosomal markers are used in forensics. In addition to outlining the general mathematical framework, we devise two approaches to its practical computational implementation, involving either the inclusion-exclusion principle of probability theory or a recursion in the number of unknown contributors invoked. The two approaches scale differently, depending upon the complexity of the case and the diversity of the markers used. The performance of Y-chromosomal microsatellites (Y-STRs) as a means of trace donor discrimination has been assessed by simulation, using the derived formulas. Based upon data from the Y-chromosomal Haplotype Reference Database (YHRD), the exclusion chance of a non-contributor is shown to vary between 95% in the case of two contributors, and 70% for five contributors. With only one additional contributor, half of all contributing suspects would yield a log-likelihood ratio in favour of donorship of 1.61 or higher, although the median drops to 0.66 with four additional contributors. It must be emphasised that these estimates of the discriminatory power of Y-STRs are likely to be conservative since the simulations involved only haplotypes known to occur in YHRD.

Chromosomes, Human, Y↗
PubMed2004

Extension of the method of moments for population balances involving fractional moments and application to a typical agglomeration problem.

The method of moment (MOM) is a powerful tool for solving population balance. Nevertheless it cannot be used in every circumstance. Sometimes, in fact, it is not possible to write the governing equations in closed form. Higher moments, for instance, could appear in the evolution of the lower ones. This obstacle has often been resolved by prescribing some functional form for the particle size distribution. Another example is the occurrence of fractional moment, usually connected with the presence of fractal aggregates. For this case we propose a procedure that does not need any assumption on the form of the distribution but it is based on the "moments generating function" (that is the Laplace transform of the distribution). An important result of probability theory is that the kth derivative of the moments generating function represents the kth moment of the original distribution. This result concerns integer moments but, taking in account the Weyl fractional derivative, could be extended to fractional orders. Approximating fractional derivative makes it possible to express the fractional moments in terms of the integer ones and so to use regularly the method of moments.

Journal Article↗