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A method for calculating probability functions and moments of a distribution of isotopomers, constructed by Kelleher and Masterson (2), is described. The method involves the use of the so-called probability-generating functions, a mathematical device especially convenient for the purpose of calculation of probabilistic quantities in discrete models of the Kelleher-Masterson type.
We introduce and study an artificial neural network inspired by the probabilistic receptor affinity distribution model of olfaction. Our system consists of N sensory neurons whose outputs converge on a single processing linear threshold element. The system's aim is to model discrimination of a single target odorant from a large number p of background odorants within a range of odorant concentrations. We show that this is possible provided p does not exceed a critical value p(c) and calculate the critical capacity alpha(c) = p(c)/N. The critical capacity depends on the range of concentrations in which the discrimination is to be accomplished. If the olfactory bulb may be thought of as a collection of such processing elements, each responsible for the discrimination of a single odorant, our study provides a quantitative analysis of the potential computational properties of the olfactory bulb. The mathematical formulation of the problem we consider is one of determining the capacity for linear separability of continuous curves, embedded in a large-dimensional space. This is accomplished here by a numerical study, using a method that signals whether the discrimination task is realizable, together with a finite-size scaling analysis.
Successful retrieval of a corpus of literature on a broad topic can be difficult. This study demonstrates a method to retrieve the dental and craniofacial research literature. We explored MeSH manually for dental or craniofacial indexing terms. MEDLINE was searched using these terms, and a random sample of references was extracted from the resulting set. Sixteen dental research experts categorized these articles, reading only the title and abstract, as either: (1) dental research, (2) dental non-research, (3) non-dental, or (4) not sure. Identify Patient Sets (IPS), a probabilistic text classifier, created models, based on the presence or absence of words or UMLS phrases, that distinguished dental research articles from all others. These models were applied to a test set with different inputs for each article: (1) title and abstract only, (2) MeSH terms only, or (3) both. By title and abstract only, IPS correctly classified 64% of all dental research articles present in the test set. The percentage of correctly classified dental research articles in this retrieved set was 71%. MeSH term inclusion decreased performance. Computer programs that use text input to categorize articles may aid in retrieval of a broad corpus of literature better than indexing terms or key words alone.
PURPOSE: To describe the clinical and economic consequences of image-guided core biopsy versus surgical excisional biopsy of mammographically identified breast lesions. PATIENTS AND METHODS: Clinical and economic data were collected for 1121 patients undergoing core biopsies and 501 patients undergoing surgical biopsies between 1996 and 1998. Lesions were classified according to mammographic degree of suspicion and type of radiographic abnormality. Costs were measured from the societal perspective. A decision analytic model was constructed, with probabilistic sensitivity analysis. RESULTS: Lesions diagnosed via core versus surgical biopsy were less likely to be masses (39% v 55%), less likely to be classified as high cancer suspicion (17% v 26%), and less likely to be treated with a single procedure (74% v 81%; P <.001 for each). Cancers diagnosed by a surgical biopsy were less likely to have had a single operative procedure (33% v 84%) and were associated with higher total costs whether mastectomy (US dollars 2775 v US dollars 1849) or lumpectomy (US dollars 2112 v US dollars 1365) was used. Sensitivity analysis showed core biopsy optimal in 95.4% of trials. Core biopsy was favored for low-suspicion lesions, calcifications, and masses, and overall for patients who underwent lumpectomy alone. CONCLUSION: Image-guided core biopsy can be cost-saving compared with surgical biopsy, particularly when the mammographic abnormality is classified as low suspicion or consists of calcifications or masses. Moving to a policy in which core biopsy is the preferred approach in these settings has the potential to result in significant cost savings.
Diffusive wave phased arrays have been demonstrated to be a sensitive method of detecting inhomogeneities embedded in heavily scattering media. However, the increase in sensitivity is coupled with an increase in noise, so that the optimum performance may not be obtained when the sources are modulated in antiphase. The performance of a range of configurations in the presence of Gaussian noise is investigated by using probabilistic detection theory. A model of diffusive wave propagation through scattering media is used to demonstrate that the phase performance can be improved by controlling the relative phase difference between the two sources. However, the best performance is obtained by using the amplitude response of a single source system. The major benefit of a phased array system is therefore the rejection of common systematic noise.
Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.
INTRODUCTION: The purpose of this article is to demonstrate the application and feasibility of using value of information analysis to help set priorities for research as part of the UK National Health Service (NHS) Health Technology Assessment Programme. Probabilistic decision analysis and value of information methods were applied to a research topic under consideration by the National Coordinating Centre for Health Technology Assessment (NCCHTA), in the UK. The case study presented considers whether long-term, low-dose antibacterial treatment of recurrent urinary tract infections (UTIs) in children is effective and cost effective compared with short-term antibacterial therapy. METHODS: A probabilistic decision-analytic model was developed, within which evidence from published sources was synthesised. Eight subgroups were considered and defined in terms of sex and presence of vesico-ureteral reflux (VUR). Costs were assessed from an NHS perspective, and benefits were expressed as quality-adjusted life-years (QALYs). Simulation methods were used to determine the probability that alternative therapies would be cost effective at a range of threshold values that the NHS may attach to an additional QALY. Value of information analysis was used to quantify the cost of uncertainty associated with the decision about which therapy to adopt, which indicates the maximum value of future research. The feasibility and practicality of using value of information methods to help inform research prioritization was evaluated. RESULTS: At a threshold value for an additional QALY of 30,000 pound , long-term antibacterial treatment may be regarded as cost effective for all eight patient groups. There was, however, substantial uncertainty surrounding the choice of antibacterial. DISCUSSION/CONCLUSION: The use of value of information methods was feasible and could inform research prioritization for the NHS. In the context of this specific decision faced by the NHS, the results show that long-term low-dose antibacterials for preventing recurrent UTIs may be cost effective, based on current evidence. However, the analysis suggests that further primary research with longer follow-up may be worthwhile, particularly for girls with no VUR.
Interest in applying probabilistic conjoint measurement (PCM) models, such as those devised by the late Georg Rasch, to health status and quality of life data has grown significantly in the last few years. Applications have yet, however, to fully realize the opportunities for scientific generalization and practical convenience PCM offers. This article fleshes out the substance of some of these opportunities by comparing eight separate PCM calibrations of the SF-36 ten-item physical functioning scale (PF-10). The initial average correlation across the 28 pairs of calibrations is .84; after taking advantage of the PCM model's capacity to account for missing data by omitting from the comparisons items that vary due to sample idiosyncracies, the average correlation is .90. Opportunities for, and limitations on, generalization from PF-10 measures are explored.
Gene expression profiling by microarray technology has been successfully applied to classification and diagnostic prediction of cancers. Various machine learning and data mining methods are currently used for classifying gene expression data. However, these methods have not been developed to address the specific requirements of gene microarray analysis. First, microarray data is characterized by a high-dimensional feature space often exceeding the sample space dimensionality by a factor of 100 or more. In addition, microarray data exhibit a high degree of noise. Most of the discussed methods do not adequately address the problem of dimensionality and noise. Furthermore, although machine learning and data mining methods are based on statistics, most such techniques do not address the biologist's requirement for sound mathematical confidence measures. Finally, most machine learning and data mining classification methods fail to incorporate misclassification costs, i.e. they are indifferent to the costs associated with false positive and false negative classifications. In this paper, we present a probabilistic neural network (PNN) model that addresses all these issues. The PNN model provides sound statistical confidences for its decisions, and it is able to model asymmetrical misclassification costs. Furthermore, we demonstrate the performance of the PNN for multiclass gene expression data sets. Here, we compare the performance of the PNN with two machine learning methods, a decision tree and a neural network. To assess and evaluate the performance of the classifiers, we use a lift-based scoring system that allows a fair comparison of different models. The PNN clearly outperformed the other models. The results demonstrate the successful application of the PNN model for multiclass cancer classification.
OBJECTIVE: Hip fracture is a common complication of osteoporosis, resulting in significant morbidity and mortality, with a high financial cost to the healthcare system. Hip protectors have been advocated as an effective method to prevent hip fractures in high-risk individuals. This study models the cost-effectiveness of hip protectors in the prevention of osteoporosis related hip fractures in elderly nursing home residents. METHODS: An incremental cost-effectiveness analysis was performed comparing hip protectors to "no treatment" and to "calcium and vitamin D supplements." The study population was a hypothetical cohort of 1000 nursing home residents. A societal perspective, with a lifetime time horizon, was adopted. Data regarding costs, effectiveness, and quality of life measures were collected from the current literature and from Peace Arch Hospital, a community hospital in White Rock, British Columbia, Canada. Sensitivity analysis was performed. RESULTS: Hip protector use was found to be a dominant strategy compared to no treatment and to calcium and vitamin D supplements. Dominance implies lower cost and higher effect, generating cost-effectiveness ratios less than zero. Dominance with respect to cost and effectiveness of hip protectors in preventing hip fractures persisted when the model was subjected to probabilistic sensitivity analysis. CONCLUSION: Cost-effectiveness analysis suggests that hip protectors could save money while preventing hip fractures and improving quality of life in nursing home residents.
Ragweed is the dominant type of the atmospheric spora of North America. In this paper we present a forecasting model based on the probabilistic distribution of pollen curves, which was applied to four years of sampling. Except for rapid (24 hours) but large fluctuations of the pollen concentration, our algorithm allows for an adequate estimate of the exposure risk. However, these rapid fluctuations can account for up to 40% of the annual pollen sum.
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We posit that chance plays a major role in the occurrence of many common malformations that cluster in families but recur less frequently than expected for simple Mendelian traits. Once the role of random effects is accepted, the segregation of such malformations may be explained on the basis of Mendelian transmission of a single abnormal gene that predisposes to, but does not always result in, the abnormal phenotype. We apply a stochastic (probabilistic) single-gene model to the occurrence of malformations in mouse and man. The stochastic single-gene model suggests the feasibility of isolating individual genes that determine morphogenesis and sets limits on the precision with which the recurrence of malformations can be predicted.
To evaluate some of the consequences of including probabilistic processes (e.g. quantal noise) in a computable model of light-adaptation dynamics, we considered the behavior of a general class of models. These models contain four stages: (1) early noise; (2) a deterministic filtering and gain-changing stage; (3) late noise; (4) a decision rule that is either an ideal (signal-known-exactly) detector or a peak-trough detector. With the ideal detector and without late noise, the observer's sensitivity as a function of mean luminance and temporal frequency is not affected by the filtering and gain-changing stage. Consequently, if the early noise is entirely quantal fluctuations, sensitivity will always be a square-root function of mean luminance and a uniform (flat) function of temporal frequency. This latter prediction is contradicted by all known data; either the ideal-detector is the wrong decision rule or sensitivity is almost always limited by sources of noise other than quantal fluctuations. With the peak-trough detector, however, with or without late noise, the observer's sensitivity as a function of temporal frequency does reflect the sensitivity of the low-level filtering and gain-changing stage. Late noise is needed, however, if the observer's sensitivity as a function of mean luminance is to go through both a square-root and a Weber region. Comparing these conclusions to similar work on the spatial frequency dimension highlights differences between the spatial and temporal frequency domains. Finally, on the basis of these analyses and evidence from the literature, we question whether quantal fluctuations limit visual sensitivity under any condition.
If a common ancestor of all living humans is defined as an individual who is a genealogical ancestor of all present-day people, the most recent common ancestor (MRCA) for a randomly mating population would have lived in the very recent past. However, the random mating model ignores essential aspects of population substructure, such as the tendency of individuals to choose mates from the same social group, and the relative isolation of geographically separated groups. Here we show that recent common ancestors also emerge from two models incorporating substantial population substructure. One model, designed for simplicity and theoretical insight, yields explicit mathematical results through a probabilistic analysis. A more elaborate second model, designed to capture historical population dynamics in a more realistic way, is analysed computationally through Monte Carlo simulations. These analyses suggest that the genealogies of all living humans overlap in remarkable ways in the recent past. In particular, the MRCA of all present-day humans lived just a few thousand years ago in these models. Moreover, among all individuals living more than just a few thousand years earlier than the MRCA, each present-day human has exactly the same set of genealogical ancestors.
BACKGROUND: Algorithms that locate evolutionarily conserved sequences have become powerful tools for finding functional DNA elements, including transcription factor binding sites; however, most methods do not take advantage of an explicit model for the constrained evolution of functional DNA sequences. RESULTS: We developed a probabilistic framework that combines an HKY85 model, which assigns probabilities to different base substitutions between species, and weight matrix models of transcription factor binding sites, which describe the probabilities of observing particular nucleotides at specific positions in the binding site. The method incorporates the phylogenies of the species under consideration and takes into account the position specific variation of transcription factor binding sites. Using our framework we assessed the suitability of alignments of genomic sequences from commonly used species as substrates for comparative genomic approaches to regulatory motif finding. We then applied this technique to Saccharomyces cerevisiae and related species by examining all possible six base pair DNA sequences (hexamers) and identifying sequences that are conserved in a significant number of promoters. By combining similar conserved hexamers we reconstructed known cis-regulatory motifs and made predictions of previously unidentified motifs. We tested one prediction experimentally, finding it to be a regulatory element involved in the transcriptional response to glucose. CONCLUSION: The experimental validation of a regulatory element prediction missed by other large-scale motif finding studies demonstrates that our approach is a useful addition to the current suite of tools for finding regulatory motifs.
Clinicians are beings with finite minds and thus need to use simplified models of the world in making decisions [1]. However, these models need not be oversimplified, as are the models encouraged by the prevalent view of science, the Mechanistic Paradigm, which are articulated as rigid maxims. A more current view of science, the Probabilistic paradigm, encourages more complex models, which can be articulated as the more flexible maxims used with insight by the wise clinician.
The kinetics of biodegradation of mixtures of polycyclic aromatic hydrocarbons (PAHs) by Sphingomonas paucimobilis strain EPA505 were investigated. The investigation focused on three- and four-ring PAHs, specifically 2-methylphenanthrene, fluoranthene, and pyrene. Uptake rates in aerobic batch suspended cultivations were measured for the individual PAHs and their binary and ternary mixtures. It was observed that kinetics were influenced by the mixture composition and the kinetic properties of the components. A material balance equation containing the Monod model was numerically fitted to uptake data to determine extant kinetic parameters for the individual PAHs. Similarly, equations containing kinetic interaction models derived from enzyme kinetics were fitted to the uptake data obtained from experiments with binary and ternary mixtures. The investigation considered the following interaction types: no-interaction (Monod), pure competitive interaction, noncompetitive or mixed-type interaction, uncompetitive inhibition, and nonspecific interaction based on pure competition (SKIP). Model fit was evaluated based on probabilistic and statistical criteria and inferences were reached about underlying interaction mechanisms based on model fit. Mixture kinetics were most adequately simulated by the pure competitive interaction model with mutual substrate exclusivity. This model is fully predictive, relying only on parameters determined in the sole-PAH experiments. It was shown that for low percent inhibition values and with limited data, pure competitive interaction kinetics may not be evident, resembling no-interaction kinetics. This study is a reasonable starting point for understanding and modeling biodegradation of complex PAH mixtures in engineered and natural systems.