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PubMedDate not supplied

Probabilistic Markov model to assess the cost-effectiveness of bronchodilator therapy in COPD patients in different countries.

OBJECTIVES: The development of a probabilistic Markov model with a time horizon of 1 year to compare the cost-effectiveness of three bronchodilators: 1) the new long-acting anticholinergic tiotropium; 2) the short-acting anticholinergic ipratropium; and 3) the long-acting beta 2-agonist salmeterol, for the treatment of patients with chronic obstructive pulmonary disease (COPD) in different countries. In this article we compare The Netherlands and Canada. METHODS: The Markov model was structured along disease severity states and exacerbations. Transition probabilities between disease states and exacerbation probabilities were derived from patient-level data from six randomized controlled trials assessing the efficacy and safety of tiotropium. Resource utilization during exacerbations and maintenance treatment for The Netherlands were derived from two clinical trials, whereas for Canada these data were obtained from a countrywide observational study that used similar inclusion criteria as the trials. Second-order Monte Carlo simulations were undertaken in which values were randomly drawn from distributions of these parameters. Outcomes of the model are yearly treatment costs, exacerbations, and quality-adjusted life months. RESULTS: The mean difference in the number of exacerbations was 0.17 (95% uncertainty interval: -0.02-0.37) in favor of tiotropium when compared with salmeterol and the difference between salmeterol and ipratropium was 0.12 (-0.17-0.44) in favor of salmeterol. The number of quality-adjusted life months did not substantially differ between treatment groups and varied from 8.42 (SE 0.41) in the tiotropium group to 8.17 (0.46) in the salmeterol group and 8.11 (0.50) in the ipratropium group. In The Netherlands, costs in the tiotropium group were 42 Euros (-484-353) lower than in the salmeterol group, whereas costs in the salmeterol group were 128 Euros (-795-457) lower than in the ipratropium group. In Canada, costs were consistently lower than in The Netherlands and nearly the same in all treatment groups. Differences between the two countries were primarily a result of a higher length of hospital stay in case of an exacerbation in The Netherlands. The cost-effectiveness acceptability frontier of exacerbations showed that tiotropium was associated with the maximum expected net benefit for all values of the ceiling ratio above 0 Euros (The Netherlands) and 10 Euros (Canada) in the base case analysis. CONCLUSIONS: This probabilistic model-based economic evaluation demonstrates how clinical trial data can be combined and integrated with country-specific information about resource utilization and unit cost to assess the cost-effectiveness of bronchodilators in COPD patients. Quality-adjusted life months did not substantially differ between treatment groups. In terms of exacerbations, tiotropium was associated with maximum expected net benefit for plausible values of the ceiling ratio. In sensitivity analyses, this outcome was most sensitive to changes in exacerbation rates.

Adrenergic beta-2 Receptor Agonists↗

PubMed2004

Probabilistic kinetic model of slow oxidation of low-density lipoprotein: II. Experiments.

Theoretical probabilistic kinetic model has been applied to describe the measurements of several oxidation markers as a function of time, during slow oxidation of low-density lipoprotein (LDL). It has been demonstrated that such a process could be described as tocopherol-mediated peroxidation (TMP), initiated and sustained by the action of copper ions, present in LDL in trace amounts. In that process concentration of alpha-tocopherol remains essentially unaltered. Tocopherol and copper ions act as catalysts, oscillating between the oxidized and reduced states. The fitting of the theoretical model to the experimental data resulted in determination of the numerical values for the kinetic parameters. It has been found that the parameter values used for the fitting of the data collected for a number of samples from various donors differ rather little. The kinetic chain length of 1.3 (in presence of co-antioxidants) and 2.9 (in the absence of co-antioxidants) is shorter than found by others. The difference probably comes from the much lower concentration of copper ions in our systems (about 0.1 ion per LDL particle).

Copper↗

PubMed1999

A model of probabilistic category learning.

A new connectionist model (named RASHNL) accounts for many "irrational" phenomena found in nonmetric multiple-cue probability learning, wherein people learn to utilize a number of discrete-valued cues that are partially valid indicators of categorical outcomes. Phenomena accounted for include cue competition, effects of cue salience, utilization of configural information, decreased learning when information is introduced after a delay, and effects of base rates. Experiments 1 and 2 replicate previous experiments on cue competition and cue salience, and fits of the model provide parameter values for making qualitatively correct predictions for many other situations. The model also makes 2 new predictions, confirmed in Experiments 3 and 4. The model formalizes 3 explanatory principles: rapidly shifting attention with learned shifts, decreasing learning rates, and graded similarity in exemplar representation.

Cues↗

PubMed2003

A multi-scale probabilistic network model for detection, synthesis and compression in mammographic image analysis.

We develop a probabilistic network model over image spaces and demonstrate its broad utility in mammographic image analysis, particularly with respect to computer-aided diagnosis. The model employs a multi-scale pyramid decomposition to factor images across scale and a network of tree-structured hidden variables to capture long-range spatial dependencies. This factoring makes the computation of the density functions local and tractable. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree. The model parameters are found with maximum likelihood estimation using the expectation-maximization algorithm. The utility of the model is demonstrated for three applications: (1) detection of mammographic masses for computer-aided diagnosis; (2) qualitative assessment of model structure through mammographic synthesis; and (3) compression of mammographic regions of interest.

Female↗

PubMed2006

The effectiveness of mutation operation in the case of Estimation of Distribution Algorithms.

The Estimation of Distribution Algorithms are a class of evolutionary algorithms which adopt probabilistic models to reproduce individuals in the next generation, instead of conventional crossover and mutation operators. In this paper, mutation operators are incorporated into Estimation of Distribution Algorithms in order to maintain the diversities in EDA populations. Two kinds of mutation operators are examined: a bitwise mutation operator and a mutation operator taking account into the probabilistic model. In experiments, we do not only compare the proposed methods with conventional EDAs on a few fitness functions but also analyze sampled probabilistic models by using KL-divergence. The experimental results shown in this paper elucidate that the mutation operator taking account into the probabilistic model improve the search ability of EDAs.

Algorithms↗

PubMed2005

Analytically solvable model of probabilistic network dynamics.

We present a simple model of network dynamics that can be solved analytically for fully connected networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random networks. A comparison with the scale-free network, though qualitatively similar, shows the effect of distinct topology.

Journal Article↗

PubMed2003

Probabilistic graphical models for computational biomedicine.

BACKGROUND: As genomics becomes increasingly relevant to medicine, medical informatics and bioinformatics are gradually converging into a larger field that we call computational biomedicine. OBJECTIVES: Developing a computational framework that is common to the different disciplines that compose computational biomedicine will be a major enabler of the further development and integration of this research domain. METHODS: Probabilistic graphical models such as Hidden Markov Models, belief networks, and missing-data models together with computational methods such as dynamic programming, Expectation-Maximization, data-augmentation Gibbs sampling, and the Metropolis-Hastings algorithm provide the tools for an integrated probabilistic approach to computational biomedicine. RESULTS AND CONCLUSIONS: We show how graphical models have already found a broad application in different fields composing computational biomedicine. We also indicate several challenges that lie at the interface between medical informatics, statistical genomics, and bioinformatics. We also argue that graphical models offer a unified framework making it possible to integrate in a statistically meaningful way multiple models ranging from the molecular level to cellular and to clinical levels. Because of their versatility and firm statistical underpinning, we assert that probabilistic graphical models can serve as the lingua franca for many computationally intensive approaches to biology and medicine. As such, graphical models should be a foundation of the curriculum of students in these fields. From such a foundation, students could then build towards specific computational methods in medical informatics, medical image analysis, statistical genetics, or bioinformatics while keeping the communication open between these areas.

Computational Biology↗

PubMedDate not supplied

Probabilistic kinetic model of slow oxidation of low-density lipoprotein. 3. Hydroperoxide-free initiation.

A theoretical model is presented that explains slow copper-induced oxidation of low-density lipoprotein in the systems free of seeded hydroperoxydes. The model is based on the probabilistic kinetic theory, modified to take into account different radical generation rates by oxidized and reduced forms of the metal ions. It is shown that the initiation and progression of the LDL oxidation can take place in any LDL dispersion by metal-induced oxidation of alpha-tocopherol, one of the constituents of LDL, and formation of slowly reacting alpha-tocopheroxyl radical. Selected values of several adjustable parameters define actual temporal profiles of the quantities defining the oxidation process.

Algorithms↗

PubMed2004

The use of probabilistic decision models in technology assessment : the case of total hip replacement.

There is increasing recognition that decision modelling is central to health technology assessment and, in particular, to analyses to support formal decision making regarding the funding of the use of new technologies. In part, the key role of decision analysis stems from the need to handle multiple sources of uncertainty in the available evidence. The use of probabilistic decision analysis is a means of reflecting the parameter uncertainty in models and presenting this in a comprehensible manner to decision makers. In this article, we demonstrate the potential role of probabilistic models using the case study of total hip replacement surgery.A cost-effectiveness model was constructed to compare the Charnley and Spectron hip prostheses in terms of lifetime costs and quality-adjusted life-years (QALYs). Revision rates were estimated from the Swedish National Total Hip Arthroplasty Register (1992-2000); the risk of revision with the Spectron prosthesis relative to the Charnley prosthesis was 0.67 (95% confidence interval [CI] 0.32, 1.02) for early revisions and 0.26 (95% CI 0.07, 0.46) for late revisions. This lower revision risk resulted in the Spectron generating more QALYs than the Charnley prosthesis. Based on mean costs and QALYs, the Spectron results in cost savings in younger patients, and generates incremental cost-effectiveness ratios of between pound1000 and pound16 000 in older patient groups. The probabilistic results from the model indicated that, if it is assumed that decision makers are willing to pay up to pound20 000 per additional QALY, the probability of the Spectron being the more cost-effective prosthesis ranged between 70% and 100%, depending on the age and sex of the patient.This article looks at the application of probabilistic decision modelling using total hip replacement as a case study to emphasis the need for decision models to quantify all sources of parameter uncertainty and to clearly distinguish parameter uncertainty from subgroup heterogeneity.

Adult↗

PubMed2003

Application of a probabilistic microstructural model to determine reference length and toe-to-linear region transition in fibrous connective tissue.

This study shows how a probabilistic microstructural model for fibrous connective tissue behavior can be used to objectively describe soft tissue low-load behavior. More specifically, methods to determine tissue reference length and the transition from the strain-stiffening "toe-region" to the more linear region of the stress-strain curve of fibrous connective tissues are presented. According to a microstructural model for uniaxially loaded collagenous tissues, increasingly more fibers are recruited and bear load with increased tissue elongation. Fiber recruitment is represented statistically according to a Weibull probability density function (PDF). The Weibull PDF location parameter in this formulation corresponds to the stretch at which the first fibers begin to bear load and provides a convenient method of determining reference length. The toe-to-linear region transition is defined by utilizing the Weibull cumulative distribution function (CDF) which relates the fraction of loaded fibers to the tissue elongation. These techniques are illustrated using representative tendon and ligament data from the literature, and are shown to be applicable retrospectively to data from specimens that are not heavily preloaded. The reference length resulting from this technique provides an objective datum from which to calculate stretch, strain, and tangent modulus, while the Weibull CDF provides an objective parameter with which to characterize the limits of low-load behavior.

Animals↗

PubMed2006

Probabilistic transport model with two critical mechanisms for magnetically confined plasmas.

A consistent description of transitions to improved confinement regimes in terms of a probabilistic transport model is presented. The model has two thresholdlike mechanisms, acting, respectively, on the first and second spatial derivatives of the density. These mechanisms allow switching between three different transport channels: one corresponding to classical diffusion and the other two to different scale-free transport mechanisms. The dependence of the transport properties on the second derivative models the appearance of a sheared radial electric field that causes a reduction of transport. The results of the model reproduce the enhancements of confinement time and fluctuations (associated to edge localized modes) that take place during transitions, when the fueling rate is increased. The model could be of relevance beyond the field of plasma physics as a general transport model with critical parameters.

Journal Article↗

PubMed2004

Inferring cellular networks using probabilistic graphical models.

High-throughput genome-wide molecular assays, which probe cellular networks from different perspectives, have become central to molecular biology. Probabilistic graphical models are useful for extracting meaningful biological insights from the resulting data sets. These models provide a concise representation of complex cellular networks by composing simpler submodels. Procedures based on well-understood principles for inferring such models from data facilitate a model-based methodology for analysis and discovery. This methodology and its capabilities are illustrated by several recent applications to gene expression data.

Bayes Theorem↗

PubMedDate not supplied

A probabilistic ribbon model for shape analysis of the cerebral sulci: application to the central sulcus.

PURPOSE: An approach for quantifying the shapes of the cerebral sulci is presented, utilizing a probabilistic geometric model, and it is applied to the central sulcus. METHOD: The geometric structure of the central sulcus is determined from a set of outlines on cross-sectional images and is used by a procedure that automatically labels the major crest lines, i.e., curves of locally maximal curvature, along the sulcus. An automated procedure then determines a parametric representation of the central sulcus that is consistent across individuals, in that it assigns the same parametric coordinates to corresponding regions of the sulcus. RESULTS: The method is applied to the central sulci from 20 subjects. The use of this shape representation in cortical morphometric analysis applications is demonstrated, in particular in obtaining local depth and curvature measurements of a sulcus as well as in determining average shapes and variability. CONCLUSION: With this method, we were able to build parametric representations of the sulcal ribbons by preserving anatomical homologies.

Anatomy, Cross-Sectional↗

PubMed1997

Improved probabilistic decompression model risk predictions using linear-exponential kinetics.

Using a data base of 2,383 air and nitrogen-oxygen dives resulting in 131 cases of decompression sickness (DCS), risk functions were developed for a set of probabilistic decompression models according to survival analysis techniques. Parameters were optimized using the method of maximum likelihood Gas kinetics were either traditional exponential uptake and elimination, or an exponential uptake followed by linear elimination (LE kinetics) when calculated supersaturation was excessive. Risk functions either used the calculated relative gas supersaturation directly, or a delayed risk using a time integral of prior supersaturation. The most successful model (considering both incidence and time of onset of DCS) used supersaturation risk, and LE kinetics (in only 1 of 3 parallel compartments). Several methods of explicitly incorporating metabolic gases in physiologically plausible functions were usually found in lumped threshold terms and did not explicitly affect the overall data fit. The role of physiologic fidelity vs. empirical data fitting ability in accounting for model success is discussed.

Decompression Sickness↗

PubMed1991

Probabilistic mental models: a Brunswikian theory of confidence.

Research on people's confidence in their general knowledge has to date produced two fairly stable effects, many inconsistent results, and no comprehensive theory. We propose such a comprehensive framework, the theory of probabilistic mental models (PMM theory). The theory (a) explains both the overconfidence effect (mean confidence is higher than percentage of answers correct) and the hard-easy effect (overconfidence increases with item difficulty) reported in the literature and (b) predicts conditions under which both effects appear, disappear, or invert. In addition, (c) it predicts a new phenomenon, the confidence-frequency effect, a systematic difference between a judgment of confidence in a single event (i.e., that any given answer is correct) and a judgment of the frequency of correct answers in the long run. Two experiments are reported that support PMM theory by confirming these predictions, and several apparent anomalies reported in the literature are explained and integrated into the present framework.

Adult↗

PubMed2005

Probabilistic Gompertz model of irreversible growth.

Characterizing organism growth within populations requires the application of well-studied individual size-at-age models, such as the deterministic Gompertz model, to populations of individuals whose characteristics, corresponding to model parameters, may be highly variable. A natural approach is to assign probability distributions to one or more model parameters. In some contexts, size-at-age data may be absent due to difficulties in ageing individuals, but size-increment data may instead be available (e.g., from tag-recapture experiments). A preliminary transformation to a size-increment model is then required. Gompertz models developed along the above lines have recently been applied to strongly heterogeneous abalone tag-recapture data. Although useful in modelling the early growth stages, these models yield size-increment distributions that allow negative growth, which is inappropriate in the case of mollusc shells and other accumulated biological structures (e.g., vertebrae) where growth is irreversible. Here we develop probabilistic Gompertz models where this difficulty is resolved by conditioning parameter distributions on size, allowing application to irreversible growth data. In the case of abalone growth, introduction of a growth-limiting biological length scale is then shown to yield realistic length-increment distributions.

Age Factors↗

PubMedDate not supplied

Mental models and probabilistic thinking.

This paper outlines the theory of reasoning based on mental models, and then shows how this theory might be extended to deal with probabilistic thinking. The same explanatory framework accommodates deduction and induction: there are both deductive and inductive inferences that yield probabilistic conclusions. The framework yields a theoretical conception of strength of inference, that is, a theory of what the strength of an inference is objectively: it equals the proportion of possible states of affairs consistent with the premises in which the conclusion is true, that is, the probability that the conclusion is true given that the premises are true. Since there are infinitely many possible states of affairs consistent with any set of premises, the paper then characterizes how individuals estimate the strength of an argument. They construct mental models, which each correspond to an infinite set of possibilities (or, in some cases, a finite set of infinite sets of possibilities). The construction of models is guided by knowledge and beliefs, including lay conceptions of such matters as the "law of large numbers". The paper illustrates how this theory can account for phenomena of probabilistic reasoning.

Humans↗

PubMed2001

A probabilistic union model with automatic order selection for noisy speech recognition.

A critical issue in exploiting the potential of the sub-band-based approach to robust speech recognition is the method of combining the sub-band observations, for selecting the bands unaffected by noise. A new method for this purpose, i.e., the probabilistic union model, was recently introduced. This model has been shown to be capable of dealing with band-limited corruption, requiring no knowledge about the band position and statistical distribution of the noise. A parameter within the model, which we call its order, gives the best results when it equals the number of noisy bands. Since this information may not be available in practice, in this paper we introduce an automatic algorithm for selecting the order, based on the state duration pattern generated by the hidden Markov model (HMM). The algorithm has been tested on the TIDIGITS database corrupted by various types of additive band-limited noise with unknown noisy bands. The results have shown that the union model equipped with the new algorithm can achieve a recognition performance similar to that achieved when the number of noisy bands is known. The results show a very significant improvement over the traditional full-band model, without requiring prior information on either the position or the number of noisy bands. The principle of the algorithm for selecting the order based on state duration may also be applied to other sub-band combination methods.

Algorithms↗