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PubMed2002

The use of information graphs to evaluate and compare diagnostic tests.

OBJECTIVES: The purpose of this communication is to demonstrate the use of "information graphs" as a means of characterizing diagnostic test performance. METHODS: Basic concepts in information theory allow us to quantify diagnostic uncertainty and diagnostic information. Given the probabilities of the diagnoses that can explain a patient's condition, the entropy of that distribution is a measure of our uncertainty about the diagnosis. The relative entropy of the posttest probabilities with respect to the pretest probabilities quantifies the amount of information gained by diagnostic testing. Mutual information is the expected value of relative entropy and, hence, provides a measure of expected diagnostic information. These concepts are used to derive formulas for calculating diagnostic information as a function of pretest probability for a given pair of test operating characteristics. RESULTS: Plots of diagnostic information as a function of pretest probability are constructed to evaluate and compare the performance of three tests commonly used in the diagnosis of coronary artery disease. The graphs illustrate the critical role that the pretest probability plays in determining diagnostic test information. CONCLUSIONS: Information graphs summarize diagnostic test performance and offer a way to evaluate and compare diagnostic tests.

Computer Simulation↗
PubMed2005

Distributed neural representation of expected value.

Anticipated reward magnitude and probability comprise dual components of expected value (EV), a cornerstone of economic and psychological theory. However, the neural mechanisms that compute EV have not been characterized. Using event-related functional magnetic resonance imaging, we examined neural activation as subjects anticipated monetary gains and losses that varied in magnitude and probability. Group analyses indicated that, although the subcortical nucleus accumbens (NAcc) activated proportional to anticipated gain magnitude, the cortical mesial prefrontal cortex (MPFC) additionally activated according to anticipated gain probability. Individual difference analyses indicated that, although NAcc activation correlated with self-reported positive arousal, MPFC activation correlated with probability estimates. These findings suggest that mesolimbic brain regions support the computation of EV in an ascending and distributed manner: whereas subcortical regions represent an affective component, cortical regions also represent a probabilistic component, and, furthermore, may integrate the two.

Adult↗
PubMed2006

Does this patient have deep vein thrombosis?

CONTEXT: Outpatients with suspected deep vein thrombosis (DVT) have nonspecific signs and symptoms. Missed DVT diagnosis may result in fatal pulmonary embolism. Since many patients may have DVT, a selective and efficient diagnostic process is needed. OBJECTIVE: To systematically review trials that determined the prevalence of DVT using clinical prediction rules either with or without D-dimer, for the diagnosis of DVT. DATA SOURCES: English- and French-language studies were identified from MEDLINE from 1990 to July 2004 and supplemented by a review of all relevant bibliographies. STUDY SELECTION: We included studies that prospectively enrolled consecutive, unselected outpatients with suspected DVT and applied clinical prediction rules before D-dimer testing or diagnostic imaging. All studies included sufficient information to allow the calculation of the prevalence of DVT for at least 1 of the 3 clinical probability estimates (low, moderate, or high). We required that patients be followed up for a minimum 3-month period. Unless the clinical model incorporated prior DVT, studies were excluded if patients with a history of prior DVT were enrolled. DATA EXTRACTION: Two reviewers independently reviewed and abstracted data for estimating the prevalence of DVT, sensitivity, specificity, and likelihood ratios (LRs) of D-dimer in each of the 3 clinical probability estimates. Data for the D-dimer in all studies were pooled and analyzed as high-sensitivity/low-specificity test or a moderate-sensitivity/moderate-specificity test. DATA SYNTHESIS: Fourteen studies involving more than 8000 patients used 1 clinical prediction rule for diagnosing DVT, of which 11 incorporated D-dimer testing in the diagnostic algorithm. The prevalence of DVT in the low, moderate, and high clinical probability groups was 5.0% (95% CI, 4.0%-8.0%), 17% (95% CI, 13%-23%), and 53% (95% CI, 44%-61%), respectively. The overall prevalence of DVT was 19% (95% CI, 16%-23%). Pooling all studies, the sensitivity, specificity, and negative LRs of D-dimer testing in the low probability group were 88% (95% CI, 81%-92%), 72% (95% CI, 65%-78%), and 0.18% (95% CI, 0.12-0.18); in the moderate probability group: 90% (95% CI, 80%-95%), 58% (95% CI, 49%-67%), and 0.19% (95% CI, 0.11-0.32); and in the high probability group: 92% (95% CI, 85%-96%), 45% (95% CI, 37%-52%), and 0.16% (95% CI, 0.09-0.30). The LRs for a normal result on a high or moderately sensitive D-dimer assay among patients with: (1) low clinical suspicion were 0.10 (95% CI, 0.03-0.37) and 0.20 (95% CI, 0.12-0.31); (2) moderate clinical suspicion were 0.05 (95% CI, 0.01-0.21) and 0.23 (95% CI, 0.13-0.39); and (3) high clinical suspicion were 0.07 (95% CI, 0.03-0.18) and 0.15 (95% CI, 0.10-0.38). CONCLUSIONS: Diagnostic accuracy for DVT improves when clinical probability is estimated before diagnostic tests. Patients with low clinical probability on the predictive rule have prevalence of DVT of less than 5%. In low-probability patients with negative D-dimer results, diagnosis of DVT can be excluded without ultrasound; in patients with high clinical suspicion for DVT, results should not affect clinical decisions.

Algorithms↗
PubMed1994

Hits to bone cell nuclei from nonuniform radioactive labels.

The stochastic aspects of alpha-particle traversals through nuclei of bone-lining cells from nonuniform radioactive labels are worked out. Both the residence time of the target and the hit rate are considered random variables. It is shown that with any type of bone remodeling the fraction of cells not hit increases with increasing nonuniformity of the label concentration. Thus, a completely uniform concentration represents the most dangerous situation. A possible negative correlation between residence times and hit rates, observed in some experiments, tends to decrease the probability of alpha-particle hits. As a practical application, the theory is applied to the International Commission on Radiological Protection model of the distribution of 239Pu in the human body. In the case of 50 years of chronic ingestion of 1 annual limit of intake (ALI) per year for class W and chronic inhalation of 1 ALI/year for class Y compounds, more than 19.4 and 8.5% of the nuclei of bone-lining cells are traversed by at least one alpha-particle, respectively.

Alpha Particles↗
PubMed1989

Theories of probabilistic reinforcement.

In three experiments, pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck at a red key led to a delay of 5 s and then a possible reinforcer. A peck at a green key led to an adjusting delay and then a certain reinforcer. This delay was adjusted over trials so as to estimate an indifference point, or a duration at which the two alternatives were chosen about equally often. In Experiments 1 and 2, the intertrial interval was varied across conditions, and these variations had no systematic effects on choice. In Experiment 3, the stimuli that followed a choice of the red key differed across conditions. In some conditions, a red houselight was presented for 5 s after each choice of the red key. In other conditions, the red houselight was present on reinforced trials but not on nonreinforced trials. Subjects exhibited greater preference for the red key in the latter case. The results were used to evaluate four different theories of probabilistic reinforcement. The results were most consistent with the view that the value or effectiveness of a probabilistic reinforcer is determined by the total time per reinforcer spent in the presence of stimuli associated with the probabilistic alternative. According to this view, probabilistic reinforcers are analogous to reinforcers that are delivered after variable delays.

Animals↗
PubMed2005

[Judd-Ofelt spectral theory].

In this article, the development and application of Judd-Ofelt spectral theory(J-O theory) was reviewed briefly. J-O theory was used to analyze the absorption and emission spectra of rare earth ions in solids, and compute their transition probabilities, line strengths, energy lifetimes, emission cross sections, and so on. When J-mixing was considered in J-O theory, the theoretical and experimental results were more consistent. The spectra of Pr3+ can be analyzed relatively accurately with modified J-O theory. The spectral properties of anisotropic crystal can be analyzed from the unpolarized-light transmission spectrum of a quadratic sample without special-orientation processing. The overlapped absorption bands can be treated as one band approximatively. The J-O parameters can also be calculated with fluorescence lifetimes.

Algorithms↗
PubMed2003

Evolution equation of population genetics: relation to the density-matrix theory of quasiparticles with general dispersion laws.

The Waxman-Peck theory of population genetics is discussed in regard of soil bacteria. Each bacterium is understood as a carrier of a phenotypic parameter p. The central objective is the calculation of the probability density with respect to p, Phi(p,t;p(0)), of the carriers living at time t>0, provided that initially at t(0)=0, all bacteria carried the phenotypic parameter p(0)=0. The theory involves two small parameters: the mutation probability mu and a parameter gamma involved in a function w(p) defining the fitness of the bacteria to survive the generation time tau and give birth to an offspring. The mutation from a state p to a state q is defined by a Gaussian with a dispersion sigma(2)(m). The author focuses our attention on a function phi(p,t) which determines uniquely the function Phi(p,t;p(0)) and satisfies a linear equation (Waxman's equation). The Green function of this equation is mathematically identical with the one-particle Bloch density matrix, where mu characterizes the order of magnitude of the potential energy. (In the x representation, the potential energy is proportional to the inverted Gaussian with the dispersion sigma(2)(m)). The author solves Waxman's equation in the standard style of a perturbation theory and discusses how the solution depends on the choice of the fitness function w(p). In a sense, the function c(p)=1-w(p)/w(0) is analogous to the dispersion function E(p) of fictitious quasiparticles. In contrast to Waxman's approximation, where c(p) was taken as a quadratic function, c(p) approximately gammap(2), the author exemplifies the problem with another function, c(p)=gamma[1-exp(-ap(2))], where gamma is small but a may be large. The author shows that the use of this function in the theory of the population genetics is the same as the use of a nonparabolic dispersion law E=E(p) in the density-matrix theory. With a general function c(p), the distribution function Phi(p,t;0) is composed of a delta-function component, N(t)delta(p), and a blurred component. When discussing the limiting transition for t--> infinity, the author shows that his function c(p) implies that N(t)-->N( infinity ) not equal 0 in contrast with the asymptotics N(t)-->0 resulting from the use of Waxman's function c(p) approximately p(2).

Journal Article↗
PubMed2000

Tumour control probability: a formulation applicable to any temporal protocol of dose delivery.

An analytic expression for the tumour control probability (TCP), valid for any temporal distribution of dose, is discussed. The TCP model, derived using the theory of birth-and-death stochastic processes, generalizes several results previously obtained. The TCP equation is [equation: see text] where S(t) is the survival probability at time t of the n clonogenic tumour cells initially present (at t = 0), and b and d are, respectively, the birth and death rates of these cells. Equivalently, b = 0.693/Tpot and d/b is the cell loss factor of the tumour. In this expression t refers to any time during or after the treatment; typically, one would take for t the end of the treatment period or the expected remaining life span of the patient. This model, which provides a comprehensive framework for predicting TCP, can be used predictively, or--when clinical data are available for one particular treatment modality (e.g. fractionated radiotherapy)--to obtain TCP-equivalent regimens for other modalities (e.g. low dose-rate treatments).

Brachytherapy↗
PubMed2003

The psycho-social impact of infertility on young male cancer survivors: a qualitative investigation.

Intensive treatment regimes that are known to have a potential risk of infertility sometimes have to be given to boys who have aggressive malignant disease. Long-term care must therefore include further discussion of these patients' impaired fertility. This study describes the results of a series of semi-structured interviews with 15 young male cancer survivors regarding their experience of receiving feedback on their probable fertility status. All the interviews were conducted by a psychologist formerly uninvolved with their treatment. The interviews were analysed qualitatively using a grounded theory approach. The findings of the study are organised under four headings: (a) Emotional reaction to news of probable infertility. (b) Coping style adopted. (c) Response to the offer of semen analysis. (d) Implications for clinical practice.The results of this thematic analysis are compared to the wider research literature in oncology and health psychology.

Adaptation, Psychological↗
PubMed1992

[Pathological gambling: literature revue].

This paper summarizes the current literature on pathological gambling. Interest in gambling has been present in every society but treated as an object of sociopolitical or literary interest. It is only from the beginning of this century that psychiatry began to look at pathological gambling, first with Freud and his writing on Dostoïevsky then with other theories like the learning theory, studies on substance dependence, the links with affective syndromes and the psychobiological studies. These studies are presented and discussed. Finally, the authors offer some guidelines for an approach to a pathological gambler.

Behavior, Addictive↗
PubMed1991

A computational model of approximate Bayesian inference for associating clinical algorithms with decision analyses.

The lack of rationale or explanation is a major deficiency of clinical algorithms. To address this issue, the authors present a computational model for associating decision analyses with clinical algorithms. Automata theory is used to model categorical reasoning with approximate Bayesian inference based on probability intervals. This approximation reduces the number of computations to linear-order instead of the exponential-order combinations of clinical findings in exact Bayes. The linkage of decision analyses and clinical algorithms by means of this model exploits a new concept of "regular" clinical algorithms and their equivalency in theory and provides valuable perspectives in practice for developers of clinical algorithms.

Algorithms↗
PubMed1986

The uses of spatial analysis in medical geography: a review.

This paper is a review of how geographers and others have used spatial analysis to study disease and health care delivery patterns. Point, line, area and surface patterns, as well as map comparisons and relative spaces are discussed. Problems encountered in applying spatial analytic techniques in medical geography are pointed out. The paper is intended to stimulate discussion about where medical geography can and should go in this area of study. Point pattern techniques include standard distance, standard deviational ellipses, gradient analysis and space and space-time clustering. Line methods include random walks, vectors and graph theory or network analysis. Under areas, location quotients, standardized mortality ratios, Poisson probabilities, space and space-time clustering, autocorrelation measures and hierarchical clustering are discussed. Surface techniques mentioned are isolines and trend surfaces. For map comparisons, Lorenz curves, coefficients of areal correspondence and correlation coefficients have been used. Case-control matching, acquaintance networks, multidimensional scaling and cluster analysis are examples of methods that are based on relative or non-metric spaces. The review gives rise to the discussion of several general points: problems encountered in spatial analysis, theory building and verification, the appropriate role of technique and computer use. Some suggestions are made for further use of spatial analytic techniques in medical geography: Monte Carlo simulation of point patterns, network analysis to study referral systems and health care for pastoralists, geographic information systems to assess environmental risk, difference mapping for disease and risk factor map comparisons and multidimensional scaling to measure social distance.

Cross-Sectional Studies↗
PubMedDate not supplied

Qualitative theory of compartmental systems with lags.

Dynamic models of many processes in the biological and physical sciences give systems of ordinary differential equations called compartmental systems. Often, these systems include time lags; in this context, continuous probability density functions (pdfs) of lags are far more important than discrete lags. There is a relatively complete theory of compartmental systems without lags, both linear and non-linear [SIAM Rev. 35 (1993) 43]. The authors extend their previous work on compartmental systems without lags to show that, for discrete lags and for a very large class of pdfs of continuous lags, compartmental systems with lags are equivalent to larger compartmental systems without lags. Consequently, the properties of compartmental systems with lags are the same as those of compartmental systems without lags. For a very large class of compartmental systems with time lags, one can show that the time lags themselves can be generated by compartmental systems without lags. Thus, such systems can be partitioned into a main system, which is the original system without the lags, plus compartmental subsystems without lags that generate the lags. The latter may be linear or non-linear and may be inserted into main systems that are linear or non-linear. The state variables of the compartmental lag subsystems are hidden variables in the formulation with explicit lags.

Body Fluid Compartments↗
PubMed1999

Correlation functions in the two-dimensional random-field Ising model.

Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions G in the two-dimensional random-field Ising model, on long strips of width L=3-15 sites, for binary field distributions at generic distance R, temperature T, and field intensity h(0). For moderately high T, and h(0) of the order of magnitude used in most experiments, the distributions are singly peaked, though rather asymmetric. For low temperatures the single-peaked shape deteriorates, crossing over towards a double-delta ground-state structure. A connection is obtained between the probability distribution for correlation functions and the underlying distribution of accumulated field fluctuations. Analytical expressions are in good agreement with numerical results for R/L > or approximately 1, low T, h(0) not too small, and near G=1. From a finite-size ansatz at T=T(c)(h(0)=0), h(0)-->0, averaged correlation functions are predicted to scale with L(y)h(0), y=7/8. From numerical data we estimate y=0.875+/-0.025, in excellent agreement with theory. In the same region, the rms relative width W of the probability distributions varies for fixed R/L=1 as W approximately h(kappa)(0) f(L h(u)(0)) with kappa approximately 0.45, u approximately 0.8; f(x) appears to saturate when x-->infinity, thus implying W approximately h(kappa)(0) in d=2.

Journal Article↗
PubMed1998

Polymer Brushes: From Self-Consistent Field Theory to Classical Theory.

We consider planar brushes formed by end-grafted polymers with moderate to strong excluded-volume interactions. We first rederive the mean-field theory and solve the resulting self-consistent equations numerically. In the continuum limit, the results depend sensitively on a single parameter, beta, whose square is the ratio of the scaling prediction for the brush height to the unperturbed polymer radius of gyration, and which measures therefore the degree to which the polymers are stretched. For large values of beta, the density profile is close to parabolic, as predicted by the infinite-stretching theory of Zhulina et al. and of Milner et al. As beta decreases, the profile deviates strongly from a parabolic one. By calculating the most probable paths and comparing their contribution to various properties with those obtained from the full self-consistent theory, we determine the effect of the fluctuations about such paths. At large values of beta, these effects are very small everywhere. As beta decreases, fluctuation effects on the density profile become increasingly important near the grafting surface, but remain small far from it. For all values of beta, we find that polymer paths which begin far from the grafting surface are strongly, and almost uniformly, stretched throughout their length, including their free end points. Paths which begin close to the grafting surface are also stretched, but they initially move away from the grafting surface before reaching a maximum height and then returning to it. The classical theory is then derived from the self-consistent field equations by retaining, for each end point location, only that single trajectory which minimizes the free energy of the system. This free energy contains an entropy, of relative weight beta-1, which arises from the distribution of end points. Even for brushes which are only moderately stretched, the results of the classical theory for the brush profile and polymer end point distribution agree well with those of the full self-consistent theory except near the grafting surface itself. There the density profile as calculated in the self-consistent theory shows a characteristic decrease which is not captured by the classical theory. However it does capture the fact that the individual polymer paths are stretched in general throughout their length, including the end points, and yields nonmonotonic paths for polymers whose end points are close to the grafting surface. In addition, it reproduces extremely well the form of the density distribution far from the grafting surface, which is essentially Gaussian. This results from the fact that the stretching energy dominates the interaction energy of those polymers which extend far from the grafting surface, so that their behavior is nearly ideal. In the limit of infinite stretching, beta --> infinity, the theory reduces to that of Zhulina et al. and of Milner et al.

Journal Article↗
PubMed2005

Finding useful questions: on Bayesian diagnosticity, probability, impact, and information gain.

Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment, medical diagnosis, and the selection task are shown to not discriminate among these norms as descriptive models of human intuitions and behavior. Computational optimization found situations in which information gain, probability gain, and impact strongly contradict Bayesian diagnosticity. In these situations, diagnosticity's claims are normatively inferior. Results of a new experiment strongly contradict the predictions of Bayesian diagnosticity. Normative theoretical concerns also argue against use of diagnosticity. It is concluded that Bayesian diagnosticity is normatively flawed and empirically unjustified.

Bayes Theorem↗