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PubMed2005

Concepts and clinical trials of dose-dense chemotherapy for breast cancer .

This article will review the strategy of dose-dense administration of chemotherapy for breast cancer. Increased dose density is achieved by reducing the interval between each dose of chemotherapy. The cumulative drug dose remains constant, but the same amount of drug is administered over a shorter period. Mathematical models of tumor growth have provided the basis for the clinical application of dose-dense chemotherapy. The Norton-Simon model suggests that increasing the dose density of chemotherapy will increase efficacy by minimizing the opportunity for regrowth of tumor cells between cycles of chemotherapy. Intergroup trial 9741, coordinated by the Cancer and Leukemia Group B (CALGB), tested the 2 hypotheses that dose-dense and sequential administration of chemotherapy regimens incorporating doxorubicin, cyclophosphamide, and paclitaxel would improve disease-free survival and overall survival. A statistically significant 4-year disease-free survival advantage was detected for the 2 dose-dense regimens compared with the regimens administered every 3 weeks. The mathematical concepts and previous clinical trials of dose density that contributed to the design of CALGB 9741 will be reviewed. The strengths and limitations of CALGB 9741 will then be discussed before the presentation of future directions of research and recommendations for clinical practice today.

Antineoplastic Combined Chemotherapy Protocols↗

PubMed1998

Curriculum integration in nutrition and mathematics.

Today's school-aged children face a multitude of health issues that affect their well-being and academic performance. Partnerships have developed between health and education agencies to help American children succeed at math and science and to prepare them to make healthful, lifelong decisions. Curriculum integration provides a framework for children to apply knowledge from several disciplines and to use this knowledge to solve real-life problems at work and at play. Goals for instruction focus on the needs not only of the individual but also of society. Nutrition science and mathematics form a natural partnership. Nutrition science incorporates numerous mathematical concepts and procedures such as sorting, classifying, statistics, probability, estimation, and rates and proportion. In preparation for participation in a global and technological society that will require citizens to be quantitative thinkers, educators must endeavor to assist all children in becoming adults who are mathematically literate and competent.

Adolescent↗

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↗

PubMed1994

[A new methodologic approach for determining right ventricular volumes from transesophageal echocardiography].

In order to develop a concept of right ventricular volume estimation accounting for variance in positioning of the transesophageal transducer, non-linear scale transformations of suitable measurements of areas and perimeters were used in a new modeling-approach. This type of modeling supposes self-similarity of ventricular dimensions, a mathematical concept generalizing the notion of proportionality. In a study using right ventricular casts, we were able to demonstrate the geometry of right ventricles complies with these assumptions. The resulting multivariate power law volume estimators were developed by non-linear data fitting by learning-analyses based upon angiographic reference volumes and two areas derived from non-orthogonal sections using a monoplane transducer in a first series of studies, and two orthogonal areas with corresponding perimeters using a biplane device in a second series. Correction factors for systolic and diastolic volumes were applied. By prospective test-analyses angiographic and TEE-derived volumes were compared to evaluate our volume estimator and good agreement was found. Trend was evaluated by correlation amounts to r = 0.95 (n = 22) in series 1 with monoplane transducer, and r = 0.9 (n = 20) in series 2 with biplane transducer. This approach is of use in monitoring right ventricular function in cases with unsuitable transthoracical windows, e.g., in cardiac surgery postoperatively.

Adult↗

PubMed1981

Evidence, information, and surprise.

A numerical measure for "evidence" is defined in a probabilistic framework. The established mathematical concept of information or entropy (as defined in ergodic theory) can be obtained from this definition in a special case, although in general information in a special case, although in general information is greater than evidence. In another, somewhat complementary, special case a numerical measure for "surprise" is derived from the definition of evidence. Some applications of the new concept of evidence are discussed, concerning statistics in general and the special kind of statistics performed by neurophysiologists, when they analyze the "response" of neurons, and perhaps by the neurons themselves.

Axons↗

PubMed2003

Making ecosystem models viable.

Viability conditions permit to characterize all processes compatible with given constraints, notably of available food, so that there exists at least one possibility for the system to perpetuate itself forever. The concept of contingent cone to a set of constraints permits to identify two classes of corrections to apply to equations of natural growth. Usual basic models convey those corrections only in certain regions of the parameter space. A general model-building stemming from the constraints is presented. Experimental populations from historical case studies highlight the mathematical concept of viability corrections.

Animals↗

PubMed2005

An exploration into the most effective way to teach drug calculation skills to nursing students.

Drug calculations are an essential skill for nurses. Nurses need to be able to perform them accurately to calculate correct dosages of drugs to administer to patients. Incorrect calculations can cause drug errors and potential harm to patients (; ). For student nurses therefore learning how to calculate drug dosages is an important skill that they need to be taught during their nurse training. This paper describes an action research project undertaken to explore the most effective way of teaching drug calculations to a group if 2nd year diploma and degree pre registration nurses. The evaluation of this project has demonstrated that a three stage approach to drug calculation appears to be an effective teaching strategy. These stages involve addressing mathematical concepts, teaching drug calculation formulae and then practising these skills in a clinical setting.

Attitude of Health Personnel↗

PubMed1991

First principles of magnetic resonance angiography.

For several years, magnetic resonance imaging (MRI) has shown promise as a noninvasive tool for the study of the vascular system. One interesting format, so-called MR angiography, produces results resembling conventional x-ray angiographic images. This article lays a solid, rigorous foundation for an intuitive understanding of these effects without the use of advanced mathematical concepts. The current state of the art in data acquisition and postprocessing is illustrated. Finally, relevant hemodynamic concepts are introduced, in order to characterize the physiology of complex blood flow at bifurcations. MR angiography is particularly sensitive to artifacts associated with complex flow. The article ends with a call to investigate these phenomena, because they will directly affect the success of MR angiography as a technique.

Angiography↗

PubMedDate not supplied

General performance on a numeracy scale among highly educated samples.

BACKGROUND: Numeracy, how facile people are with basic probability and mathematical concepts, is associated with how people perceive health risks. Performance on simple numeracy problems has been poor among populations with little as well as more formal education. Here, we examine how highly educated participants performed on a general and an expanded numeracy scale. The latter was designed within the context of health risks. METHOD: A total of 463 men and women aged 40 and older completed a 3-item general and an expanded 7-item numeracy scale. The expanded scale assessed how well people 1) differentiate and perform simple mathematical operations on risk magnitudes using percentages and proportions, 2) convert percentages to proportions, 3) convert proportions to percentages, and 4) convert probabilities to proportions. RESULTS: On average, 18% and 32% of participants correctly answered all of the general and expanded numeracy scale items, respectively. Approximately 16% to 20% incorrectly answered the most straightforward questions pertaining to risk magnitudes (e.g., Which represents the larger risk: 1%, 5%, or 10%?). A factor analysis revealed that the general and expanded risk numeracy items tapped the construct of global numeracy. CONCLUSIONS: These results suggest that even highly educated participants have difficulty with relatively simple numeracy questions, thus replicating in part earlier studies. The implication is that usual strategies for communicating numerical risk may be flawed. Methods and consequences of communicating health risk information tailored to a person's level of numeracy should be explored further.

Adult↗

PubMed1992

Chaos theory--a useful addition to the critical care curriculum?

Chaos theory (non-linear dynamics) is a relatively new mathematical concept. It shows that many apparently random processes and structures have in fact a simple underlying order. The theory is being applied increasingly to explain physiological processes and epidemiological findings, as well as in non-health areas, such as modelling weather systems. The author argues for its future inclusion as a modular option in post-registration critical care/high technology nursing courses.

Critical Care↗

PubMed2003

The 'common mole' from the point of view of digital dermoscopy analysis: subjective vs. objective evaluation of easy pigmented skin lesions.

BACKGROUND: The term 'common mole', often used to describe a subset of benign pigmented skin lesions, is traditionally defined on the basis of morpho-chromatic features. In recent years, certain research groups have developed equipment and methods, such as digital dermoscopy analysis, that enable objective evaluation of pigmented skin lesions. OBJECTIVE: In this study we use a digital dermoscopy analyser trained for the recognition of pigmented skin lesions to compare the subjective definition of 'common' and the mathematical concept of 'close to the mean of measurements'. METHODS: A subset (100) of digital images of flat pigmented lesions, obtained in daily practice, were classified by trained and non-expert clinicians as common moles (60) or clear-cut melanoma (40), and processed with a DB-Mips analyser. The resulting parameters, validated by a classifier, were used to evaluate Hotelling's T2 multivariate distances from the mean. RESULTS: 'Common' moles could not be clearly defined in terms of closeness to the means of objectively evaluated parameters. Their diagnosis indudes many other evaluations and clusters of variables. CONCLUSION: The clinical semantics of the term 'common' does not conform to any unambiguous mathematical definition.

Diagnosis, Computer-Assisted↗

PubMedDate not supplied

A brief primer on automated signal detection.

BACKGROUND: Statistical techniques have traditionally been underused in spontaneous reporting systems used for postmarketing surveillance of adverse drug events. Regulatory agencies, pharmaceutical companies, and drug monitoring centers have recently devoted considerable efforts to develop and implement computer-assisted automated signal detection methodologies that employ statistical theory to enhance screening efforts of expert clinical reviewers. OBJECTIVE: To provide a concise state-of-the-art review of the most commonly used automated signal detection procedures, including the underlying statistical concepts, performance characteristics, and outstanding limitations, and issues to be resolved. DATA SOURCES: Primary articles were identified by MEDLINE search (1965-December 2002) and through secondary sources. STUDY SELECTION AND DATA EXTRACTION: All of the articles identified from the data sources were evaluated and all information deemed relevant was included in this review. DATA SYNTHESIS: Commonly used methods of automated signal detection are self-contained and involve screening large databases of spontaneous adverse event reports in search of interestingly large disproportionalities or dependencies between significant variables, usually single drug-event pairs, based on an underlying model of statistical independence. The models vary according to the underlying model of statistical independence and whether additional mathematical modeling using Bayesian analysis is applied to the crude measures of disproportionality. There are many potential advantages and disadvantages of these methods, as well as significant unresolved issues related to the application of these techniques, including lack of comprehensive head-to-head comparisons in a single large transnational database, lack of prospective evaluations, and the lack of gold standard of signal detection. CONCLUSIONS: Current methods of automated signal detection are nonclinical and only highlight deviations from independence without explaining whether these deviations are due to a causal linkage or numerous potential confounders. They therefore cannot replace expert clinical reviewers, but can help them to focus attention when confronted with the difficult task of screening huge numbers of drug-event combinations for potential signals. Important questions remain to be answered about the performance characteristics of these methods. Pharmacovigilance professionals should take the time to learn the underlying mathematical concepts in order to critically evaluate accumulating experience pertaining to the relative performance characteristics of these methods that are incompletely defined.

Automation↗

PubMedDate not supplied

Decision analysis: theory and methods in clinical development and monitoring of clinical trials.

Decision analysis has been widely used in business, first in operational research, later in economic studies. It is now spreading to medical training. We review methodology of decision analysis which is simple, rational and based on the environmental conditions. When clinical judgments are uncertain, the most appropriate strategy is helped by the use of standard/bayesian probabilities quantifying the risks of each strategy, and the design of decision trees visualizing each outcome. If the probabilities are not suitable, other mathematical concepts such as Markov process are interesting but are still being worked on. Multicriteria analysis, a branch of graph theory, is also a flexible and reliable tool allowing differentiation and ordering strategies. It also takes into account the psychological characteristic of the decision makers. We then illustrate decision analysis by describing computerized systems for monitoring clinical trials, fitted to control the trial data able to estimate the different strategies.

Clinical Medicine↗

PubMed1990

Gender differences in mathematics performance: a meta-analysis.

Reviewers have consistently concluded that males perform better on mathematics tests than females do. To make a refined assessment of the magnitude of gender differences in mathematics performance, we performed a meta-analysis of 100 studies. They yielded 254 independent effect sizes, representing the testing of 3,175,188 Ss. Averaged over all effect sizes based on samples of the general population, d was -0.05, indicating that females outperformed males by only a negligible amount. For computation, d was -0.14 (the negative value indicating superior performance by females). For understanding of mathematical concepts, d was -0.03; for complex problem solving, d was 0.08. An examination of age trends indicated that girls showed a slight superiority in computation in elementary school and middle school. There were no gender differences in problem solving in elementary or middle school; differences favoring men emerged in high school (d = 0.29) and in college (d = 0.32). Gender differences were smallest and actually favored females in samples of the general population, grew larger with increasingly selective samples, and were largest for highly selected samples and samples of highly precocious persons. The magnitude of the gender difference has declined over the years; for studies published in 1973 or earlier d was 0.31, whereas it was 0.14 for studies published in 1974 or later. We conclude that gender differences in mathematics performance are small. Nonetheless, the lower performance of women in problem solving that is evident in high school requires attention.

Aptitude↗

PubMed2002

Regularity in irregular echinoids.

Using the mathematical concept of eutactic star, we prove that it is possible to define a morphospace for irregular echinoids by using a single parameter. In particular, we have found an extraordinary geometric property in the flower-like patterns of the five ambulacral petals of these animals. This property is fulfilled with great accuracy for a large collection of fossil specimens and provides new insights in the study of the viable skeletal designs of extinct and/or living organisms.

Animals↗

PubMed1994

Mapping the human lung using Delaunay tessellation.

A computer protocol is (1) developed and (2) applied to the human body for medical research. Delaunay tessellation is used to derive an algorithm to describe the structure of the lung. This may be the first application of that mathematical concept to a physiological system. The lung is a complex yet systematic network of pathways described herein with cited dimensions and angles. Its terminal points are the most distal airways, alveolar sacs, defined by their (x, y, z) coordinates. We have addressed that spatial array as a set of points in 3-D space, and, visualized the physical boundary of a lung as the surface of the convex hull of that set in R3. As documented, the enveloping surface of the computer lung closely describes the outer contours of human lungs depicted in clinical studies. Therefore, the model has immediate and salient implications to problems in medicine where respiratory function and morphology have integral roles, specifically, thoracic surgery and aerosol therapy. Examples include the removal of lobes damaged by respiratory diseases such as cystic fibrosis and cancer, and the definition of lung boundaries for gamma camera, PET, and SPECT images. Importantly, the model can be varied to simulate the intersubject differences that physicians experience among a patient population. The mathematical simulations performed in this work are intended to be complementary to laboratory investigations in the medical arena. By providing accurate 3-D, quantitative descriptions of human lungs the supercomputer can be actively integrated into the clinical environment.

Algorithms↗

PubMed2001

Addition patterns, codes and contact graphs for fullerene derivatives.

The mathematical concept of the d-code and its associated contact graph give a model for sterically constrained addition patterns in fullerene derivatives C60Xm and C70Xm. In combination with simple electronic arguments, the stoichiometries, symmetries, and location of addends can be predicted, yielding a small number of candidates for further study. For example, sterically and optimal solutions C60Xm with pairwise separation of d bonds between addends are found at m(d) = 24(2), 12(3), 6(4,5), 2(6 to 9). The solution for C60X24 is unique, and the model selects 12 candidates for C60X12 from a starting set of 11661527060 possibilities.

Carbon↗

PubMed1992

The theoretical application of inclined hinges with the Ilizarov external fixator for simultaneous angulation and rotation correction.

The mathematical concepts of single-cut osteotomies for simultaneous correction of angulation and rotation have been adapted and simplified for gradual distraction-osteogenic correction with the Ilizarov external fixator. Validation studies were performed analytically, using a solid modeling analysis, and experimentally with an Ilizarov external fixator mounted on a wood dowel. The resultant equations have been simplified and are easy to use. Starting from the hinge which would correct the angulation, the axis must be reoriented in the horizontal plane by half the rotation deformity (R/2) and given an inclination slope equal to the rotation divided by the angulation (R/A).

Biomechanical Phenomena↗