L'Hospital type rules for oscillation, with applications.
Likelihood for interval-censored observations from multi-state models.
We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation al the likelihood for the illness-death model based on applying Jacod´s formula to an observed bivariate counting...
Linking population genetics to phylogenetics
Population geneticists study the variability of gene sequences within a species, whereas phylogeneticists compare gene sequences between species and usually have only one representative sequence per species. Stochastic models in population genetics are used to determine probability distributions for gene frequencies and to predict the probability that a new mutation will become fixed in a population. Stochastic models in phylogenetics describe the substitution process in the single sequence that...
Locally weighted neural networks for an analysis of the biosensor response
This paper presents a semi-global mathematical model for an analysis of a signal of amperometric biosensors. Artificial neural networks were applied to an analysis of the biosensor response to multi-component mixtures. A large amount of the learning and test data was synthesized using computer simulation of the biosensor response. The biosensor signal was analyzed with respect to the concentration of each component of the mixture. The paradigm of locally weighted linear regression was used for retraining...
Mathematical and Computational Models in Tumor Immunology
The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies:...
Meta-analysis techniques applied in prevalence rate estimation
In some cases, the estimators obtained in compound tests have better features than the traditional ones, obtained from individual tests, cf. Sobel and Elashoff (1975), Garner et al. (1989) and Loyer (1983). The bias, the efficiency and the robustness of these estimators are investigated in several papers, e.g. Chen and Swallow (1990), Hung and Swallow (1999) and Lancaster and Keller-McNulty (1998). Thus, the use of estimators based on compound tests not only allows a substantial saving of...
Méthode d'interprétation d'une classification hiérarchique d'attributs-modalités pour l'«explication» d'une variable; application à la recherche d'un seuil critique de la tension artérielle systolique et des indicateurs de risque cardiovasculaire
Modèles de séries chronologiques avec seuils
Modelización de la distribución espacial de quistes en el estómago de la marsopa mediante un proceso de Gibbs.
En un trabajo previo (Balaguer et al., 1992) los autores estudiaron la distribución espacial de los quistes en el estómago de la marsopa para contrastar su compatibilidad con la hipótesis de aleatoriedad espacial completa (AEC). El resultado condujo a rechazar la hipótesis señalando en la dirección de un patrón agregado, confirmando la sospecha inicial de los zoólogos.Este trabajo completa aquel estudio en la dirección que parece más coherente a sus autores: la de conjeturar un modelo puntual espacial...
Modelos para la asignación de tratamiento.
In this paper the problem of treatment allocation is studied from the predictive decision theoretical point of view. The utility of obtaining some final characteristics y when a treatment a is applied to a person with initial facet x is assumed to be known. The problem is then reduced to the derivation of the expected utility of a given x, by means of either prognostic or diagnostic distributions.To find prognostic distributions, regression models and appropriate partitions of the population, according...
Multiscale estimation of cell kinetics.
Neuromorphic features of probabilistic neural networks
We summarize the main results on probabilistic neural networks recently published in a series of papers. Considering the framework of statistical pattern recognition we assume approximation of class-conditional distributions by finite mixtures of product components. The probabilistic neurons correspond to mixture components and can be interpreted in neurophysiological terms. In this way we can find possible theoretical background of the functional properties of neurons. For example, the general...
Node assignment problem in Bayesian networks
This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.
Noninvasive monitoring of hepatic damage from hepatitis C virus infection.
Nonparametric bivariate estimation for successive survival times.
Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for the second...
On a class of distribution-free tests for growth curves analyses
On an asymptotic optimality property of play-the-winner and vector-at-a-time sampling.
Simon and Weiss (1975) consider the formulation of the clinical trial as a selection procedure (Bechhofer, Kiefer and Sobel, 1968). The object of the trial is to choose the better treatment with probability ≥ P*, where P* is assigned, when the difference in success probabilities is ≥ Δ*, Δ* also being assigned. They consider a family of single step allocation methods for the reduction of the number of patients given the poorer treatment. Using numerical results, Simon and Weiss conclude that if...
On distribution of waiting time for the first failure followed by a limited length success run
Many doctors believe that a patient will survive a heart attack unless a succeeding attack occurs in a week. Treating heart attacks as failures in Bernoulli trials we reduce the lifetime after a heart attack to the waiting time for the first failure followed by a success run shorter than a given k. In order to test the "true" critical period of the lifetime we need its distribution. The probability mass function and cumulative distribution function of the waiting time are expressed in explicit and...
On equivalence and bioequivalence testing.
Equivalence testing is the natural approach to many statistical problems. First, its main application, bioequivalence testing, is reviewed. The basic concepts of bioequivalence testing (2×2 crossover designs, TOST, interval inclusion principle, etc.) and its problems (TOST biased character, the carryover problem, etc.) are considered. Next, equivalence testing is discussed more generally. Some applications and methods are reviewed and the relation of equivalence testing and distance-based inference...
On iterates of strong Feller operators on ordered phase spaces
Let (X,d) be a metric space where all closed balls are compact, with a fixed σ-finite Borel measure μ. Assume further that X is endowed with a linear order ⪯. Given a Markov (regular) operator P: L¹(μ) → L¹(μ) we discuss the asymptotic behaviour of the iterates Pⁿ. The paper deals with operators P which are Feller and such that the μ-absolutely continuous parts of the transition probabilities are continuous with respect to x. Under some concentration assumptions on the asymptotic transition probabilities...