Bayesian design and conduct of phase II single-arm clinical trials with binary outcomes: a tutorial

The aim of phase II single-arm clinical trials of a new drug is to determine whether it has sufficient promising activity to warrant its further development. For the last several years Bayesian statistical methods have been proposed and used. Bayesian approaches are ideal for earlier phase trials as they take into account information that accrues during a trial. Predictive probabilities are then updated and so become more accurate as the trial progresses. Suitable priors can act as pseudo samples, which make small sample clinical trials more informative. Thus patients have better chances to receive better treatments. The goal of this paper is to provide a tutorial for statisticians who use Bayesian methods for the first time or investigators who have some statistical background. In addition, real data from three clinical trials are presented as examples to illustrate how to conduct a Bayesian approach for phase II single-arm clinical trials with binary outcomes.

The Bayesian revolution in genetics

Bayesian statistics allow scientists to easily incorporate prior knowledge into their data analysis. Nonetheless, the sheer amount of computational power that is required for Bayesian statistical analyses has previously limited their use in genetics. These computational constraints have now largely been overcome and the underlying advantages of Bayesian approaches are putting them at the forefront of genetic data analysis in an increasing number of areas.

Elicitation of multivariate prior distributions: A nonparametric Bayesian approach

In the context of Bayesian statistical analysis, elicitation is the process of formulating a prior density f(.) about one or more uncertain quantities to represent a person's knowledge and beliefs. Several different methods of eliciting prior distributions for one unknown parameter have been proposed. However, there are relatively few methods for specifying a multivariate prior distribution and most are just applicable to specific classes of problems and/or based on restrictive conditions, such as independence of variables. Besides, many of these procedures require the elicitation of variances and correlations, and sometimes elicitation of hyperparameters which are difficult for experts to specify in practice. Garthwaite et al. (2005) discuss the different methods proposed in the literature and the difficulties of eliciting multivariate prior distributions. We describe a flexible method of eliciting multivariate prior distributions applicable to a wide class of practical problems. Our approach does not assume a parametric form for the unknown prior density f(.), instead we use nonparametric Bayesian inference, modelling f(.) by a Gaussian process prior distribution. The expert is then asked to specify certain summaries of his/her distribution, such as the mean, mode, marginal quantiles and a small number of joint probabilities. The analyst receives that information, treating it as a data set D with which to update his/her prior beliefs to obtain the posterior distribution for f(.). Theoretical properties of joint and marginal priors are derived and numerical illustrations to demonstrate our approach are given. (C) 2010 Elsevier B.V. All rights reserved.

Metodología para la determinación de los parámetros de planificación de los nodos e infraestructuras logísticas en un territorio, considerando en su planificación el impacto sobre los diferentes componentes territoriales

Esta tesis presenta el diseño y la aplicación de una metodología que permite la determinación de los parámetros para la planificación de nodos e infraestructuras logísticas en un territorio, considerando además el impacto de estas en los diferentes componentes territoriales, así como en el desarrollo poblacional, el desarrollo económico y el medio ambiente, presentando así un avance en la planificación integral del territorio. La Metodología propuesta está basada en Minería de Datos, que permite el descubrimiento de patrones detrás de grandes volúmenes de datos previamente procesados. Las características propias de los datos sobre el territorio y los componentes que lo conforman hacen de los estudios territoriales un campo ideal para la aplicación de algunas de las técnicas de Minería de Datos, tales como los ´arboles decisión y las redes bayesianas. Los árboles de decisión permiten representar y categorizar de forma esquemática una serie de variables de predicción que ayudan al análisis de una variable objetivo. Las redes bayesianas representan en un grafo acíclico dirigido, un modelo probabilístico de variables distribuidas en padres e hijos, y la inferencia estadística que permite determinar la probabilidad de certeza de una hipótesis planteada, es decir, permiten construir modelos de probabilidad conjunta que presentan de manera gráfica las dependencias relevantes en un conjunto de datos. Al igual que con los árboles de decisión, la división del territorio en diferentes unidades administrativas hace de las redes bayesianas una herramienta potencial para definir las características físicas de alguna tipología especifica de infraestructura logística tomando en consideración las características territoriales, poblacionales y económicas del área donde se plantea su desarrollo y las posibles sinergias que se puedan presentar sobre otros nodos e infraestructuras logísticas. El caso de estudio seleccionado para la aplicación de la metodología ha sido la República de Panamá, considerando que este país presenta algunas características singulares, entra las que destacan su alta concentración de población en la Ciudad de Panamá; que a su vez a concentrado la actividad económica del país; su alto porcentaje de zonas protegidas, lo que ha limitado la vertebración del territorio; y el Canal de Panamá y los puertos de contenedores adyacentes al mismo. La metodología se divide en tres fases principales: Fase 1: Determinación del escenario de trabajo 1. Revisión del estado del arte. 2. Determinación y obtención de las variables de estudio. Fase 2: Desarrollo del modelo de inteligencia artificial 3. Construcción de los ´arboles de decisión. 4. Construcción de las redes bayesianas. Fase 3: Conclusiones 5. Determinación de las conclusiones. Con relación al modelo de planificación aplicado al caso de estudio, una vez aplicada la metodología, se estableció un modelo compuesto por 47 variables que definen la planificación logística de Panamá, el resto de variables se definen a partir de estas, es decir, conocidas estas, el resto se definen a través de ellas. Este modelo de planificación establecido a través de la red bayesiana considera los aspectos de una planificación sostenible: económica, social y ambiental; que crean sinergia con la planificación de nodos e infraestructuras logísticas. The thesis presents the design and application of a methodology that allows the determination of parameters for the planning of nodes and logistics infrastructure in a territory, besides considering the impact of these different territorial components, as well as the population growth, economic and environmental development. The proposed methodology is based on Data Mining, which allows the discovery of patterns behind large volumes of previously processed data. The own characteristics of the territorial data makes of territorial studies an ideal field of knowledge for the implementation of some of the Data Mining techniques, such as Decision Trees and Bayesian Networks. Decision trees categorize schematically a series of predictor variables of an analyzed objective variable. Bayesian Networks represent a directed acyclic graph, a probabilistic model of variables divided in fathers and sons, and statistical inference that allow determine the probability of certainty in a hypothesis. The case of study for the application of the methodology is the Republic of Panama. This country has some unique features: a high population density in the Panama City, a concentration of economic activity, a high percentage of protected areas, and the Panama Canal. The methodology is divided into three main phases: Phase 1: definition of the work stage. 1. Review of the State of the art. 2. Determination of the variables. Phase 2: Development of artificial intelligence model 3. Construction of decision trees. 4. Construction of Bayesian Networks. Phase 3: conclusions 5. Determination of the conclusions. The application of the methodology to the case study established a model composed of 47 variables that define the logistics planning for Panama. This model of planning established through the Bayesian network considers aspects of sustainable planning and simulates the synergies between the nodes and logistical infrastructure planning.

Motor unit number estimation - A Bayesian approach

All muscle contractions are dependent on the functioning of motor units. In diseases such as amyotrophic lateral sclerosis (ALS), progressive loss of motor units leads to gradual paralysis. A major difficulty in the search for a treatment for these diseases has been the lack of a reliable measure of disease progression. One possible measure would be an estimate of the number of surviving motor units. Despite over 30 years of motor unit number estimation (MUNE), all proposed methods have been met with practical and theoretical objections. Our aim is to develop a method of MUNE that overcomes these objections. We record the compound muscle action potential (CMAP) from a selected muscle in response to a graded electrical stimulation applied to the nerve. As the stimulus increases, the threshold of each motor unit is exceeded, and the size of the CMAP increases until a maximum response is obtained. However, the threshold potential required to excite an axon is not a precise value but fluctuates over a small range leading to probabilistic activation of motor units in response to a given stimulus. When the threshold ranges of motor units overlap, there may be alternation where the number of motor units that fire in response to the stimulus is variable. This means that increments in the value of the CMAP correspond to the firing of different combinations of motor units. At a fixed stimulus, variability in the CMAP, measured as variance, can be used to conduct MUNE using the "statistical" or the "Poisson" method. However, this method relies on the assumptions that the numbers of motor units that are firing probabilistically have the Poisson distribution and that all single motor unit action potentials (MUAP) have a fixed and identical size. These assumptions are not necessarily correct. We propose to develop a Bayesian statistical methodology to analyze electrophysiological data to provide an estimate of motor unit numbers. Our method of MUNE incorporates the variability of the threshold, the variability between and within single MUAPs, and baseline variability. Our model not only gives the most probable number of motor units but also provides information about both the population of units and individual units. We use Markov chain Monte Carlo to obtain information about the characteristics of individual motor units and about the population of motor units and the Bayesian information criterion for MUNE. We test our method of MUNE on three subjects. Our method provides a reproducible estimate for a patient with stable but severe ALS. In a serial study, we demonstrate a decline in the number of motor unit numbers with a patient with rapidly advancing disease. Finally, with our last patient, we show that our method has the capacity to estimate a larger number of motor units.

Ecoregion classification using a bayesian approach and centre-focused clusters

Ecological regions are increasingly used as a spatial unit for planning and environmental management. It is important to define these regions in a scientifically defensible way to justify any decisions made on the basis that they are representative of broad environmental assets. The paper describes a methodology and tool to identify cohesive bioregions. The methodology applies an elicitation process to obtain geographical descriptions for bioregions, each of these is transformed into a Normal density estimate on environmental variables within that region. This prior information is balanced with data classification of environmental datasets using a Bayesian statistical modelling approach to objectively map ecological regions. The method is called model-based clustering as it fits a Normal mixture model to the clusters associated with regions, and it addresses issues of uncertainty in environmental datasets due to overlapping clusters.

A Bayesian approach to on-line learning

Online learning is discussed from the viewpoint of Bayesian statistical inference. By replacing the true posterior distribution with a simpler parametric distribution, one can define an online algorithm by a repetition of two steps: An update of the approximate posterior, when a new example arrives, and an optimal projection into the parametric family. Choosing this family to be Gaussian, we show that the algorithm achieves asymptotic efficiency. An application to learning in single layer neural networks is given.

A world full of surprises:Bayesian theory of surprise to quantify degrees of uncertainty

In the specific area of software engineering (SE) for self-adaptive systems (SASs) there is a growing research awareness about the synergy between SE and artificial intelligence (AI). However, just few significant results have been published so far. In this paper, we propose a novel and formal Bayesian definition of surprise as the basis for quantitative analysis to measure degrees of uncertainty and deviations of self-adaptive systems from normal behavior. A surprise measures how observed data affects the models or assumptions of the world during runtime. The key idea is that a "surprising" event can be defined as one that causes a large divergence between the belief distributions prior to and posterior to the event occurring. In such a case the system may decide either to adapt accordingly or to flag that an abnormal situation is happening. In this paper, we discuss possible applications of Bayesian theory of surprise for the case of self-adaptive systems using Bayesian dynamic decision networks. Copyright © 2014 ACM.

Newtonian perturbations on models with matter creation

Creation of cold dark matter (CCDM) can macroscopically be described by a negative pressure, and, therefore, the mechanism is capable to accelerate the Universe, without the need of an additional dark energy component. In this framework, we discuss the evolution of perturbations by considering a Neo-Newtonian approach where, unlike in the standard Newtonian cosmology, the fluid pressure is taken into account even in the homogeneous and isotropic background equations (Lima, Zanchin, and Brandenberger, MNRAS 291, L1, 1997). The evolution of the density contrast is calculated in the linear approximation and compared to the one predicted by the Lambda CDM model. The difference between the CCDM and Lambda CDM predictions at the perturbative level is quantified by using three different statistical methods, namely: a simple chi(2)-analysis in the relevant space parameter, a Bayesian statistical inference, and, finally, a Kolmogorov-Smirnov test. We find that under certain circumstances, the CCDM scenario analyzed here predicts an overall dynamics (including Hubble flow and matter fluctuation field) which fully recovers that of the traditional cosmic concordance model. Our basic conclusion is that such a reduction of the dark sector provides a viable alternative description to the accelerating Lambda CDM cosmology.

Directional Wave Spectrum Estimation Based on Vessel`s 1st-order Motions: Field Results

In this paper, 2 different approaches for estimating the directional wave spectrum based on a vessel`s 1st-order motions are discussed, and their predictions are compared to those provided by a wave buoy. The real-scale data were obtained in an extensive monitoring campaign based on an FPSO unit operating at Campos Basin, Brazil. Data included vessel motions, heading and tank loadings. Wave field information was obtained by means of a heave-pitch-roll buoy installed in the vicinity of the unit. `two of the methods most widely used for this kind of analysis are considered, one based on Bayesian statistical inference, the other consisting of a parametrical representation of the wave spectrum. The performance of both methods is compared, and their sensitivity to input parameters is discussed. This analysis complements a set of previous validations based on numerical and towing-tank results and allows for a preliminary evaluation of reliability when applying the methodology at full scale.

As the world turns: short-term human spatial memory in egocentric and allocentric coordinates

We aimed to determine whether human subjects' reliance on different sources of spatial information encoded in different frames of reference (i.e., egocentric versus allocentric) affects their performance, decision time and memory capacity in a short-term spatial memory task performed in the real world. Subjects were asked to play the Memory game (a.k.a. the Concentration game) without an opponent, in four different conditions that controlled for the subjects' reliance on egocentric and/or allocentric frames of reference for the elaboration of a spatial representation of the image locations enabling maximal efficiency. We report experimental data from young adult men and women, and describe a mathematical model to estimate human short-term spatial memory capacity. We found that short-term spatial memory capacity was greatest when an egocentric spatial frame of reference enabled subjects to encode and remember the image locations. However, when egocentric information was not reliable, short-term spatial memory capacity was greater and decision time shorter when an allocentric representation of the image locations with respect to distant objects in the surrounding environment was available, as compared to when only a spatial representation encoding the relationships between the individual images, independent of the surrounding environment, was available. Our findings thus further demonstrate that changes in viewpoint produced by the movement of images placed in front of a stationary subject is not equivalent to the movement of the subject around stationary images. We discuss possible limitations of classical neuropsychological and virtual reality experiments of spatial memory, which typically restrict the sensory information normally available to human subjects in the real world.

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Strong minimax lower bounds for learning

Minimax lower bounds for concept learning state, for example, thatfor each sample size $n$ and learning rule $g_n$, there exists a distributionof the observation $X$ and a concept $C$ to be learnt such that the expectederror of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimensionof the concept class. However, these bounds do not tell anything about therate of decrease of the error for a {\sl fixed} distribution--concept pair.\\In this paper we investigate minimax lower bounds in such a--stronger--sense.We show that for several natural $k$--parameter concept classes, includingthe class of linear halfspaces, the class of balls, the class of polyhedrawith a certain number of faces, and a class of neural networks, for any{\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distributionof $X$ and a fixed concept $C$ such that the expected error is larger thana constant times $k/n$ for {\sl infinitely many n}. We also obtain suchstrong minimax lower bounds for the tail distribution of the probabilityof error, which extend the corresponding minimax lower bounds.

The minimax distortion redundancy in empirical quantizer design

We obtain minimax lower and upper bounds for the expected distortionredundancy of empirically designed vector quantizers. We show that the meansquared distortion of a vector quantizer designed from $n$ i.i.d. datapoints using any design algorithm is at least $\Omega (n^{-1/2})$ awayfrom the optimal distortion for some distribution on a bounded subset of${\cal R}^d$. Together with existing upper bounds this result shows thatthe minimax distortion redundancy for empirical quantizer design, as afunction of the size of the training data, is asymptotically on the orderof $n^{1/2}$. We also derive a new upper bound for the performance of theempirically optimal quantizer.

A data-dependent skeleton estimate and a scale-sensitive dimension for classification

The classical binary classification problem is investigatedwhen it is known in advance that the posterior probability function(or regression function) belongs to some class of functions. We introduceand analyze a method which effectively exploits this knowledge. The methodis based on minimizing the empirical risk over a carefully selected``skeleton'' of the class of regression functions. The skeleton is acovering of the class based on a data--dependent metric, especiallyfitted for classification. A new scale--sensitive dimension isintroduced which is more useful for the studied classification problemthan other, previously defined, dimension measures. This fact isdemonstrated by performance bounds for the skeleton estimate in termsof the new dimension.