Designs for phase I clinical trials with multiple courses of subjects at different doses

The goal of this article is to provide a new design framework and its corresponding estimation for phase I trials. Existing phase I designs assign each subject to one dose level based on responses from previous subjects. Yet it is possible that subjects with neither toxicity nor efficacy responses can be treated at higher dose levels, and their subsequent responses to higher doses will provide more information. In addition, for some trials, it might be possible to obtain multiple responses (repeated measures) from a subject at different dose levels. In this article, a nonparametric estimation method is developed for such studies. We also explore how the designs of multiple doses per subject can be implemented to improve design efficiency. The gain of efficiency from "single dose per subject" to "multiple doses per subject" is evaluated for several scenarios. Our numerical study shows that using "multiple doses per subject" and the proposed estimation method together increases the efficiency substantially.

Sur les prolongements de sous-copules

L’objet du travail est d’étudier les prolongements de sous-copules. Un cas important de l’utilisation de tels prolongements est l’estimation non paramétrique d’une copule par le lissage d’une sous-copule (la copule empirique). Lorsque l’estimateur obtenu est une copule, cet estimateur est un prolongement de la souscopule. La thèse présente au chapitre 2 la construction et la convergence uniforme d’un estimateur bona fide d’une copule ou d’une densité de copule. Cet estimateur est un prolongement de type copule empirique basé sur le lissage par le produit tensoriel de fonctions de répartition splines. Le chapitre 3 donne la caractérisation de l’ensemble des prolongements possibles d’une sous-copule. Ce sujet a été traité par le passé; mais les constructions proposées ne s’appliquent pas à la dépendance dans des espaces très généraux. Le chapitre 4 s’attèle à résoudre le problème suivant posé par [Carley, 2002]. Il s’agit de trouver la borne supérieure des prolongements en dimension 3 d’une sous-copule de domaine fini.

Statistical Inference for Some Measures of System Availability

Department of Statistics, Cochin University of Science and Technology

Measuring and testing for the systemically important financial institutions

This paper analyzes the measure of systemic importance ∆CoV aR proposed by Adrian and Brunnermeier (2009, 2010) within the context of a similar class of risk measures used in the risk management literature. In addition, we develop a series of testing procedures, based on ∆CoV aR, to identify and rank the systemically important institutions. We stress the importance of statistical testing in interpreting the measure of systemic importance. An empirical application illustrates the testing procedures, using equity data for three European banks.

Efficient modeling and inference for event-related fMRI data

Event-related functional magnetic resonance imaging (efMRI) has emerged as a powerful technique for detecting brains' responses to presented stimuli. A primary goal in efMRI data analysis is to estimate the Hemodynamic Response Function (HRF) and to locate activated regions in human brains when specific tasks are performed. This paper develops new methodologies that are important improvements not only to parametric but also to nonparametric estimation and hypothesis testing of the HRF. First, an effective and computationally fast scheme for estimating the error covariance matrix for efMRI is proposed. Second, methodologies for estimation and hypothesis testing of the HRF are developed. Simulations support the effectiveness of our proposed methods. When applied to an efMRI dataset from an emotional control study, our method reveals more meaningful findings than the popular methods offered by AFNI and FSL. (C) 2008 Elsevier B.V. All rights reserved.

Condicionantes socioeconômicos e ambientais dos clubes de convergência da renda na Amazônia Legal 1985 a 2007

Este trabalho analisa a formação de clubes de convergência na Amazônia legal no período de 1985 a 2007, condicionados por variáveis socioeconômicas, institucionais e ambientais. O caráter inovador deste trabalho está em testar pela primeira vez a importância do desmatamento como condicionante ambiental da formação dos clubes de convergência na Amazônia. Foi utilizada uma metodologia não paramétrica através da estimação de densidades de núcleo, matriz de transição e estimação de núcleos estocásticos para testar as evidências de convergência entre os municípios. Os resultados confirmaram a hipótese de convergência, grande dinâmica intrasseccional da renda e a formação de três clubes de convergência entre os municípios da Amazônia legal. O capital humano aparece como importante condicionante e o rebanho bovino e área de pecuária tem fraca significância no condicionamento da renda relativa municipal. O desmatamento e as variáveis institucionais não se mostraram significantes para o crescimento econômico dos municípios da Amazônia legal.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Consistency of Concave Regression with an Application to Current-Status Data

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Venous thromboembolism in patients with acute leukemia: Prevalence, incidence, recurrence of thrombosis, risk factors, and impact on survival

Venous thromboembolism (VTE), including deep vein thrombosis (DVT) and pulmonary embolism (PE), is the third most preventable cardiovascular disease and a growing public health problem in the United States. The incidence of VTE remains high with an annual estimate of more than 600,000 symptomatic events. DVT affects an estimated 2 million American each year with a death toll of 300,000 persons per year from DVT-related PE. Leukemia patients are at high risk for both hemorrhage and thrombosis; however, little is known about thrombosis among acute leukemia patients. The ultimate goal of this dissertation was to obtain deep understanding of thrombotic issue among acute leukemia patients. The dissertation was presented in a format of three papers. First paper mainly looked at distribution and risk factors associated with development of VTE among patients with acute leukemia prior to leukemia treatment. Second paper looked at incidence, risk factors, and impact of VTE on survival of patients with acute lymphoblastic leukemia during treatment. Third paper looked at recurrence and risk factors for VTE recurrence among acute leukemia patients with an initial episode of VTE. Descriptive statistics, Chi-squared or Fisher's exact test, median test, Mann-Whitney test, logistic regression analysis, Nonparametric Estimation Kaplan-Meier with a log-rank test or Cox model were used when appropriate. Results from analyses indicated that acute leukemia patients had a high prevalence, incidence, and recurrent rate of VTE. Prior history of VTE, obesity, older age, low platelet account, presence of Philadelphia positive ALL, use of oral contraceptives or hormone replacement therapy, presence of malignancies, and co-morbidities may place leukemia patients at an increased risk for VTE development or recurrence. Interestingly, development of VTE was not associated with a higher risk of death among hospitalized acute leukemia patients.^

Nonparametric traversability estimation in partially occluded and deformable terrain

Terrain traversability estimation is a fundamental requirement to ensure the safety of autonomous planetary rovers and their ability to conduct long-term missions. This paper addresses two fundamental challenges for terrain traversability estimation techniques. First, representations of terrain data, which are typically built by the rover’s onboard exteroceptive sensors, are often incomplete due to occlusions and sensor limitations. Second, during terrain traversal, the rover-terrain interaction can cause terrain deformation, which may significantly alter the difficulty of traversal. We propose a novel approach built on Gaussian process (GP) regression to learn, and consequently to predict, the rover’s attitude and chassis configuration on unstructured terrain using terrain geometry information only. First, given incomplete terrain data, we make an initial prediction under the assumption that the terrain is rigid, using a learnt kernel function. Then, we refine this initial estimate to account for the effects of potential terrain deformation, using a near-to-far learning approach based on multitask GP regression. We present an extensive experimental validation of the proposed approach on terrain that is mostly rocky and whose geometry changes as a result of loads from rover traversals. This demonstrates the ability of the proposed approach to accurately predict the rover’s attitude and configuration in partially occluded and deformable terrain.

Robust estimation of local genetic ancestry in admixed populations using a nonparametric Bayesian approach.

We present a new haplotype-based approach for inferring local genetic ancestry of individuals in an admixed population. Most existing approaches for local ancestry estimation ignore the latent genetic relatedness between ancestral populations and treat them as independent. In this article, we exploit such information by building an inheritance model that describes both the ancestral populations and the admixed population jointly in a unified framework. Based on an assumption that the common hypothetical founder haplotypes give rise to both the ancestral and the admixed population haplotypes, we employ an infinite hidden Markov model to characterize each ancestral population and further extend it to generate the admixed population. Through an effective utilization of the population structural information under a principled nonparametric Bayesian framework, the resulting model is significantly less sensitive to the choice and the amount of training data for ancestral populations than state-of-the-art algorithms. We also improve the robustness under deviation from common modeling assumptions by incorporating population-specific scale parameters that allow variable recombination rates in different populations. Our method is applicable to an admixed population from an arbitrary number of ancestral populations and also performs competitively in terms of spurious ancestry proportions under a general multiway admixture assumption. We validate the proposed method by simulation under various admixing scenarios and present empirical analysis results from a worldwide-distributed dataset from the Human Genome Diversity Project.

Kernel-based local order estimation of nonlinear nonparametric systems

We consider the local order estimation of nonlinear autoregressive systems with exogenous inputs (NARX), which may have different local dimensions at different points. By minimizing the kernel-based local information criterion introduced in this paper, the strongly consistent estimates for the local orders of the NARX system at points of interest are obtained. The modification of the criterion and a simple procedure of searching the minimum of the criterion, are also discussed. The theoretical results derived here are tested by simulation examples.