Statistical Modeling of Trivariate Static Systems: Isotonic Models

This paper presents an improved version of a statistical trivariate modeling algorithm introduced in a short Letter by the first author. This paper recalls the fundamental concepts behind the proposed algorithm, evidences its criticalities and illustrates a number of improvements which lead to a functioning modeling algorithm. The present paper also illustrates the features of the improved statistical modeling algorithm through a comprehensive set of numerical experiments performed on four synthetic and five natural datasets. The obtained results confirm that the proposed algorithm is able to model the considered synthetic and the natural datasets faithfully

Functional Estimator Selection Techniques for Production Functions and Frontiers

This dissertation provides frameworks to select production function estimators in both the state-contingent and the general monotonic and concave cases. It first presents a Birth-Death Markov Chain Monte Carlo (BDMCMC) Bayesian algorithm to endogenously estimate the number of previously unobserved states of nature for a state-contingent frontier. Secondly, it contains a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm to determine a parsimonious piecewise linear description of a multiplicative monotonic and concave production frontier. The RJMCMC based algorithm is the first computationally efficient one-stage estimator of production frontiers with potentially heteroscedastic inefficiency distribution and environmental variables. Thirdly, it provides general framework, based on machine learning concepts, repeated learning-testing and parametric bootstrapping techniques, to select the best monotonic and concave functional estimator for a production function from a pool of functional estimators. This framework is the first to test potentially nonlinear production function estimators on actual datasets, rather than extrapolation of Monte Carlo simulation results

Irinotecan pharmacokinetics-pharmacodynamics: the clinical relevance of prolonged exposure to SN-38

We have shown previously that the terminal disposition half-life of SN-38, the active metabolite of irinotecan, is much longer than earlier thought. Currently, it is not known whether this prolonged exposure has any relevance toward SN-38-induced toxicity. Here, we found that SN-38 concentrations present in human plasma for up to 3 weeks after a single irinotecan infusion induce significant cytotoxicity in vitro. Using pharmacokinetic data from 26 patients, with sampling up to 500 h, relationships were evaluated between systemic exposure (AUC) to SN-38 and the per cent decrease in absolute neutrophil count (ANC) at nadir, or by taking the entire time course of ANC into account (AOC). The time course of SN-38 concentrations (AUC500 h) was significantly related to this AOC (P<0.001). Based on these findings, a new limited-sampling model was developed for SN-38 AUC500 h using only two timed samples: AUC500 h=(6.588×C2.5 h)+(146.4×C49.5 h)+15.53, where C2.5 h and C49.5 h are plasma concentrations at 2.5 and 49.5 h after start of infusion, respectively. The use of this limited-sampling model may open up historic databases to retrospectively obtain information about SN-38-induced toxicity in patients treated with irinotecan

Novel Methods for Multivariate Ordinal Data applied to Genetic Diplotypes, Genomic Pathways, Risk Profiles, and Pattern Similarity

Introduction: Conventional statistical methods for multivariate data (e.g., discriminant/regression) are based on the (generalized) linear model, i.e., the data are interpreted as points in a Euclidian space of independent dimensions. The dimensionality of the data is then reduced by assuming the components to be related by a specific function of known type (linear, exponential, etc.), which allows the distance of each point from a hyperspace to be determined. While mathematically elegant, these approaches may have shortcomings when applied to real world applications where the relative importance, the functional relationship, and the correlation among the variables tend to be unknown. Still, in many applications, each variable can be assumed to have at least an “orientation”, i.e., it can reasonably assumed that, if all other conditions are held constant, an increase in this variable is either “good” or “bad”. The direction of this orientation can be known or unknown. In genetics, for instance, having more “abnormal” alleles may increase the risk (or magnitude) of a disease phenotype. In genomics, the expression of several related genes may indicate disease activity. When screening for security risks, more indicators for atypical behavior may constitute raise more concern, in face or voice recognition, more indicators being similar may increase the likelihood of a person being identified. Methods: In 1998, we developed a nonparametric method for analyzing multivariate ordinal data to assess the overall risk of HIV infection based on different types of behavior or the overall protective effect of barrier methods against HIV infection. By using u-statistics, rather than the marginal likelihood, we were able to increase the computational efficiency of this approach by several orders of magnitude. Results: We applied this approach to assessing immunogenicity of a vaccination strategy in cancer patients. While discussing the pitfalls of the conventional methods for linking quantitative traits to haplotypes, we realized that this approach could be easily modified into to a statistically valid alternative to a previously proposed approaches. We have now begun to use the same methodology to correlate activity of anti-inflammatory drugs along genomic pathways with disease severity of psoriasis based on several clinical and histological characteristics. Conclusion: Multivariate ordinal data are frequently observed to assess semiquantitative characteristics, such as risk profiles (genetic, genomic, or security) or similarity of pattern (faces, voices, behaviors). The conventional methods require empirical validation, because the functions and weights chosen cannot be justified on theoretical grounds. The proposed statistical method for analyzing profiles of ordinal variables, is intrinsically valid. Since no additional assumptions need to be made, the often time-consuming empirical validation can be skipped.ranking; nonparametric; robust; scoring; multivariate

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

Dose Selection Balancing Efficacy and Toxicity Using Bayesian Model Averaging

Successful pharmaceutical drug development requires finding correct doses that provide an optimum balance between efficacy and toxicity. Competing responses to dose such as efficacy and toxicity often will increase with dose, and it is important to identify a range of doses to provide an acceptable efficacy response (minimum effective dose) while not causing unacceptable intolerance or toxicity (maximum tolerated dose). How this should be done is not self-evident. Relating efficacy to dose conditionally on possible toxicity may be problematic because whether toxicity occurs will not be known when a dose for a patient needs to be chosen. Copula models provide an appealing approach for incorporating an efficacy-toxicity association when the functional forms of the efficacy and toxicity dose-response models are known but may be less appealing in practice when the functional forms of the dose-response models and the particular copula association model are unknown. This paper explores the use of the BMA-Mod Bayesian model averaging framework that accommodates efficacy and toxicity responses to provide a statistically valid, distributionally flexible, and operationally practical model-agnostic strategy for predicting efficacy and toxicity outcomes both in terms of expected responses and in terms of predictions for individual patients. The performance of the approach is evaluated via simulation when efficacy and toxicity outcomes are considered marginally, when they are associated via gaussian and Archimedean copulas, and when they are expressed in terms of clinically meaningful categories. In all cases, the BMA-Mod strategy identified consistent ranges of acceptable doses.Comment: 23 pages, 14 figures. R code, annotated session log, and datasets available from [email protected]

Powerful modifications of William' test on trend

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Nonparametric Estimation of a Distribution Subject to a Stochastic Precedence Constraint

For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a stochastic precedence (sp) constraint is treated in detail. Two estimation approaches, one based on data shrinkage and the other involving data translation, are used to construct estimators that conform to the sp constraint, and each is shown to lead to a root n-consistent estimator of the underlying distribution. The asymptotic behavior of each of the estimators is fully characterized. Conditions are given under which each estimator is asymptotically equivalent to the corresponding empirical distribution function or, in the case of right censoring, the Kaplan–Meier estimator. In the complementary cases, evidence is presented, both analytically and via simulation, demonstrating that the new estimators tend to outperform the empirical distribution function when sample sizes are sufficiently large