Physiologically Based Liver Modeling and Risk Assessment

Because of the inherent complexity of biological systems, there is often a choice between a number of apparently equally applicable physiologically based models to describe uptake and metabolism processes in toxicology or risk assessment. These models may fit the particular data sets of interest equally well, but may give quite different parameter estimates or predictions under different (extrapolated) conditions. Such competing models can be discriminated by a number of methods, including potential refutation by means of strategic experiments, and their ability to suitably incorporate all relevant physiological processes. For illustration, three currently used models for steady-state hepatic elimination--the venous equilibration model, the parallel tube model, and the distributed sinusoidal perfusion model--are reviewed and compared with particular reference to their application in the area of risk assessment. The ability of each of the models to describe and incorporate such physiological processes as protein binding, precursor-metabolite relations and hepatic zones of elimination, capillary recruitment, capillary heterogeneity, and intrahepatic shunting is discussed. Differences between the models in hepatic parameter estimation, extrapolation to different conditions, and interspecies scaling are discussed, and criteria for choosing one model over the others are presented. In this case, the distributed model provides the most general framework for describing physiological processes taking place in the liver, and has so far not been experimentally refuted, as have the other two models. These simpler models may, however, provide useful bounds on parameter estimates and on extrapolations and risk assessments.     

A Comparison of Partially Adaptive and Reweighted Least Squares Estimation

The small sample performance of least median of squares, reweighted least squares, least squares, least absolute deviations, and three partially adaptive estimators are compared using Monte Carlo simulations. Two data problems are addressed in the paper: (1) data generated from non-normal error distributions and (2) contaminated data. Breakdown plots are used to investigate the sensitivity of partially adaptive estimators to data contamination relative to RLS. One partially adaptive estimator performs especially well when the errors are skewed, while another partially adaptive estimator and RLS perform particularly well when the errors are extremely leptokur-totic. In comparison with RLS, partially adaptive estimators are only moderately effective in resisting data contamination; however, they outperform least squares and least absolute deviation estimators.     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

Gini’s nuclear family

The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the related family of empirical measures of inequality.      

Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory

Nonlinear functions of multivariate financial time series can exhibit long memory and fractional cointegration. However, tools for analysing these phenomena have principally been justified under assumptions that are invalid in this setting. Determination of asymptotic theory under more plausible assumptions can be complicated and lengthy. We discuss these issues and present a Monte Carlo study, showing that asymptotic theory should not necessarily be expected to provide a good approximation to finite-sample behavior.     

Nonresponse weighting adjustment using estimated response probability

To reduce nonresponse bias in sample surveys, a method of nonresponse weighting adjustment is often used which consists of multiplying the sampling weight of the respondent by the inverse of the estimated response probability. The authors examine the asymptotic properties of this estimator. They prove that it is generally more efficient than an estimator which uses the true response probability, provided that the parameters which govern this probability are estimated by maximum likelihood. The authors discuss variance estimation methods that account for the effect of using the estimated response probability; they compare their performances in a small simulation study. They also discuss extensions to the regression estimator.     

New methods for fitting multiple sinusoids from irregularly sampled data

A novel framework is proposed for the estimation of multiple sinusoids from irregularly sampled time series. This spectral analysis problem is addressed as an under-determined inverse problem, where the spectrum is discretized on an arbitrarily thin frequency grid. As we focus on line spectra estimation, the solution must be sparse, i.e. the amplitude of the spectrum must be zero almost everywhere. Such prior information is taken into account within the Bayesian framework. Two models are used to account for the prior sparseness of the solution, namely a Laplace prior and a Bernoulli–Gaussian prior, associated to optimization and stochastic sampling algorithms, respectively. Such approaches are efficient alternatives to usual sequential prewhitening methods, especially in case of strong sampling aliases perturbating the Fourier spectrum. Both methods should be intensively tested on real data sets by physicists.     

Data skeletons: simultaneous estimation of multiple quantiles for massive streaming datasets with applications to density estimation

We consider the problem of density estimation when the data is in the form of a continuous stream with no fixed length. In this setting, implementations of the usual methods of density estimation such as kernel density estimation are problematic. We propose a method of density estimation for massive datasets that is based upon taking the derivative of a smooth curve that has been fit through a set of quantile estimates. To achieve this, a low-storage, single-pass, sequential method is proposed for simultaneous estimation of multiple quantiles for massive datasets that form the basis of this method of density estimation. For comparison, we also consider a sequential kernel density estimator. The proposed methods are shown through simulation study to perform well and to have several distinct advantages over existing methods.     

Model diagnostics for smoothing spline ANOVA models

The author proposes some simple diagnostics for assessing the necessity of selected terms in smoothing spline ANOVA models. The elimination of practically insignificant terms generally enhances the interpretability of the estimates and sometimes may also have inferential implications. The diagnostics are derived from Kullback‐Leibler geometry and are illustrated in the settings of regression, probability density estimation, and hazard rate estimation.     

Goodness‐of‐fit methods for matched case‐control studies

The authors propose graphical and numerical methods for checking the adequacy of the logistic regression model for matched case‐control data. Their approach is based on the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a centered Gaussian limit whose distribution can be approximated via computer simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a certain number of simulated realizations of the approximate limiting process under the null hypothesis. The proposed techniques allow one to check the functional form of each covariate, the logistic link function as well as the overall model adequacy. The authors assess the performance of the proposed methods through simulation studies and illustrate them using data from a cardiovascular study.