A Generalization of the GMANOVA-Model

It is shown that in some experimental designs the MANOVA- and the GMANOVA-model are too restrictive either to yield all hypothesis tests of interest or to reflect all known features of the design. An extension of these models is derived by relating the response vectors with the unknown model parameters by linear equations which may be completely different for each of the p components of the response vector and for each of the n independent vectors. For situations, in which a Wishart-distributed estimator for the underlying common covariance matrix is attainable, a test for any s-dimensional linear hypothesis on the model parameters is derived.     

On the relationship of anthranilic derivatives structure and the FXR (Farnesoid X receptor) agonist activity

Farnesoid X receptor (FXR) is a nuclear receptor related to lipid and glucose homeostasis and is considered an important molecular target to treatment of metabolic diseases as diabetes, dyslipidemia, and liver cancer. Nowadays, there are several FXR agonists reported in the literature and some of it in clinical trials for liver disorders. Herein, a compound series was employed to generate QSAR models to better understand the structural basis for FXR activation by anthranilic acid derivatives (AADs). Furthermore, here we evaluate the inclusion of the standard deviation (SD) of EC₅₀ values in QSAR models quality. Comparison between the use of experimental variance plus average values in model construction with the standard method of model generation that considers only the average values was performed. 2D and 3D QSAR models based on the AAD data set including SD values showed similar molecular interpretation maps and quality (Q²_LOO, Q²_(F2), and Q²_(F3)), when compared to models based only on average values. SD-based models revealed more accurate predictions for the set of test compounds, with lower mean absolute error indices as well as more residuals near zero. Additionally, the visual interpretation of different QSAR approaches agrees with experimental data, highlighting key elements for understanding the biological activity of AADs. The approach using standard deviation values may offer new possibilities for generating more accurate QSAR models based on available experimental data.     

A Bayesian A-optimal and model robust design criterion

Summary . Suppose that the true model underlying a set of data is one of a finite set of candidate models, and that parameter estimation for this model is of primary interest. With this goal, optimal design must depend on a loss function across all possible models. A common method that accounts for model uncertainty is to average the loss over all models; this is the basis of what is known as Läuter's criterion. We generalize Läuter's criterion and show that it can be placed in a Bayesian decision theoretic framework, by extending the definition of Bayesian A‐optimality. We use this generalized A‐optimality to find optimal design points in an environmental safety setting. In estimating the smallest detectable trace limit in a water contamination problem, we obtain optimal designs that are quite different from those suggested by standard A‐optimality.     

Estimation and Verification of Hypotheses in Some Zyskind-Martin Models with Missing Values

Several theorems on estimation and verification of linear hypotheses in some Zyskind-Martin (ZM) models are given. The assumptions are as follows. Let y = Xβ + e or (y, Xβ, σ²V) be a fixed model where y is a vector of n observations, X is a known matrix nXp with rank r(X) = r ≦ p < n, where p is a number of coordinates of the unknown parameter vector β, e is a random vector of errors with covariance matrix σ²V, where σ² is unknown scalar parameter, V is a known non-negative definite matrix such that R(X) ? R(V). Symbol R(A) denotes a vector space generated by columns of matrix A. The expected value of y is Xβ. In this paper four following Zyskind-Martin (ZM) models are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y y₁ y₂ involves a vector y₁ of m missing values and a vector y₂ with (n — m) observed values. A special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) test functions F are given in (2.11)) are presented. The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, Xβ, σ²I) to ZM model. Estimation of vector y₁ (cf. 3.3) of vector β (cf. th. 3.2) and of scalar σ² (cf. th. 3.4) in actual ZMa model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between y? ₁ and β is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.     

A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

Modelling publication bias and p-hacking

Publication bias and p-hacking are two well-known phenomena that strongly affect the scientific literature and cause severe problems in meta-analyses. Due to these phenomena, the assumptions of meta-analyses are seriously violated and the results of the studies cannot be trusted. While publication bias is very often captured well by the weighting function selection model, p-hacking is much harder to model and no definitive solution has been found yet. In this paper, we advocate the selection model approach to model publication bias and propose a mixture model for p-hacking. We derive some properties for these models, and we compare them formally and through simulations. Finally, two real data examples are used to show how the models work in practice.     

Detection of compound spatial patterns: further evidence for different channel interactions

It is shown that contrast interrelation functions for small compound gratings and for small compound edge-type patterns have different shapes: the former are lozenges, the latter ellipses in the normalised contrast space. These findings can be described by a simple p-norm model, comprising one channel which is most sensitive to the first pattern, another channel which is most sensitive to the second pattern and a non-linear summation of the channel outputs. Since the value of the summation exponent p is constant within but varies between pattern classes, an interpretation of the model parameters is limited to pattern class. Channel models based on the p-norm are discussed, taking into account the interpretation of the first derivative of the contrast interrelation function and the summation exponent, p. Received: 8 December 1997 / Accepted in revised form: 15 October 1999     

Lumbricus terrestris hemoglobin: A comparison of small-angle X-ray scattering and cryoelectron microscopy data

The quaternary structure of Lumbricus terrestris hemoglobin was investigated by small-angle x-ray scattering (SAXS). Based on the SAXS data from several independent experiments, a three-dimensional (3D) consensus model was established to simulate the solution structure of this complex protein at low resolution (about 3 nm) and to yield the particle dimensions. The model is built up from a large number of small spheres of different weights, a result of the two-step procedure used to calculate the SAXS model. It accounts for the arrangement of 12 subunits in a hexagonal bilayer structure and for an additional central unit of cylinder-like shape. This model provides an excellent fit of the experimental scattering curve of the protein up to h = 1 nm⁻¹ and a nearly perfect fit of the experimental distance distribution function p(r) in the whole range. Scattering curves and p(r) functions were also calculated for low-resolution models based on 3D reconstructions obtained by cryoelectron microscopy (EM). The calculated functions of these models also provide a very good fit of the experimental scattering curve (even at h > 1 nm⁻¹) and p(r) function, if hydration is taken into account and the original model coordinates are slightly rescaled. The comparison of models reveals that both the SAXS-based and the EM-based model lead to a similar simulation of the protein structure and to similar particle dimensions. The essential differences between the models concern the hexagonal bilayer arrangement (eclipsed in the SAXS model, one layer slightly rotated in the EM model), and the mass distribution, mainly on the surface and in the central part of the protein complex. © John Wiley & Sons, Inc. Biopoly 45: 289–298, 1998     

Existence of solutions of a two-dimensional boundary value problem for a system of nonlinear equations arising in growing cell populations

In the paper [A. Ben Amar, A. Jeribi, and B. Krichen, Fixed point theorems for block operator matrix and an application to a structured problem under boundary conditions of Rotenberg's model type, to appear in Math. Slovaca. (2014)], the existence of solutions of the two-dimensional boundary value problem (1) and (2) was discussed in the product Banach space L_p×L_p for p∈(1, ∞). Due to the lack of compactness on L₁ spaces, the analysis did not cover the case p=1. The purpose of this work is to extend the results of Ben Amar et al. to the case p=1 by establishing new variants of fixed-point theorems for a 2×2 operator matrix, involving weakly compact operators.     

A Stochastic Model of Gene Evolution with Time Dependent Pseudochaotic Mutations

We develop here a new class of stochastic models of gene evolution in which a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some time dependent substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. This pseudochaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which pseudochaotically mutate according to 3 time dependent substitution parameters associated with the 3 trinucleotide sites. The main result proves that under suitable assumptions, this pseudochaotic model converges to a uniform probability vector identical to that of the standard model. Furthermore, an application of this pseudochaotic model allows an evolutionary study of the 3 circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e., anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular time dependent functions for the 3 substitution parameters, precisely an exponential decrease in the 1st and 2nd trinucleotide sites and an exponential increase in the 3rd one, this pseudochaotic model retrieves the main statistical properties of the 3 circular codes observed in genes. Furthermore, it leads to a circular code asymmetry stronger than the standard model (nonpseudochaotic) and, therefore, to a better correlation with the genes.     

Estimation and Prediction of Generalized Growth Curve with Grouping Variances in AR(q) Dependence Structure

In this paper we consider maximum likelihood analysis of generalized growth curve model with the Box‐Cox transformation when the covariance matrix has AR(q) dependence structure with grouping variances. The covariance matrix under consideration is Σ = D _σ CD _σ where C is the correlation matrix with stationary autoregression process of order q, q < p and D _σ is a diagonal matrix with p elements divided into g(≤ p) groups, i.e., D _σ is a function of {σ₁, …, σ_g} and – 1 < ρ < 1 and σ_l, l = 1, …, g, are unknown. We consider both parameter estimation and prediction of future values. Results are illustrated with real and simulated data.     

Multiple two-sample testing under arbitrary covariance dependency with an application in imaging mass spectrometry

Large-scale hypothesis testing has become a ubiquitous problem in high-dimensional statistical inference, with broad applications in various scientific disciplines. One relevant application is constituted by imaging mass spectrometry (IMS) association studies, where a large number of tests are performed simultaneously in order to identify molecular masses that are associated with a particular phenotype, for example, a cancer subtype. Mass spectra obtained from matrix-assisted laser desorption/ionization (MALDI) experiments are dependent, when considered as statistical quantities. False discovery proportion (FDP) estimation and  control under arbitrary dependency structure among test statistics is an active topic in modern multiple testing research. In this context, we are concerned with the evaluation of associations between the binary outcome variable (describing the phenotype) and multiple predictors derived from MALDI measurements. We propose an inference procedure in which the correlation matrix of the test statistics is utilized. The approach is based on multiple marginal models. Specifically, we fit a marginal logistic regression model for each predictor individually. Asymptotic joint normality of the stacked vector of the marginal regression coefficients is established under standard regularity assumptions, and their (limiting) correlation matrix is estimated. The proposed method extracts common factors from the resulting empirical correlation matrix. Finally, we estimate the realized FDP of a thresholding procedure for the marginal p-values. We demonstrate a practical application of the proposed workflow to MALDI IMS data in an oncological context.     

Statistical Analysis of Factorial Diallel Design over Environments

Starting from the experimental situation that in each of a environments all mp combinations between m maternal and p paternal genotypes are raised in b replications (blocks), a linear model is formulated for a quantitative character. On the basis of this model formulae for the analysis of variance are given. The expectations of mean squares as well as the estimations of effects (general and specific combining ability and their interaction terms with environments) and their variances are given for different combinations of fixed and random factors.     

Acid–base behavior of poly (vinylpyrrolidone–vinylimidazole) copolymers

Copolymers of vinylimidazole and vinylpyrrolidone containing 0.7–24% of the former residue have been prepared. Titration behavior was examined over a range of temperature and at several ionic strengths. Intrinsic pK's, corrected for electrostatic effects, arc independent of mole fraction of imidazole residue in the copolymer. Nevertheless they are about 1.15 pK units lower than in the corresponding model small molecule, N-ethylimidazole. Enthalpies and entropies of ionization in the copolymer are changed by ionic strength. It is apparent that the charged state of an N-ethylimidazole residue placed in a macromolecular matrix is destabilized relative to the uncharged state because of changes in the local polymer or solvent environment.     

Global identifiability of latent class models with applications to diagnostic test accuracy studies: A Gröbner basis approach

Identifiability of statistical models is a fundamental regularity condition that is required for valid statistical inference. Investigation of model identifiability is mathematically challenging for complex models such as latent class models. Jones et al. used Goodman's technique to investigate the identifiability of latent class models with applications to diagnostic tests in the absence of a gold standard test. The tool they used was based on examining the singularity of the Jacobian or the Fisher information matrix, in order to obtain insights into local identifiability (ie, there exists a neighborhood of a parameter such that no other parameter in the neighborhood leads to the same probability distribution as the parameter). In this paper, we investigate a stronger condition: global identifiability (ie, no two parameters in the parameter space give rise to the same probability distribution), by introducing a powerful mathematical tool from computational algebra: the Gröbner basis. With several existing well-known examples, we argue that the Gröbner basis method is easy to implement and powerful to study global identifiability of latent class models, and is an attractive alternative to the information matrix analysis by Rothenberg and the Jacobian analysis by Goodman and Jones et al.     

Doubly robust tests of exposure effects under high-dimensional confounding

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is exacerbated in high-dimensional settings, where variable selection becomes unavoidable. This has prompted a flurry of activity in developing uniformly valid hypothesis tests for a low-dimensional regression parameter (eg, the causal effect of an exposure A on an outcome Y) in high-dimensional models. So far there has been limited focus on model misspecification, although this is inevitable in high-dimensional settings. We propose tests of the null that are uniformly valid under sparsity conditions weaker than those typically invoked in the literature, assuming working models for the exposure and outcome are both correctly specified. When one of the models is misspecified, by amending the procedure for estimating the nuisance parameters, our tests continue to be valid; hence, they are doubly robust. Our proposals are straightforward to implement using existing software for penalized maximum likelihood estimation and do not require sample splitting. We illustrate them in simulations and an analysis of data obtained from the Ghent University intensive care unit.     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model, p=1−(1+m/k)^−k, and the empirical model, p=1−exp(−am^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.     

Improved Bioreaction Kinetics for the Simulation of Continuous Ethanol Fermentation by Saccharomyces cerevisiae

A kinetic model for the production of ethanol by Saccharomyces cerevisiae has been developed from semiempirical analysis. The values for the parameters in this model were then determined by nonlinear multiple regression using the data of Bazua and Wilke ( 1977). The final equations were μ=0.427s(1-(p/101.6)^1.95)/(0.245+s), Y_X/p=0.291, and Y_X/s=0.152(1-p/302.3). This model was then used to simulate a continuous stirred tank fermentor (CSTF) and compared to other models using the same experimental data but different kinetics. The equations required to use these kinetics in a CSTF with recycle were then developed. From this simulation, it was found that, for a CSTF with recycle, the best configuration to operate is an external recycle, with a low bleed and recycle ratio.     

Two criteria for evaluating risk prediction models

Summary We propose and study two criteria to assess the usefulness of models that predict risk of disease incidence for screening and prevention, or the usefulness of prognostic models for management following disease diagnosis. The first criterion, the proportion of cases followed PCF (q) , is the proportion of individuals who will develop disease who are included in the proportion q of individuals in the population at highest risk. The second criterion is the proportion needed to follow‐up, PNF (p) , namely the proportion of the general population at highest risk that one needs to follow in order that a proportion p of those destined to become cases will be followed. PCF (q) assesses the effectiveness of a program that follows 100q % of the population at highest risk. PNF (p) assess the feasibility of covering 100p % of cases by indicating how much of the population at highest risk must be followed. We show the relationship of those two criteria to the Lorenz curve and its inverse, and present distribution theory for estimates of PCF and PNF. We develop new methods, based on influence functions, for inference for a single risk model, and also for comparing the PCFs and PNFs of two risk models, both of which were evaluated in the same validation data.