Experimental design for mixed models with application to population pharmacokinetic studies

experimental design, mixed model, random coefficient regression model, population pharmacokinetics, approximate design

Optimal designs for mixed effects poisson regression models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

Optimal designs for multivariate linear models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

The effect of patient, provider and financing regulations on the intensity of ambulatory physical therapy episodes : a multilevel analysis based on routinely available data

Background: Many studies have found considerable variations in the resource intensity of physical therapy episodes. Although they have identified several patient-and provider-related factors, few studies have examined their relative explanatory power. We sought to quantify the contribution of patients and providers to these differences and examine how effective Swiss regulations are (nine-session ceiling per prescription and bonus for first treatments). Methods: Our sample consisted of 87,866 first physical therapy episodes performed by 3,365 physiotherapists based on referrals by 6,131 physicians. We modeled the number of visits per episode using a multilevel log linear regression with crossed random effects for physiotherapists and physicians and with fixed effects for cantons. The three-level explanatory variables were patient, physiotherapist and physician characteristics. Results: The median number of sessions was nine (interquartile range 6-13). Physical therapy use increased with age, women, higher health care costs, lower deductibles, surgery and specific conditions. Use rose with the share of nine-session episodes among physiotherapists or physicians, but fell with the share of new treatments. Geographical area had no influence. Most of the variance was explained at the patient level, but the available factors explained only 4% thereof. Physiotherapists and physicians explained only 6% and 5% respectively of the variance, although the available factors explained most of this variance. Regulations were the most powerful factors. Conclusion: Against the backdrop of abundant physical therapy supply, Swiss financial regulations did not restrict utilization. Given that patient-related factors explained most of the variance, this group should be subject to closer scrutiny. Moreover, further research is needed on the determinants of patient demand.

Effect of antenatal corticosteroids on fetal growth and gestational age at birth.

OBJECTIVE: To estimate the effect of multiple courses of antenatal corticosteroids on neonatal size, controlling for gestational age at birth and other confounders, and to determine whether there was a dose-response relationship between number of courses of antenatal corticosteroids and neonatal size. METHODS: This is a secondary analysis of the Multiple Courses of Antenatal Corticosteroids for Preterm Birth Study, a double-blind randomized controlled trial of single compared with multiple courses of antenatal corticosteroids in women at risk for preterm birth and in which fetuses administered multiple courses of antenatal corticosteroids weighed less, were shorter, and had smaller head circumferences at birth. All women (n=1,858) and children (n=2,304) enrolled in the Multiple Courses of Antenatal Corticosteroids for Preterm Birth Study were included in the current analysis. Multiple linear regression analyses were undertaken. RESULTS: Compared with placebo, neonates in the antenatal corticosteroids group were born earlier (estimated difference and confidence interval [CI]: -0.428 weeks, CI -0.10264 to -0.75336; P=.01). Controlling for gestational age at birth and confounding factors, multiple courses of antenatal corticosteroids were associated with a decrease in birth weight (-33.50 g, CI -66.27120 to -0.72880; P=.045), length (-0.339 cm, CI -0.6212 to -0.05676]; P=.019), and head circumference (-0.296 cm, -0.45672 to -0.13528; P<.001). For each additional course of antenatal corticosteroids, there was a trend toward an incremental decrease in birth weight, length, and head circumference. CONCLUSION: Fetuses exposed to multiple courses of antenatal corticosteroids were smaller at birth. The reduction in size was partially attributed to being born at an earlier gestational age but also was attributed to decreased fetal growth. Finally, a dose-response relationship exists between the number of corticosteroid courses and a decrease in fetal growth. The long-term effect of these findings is unknown. CLINICAL TRIAL REGISTRATION: ClinicalTrials.gov, www.clinicaltrials.gov, NCT00187382. LEVEL OF EVIDENCE: II.

Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

From SNPs to pathways: integration of functional effect of sequence variations on models of cell signalling pathways

Background: Single nucleotide polymorphisms (SNPs) are the most frequent type of sequence variation between individuals, and represent a promising tool for finding genetic determinants of complex diseases and understanding the differences in drug response. In this regard, it is of particular interest to study the effect of non-synonymous SNPs in the context of biological networks such as cell signalling pathways. UniProt provides curated information about the functional and phenotypic effects of sequence variation, including SNPs, as well as on mutations of protein sequences. However, no strategy has been developed to integrate this information with biological networks, with the ultimate goal of studying the impact of the functional effect of SNPs in the structure and dynamics of biological networks. Results: First, we identified the different challenges posed by the integration of the phenotypic effect of sequence variants and mutations with biological networks. Second, we developed a strategy for the combination of data extracted from public resources, such as UniProt, NCBI dbSNP, Reactome and BioModels. We generated attribute files containing phenotypic and genotypic annotations to the nodes of biological networks, which can be imported into network visualization tools such as Cytoscape. These resources allow the mapping and visualization of mutations and natural variations of human proteins and their phenotypic effect on biological networks (e.g. signalling pathways, protein-protein interaction networks, dynamic models). Finally, an example on the use of the sequence variation data in the dynamics of a network model is presented. Conclusion: In this paper we present a general strategy for the integration of pathway and sequence variation data for visualization, analysis and modelling purposes, including the study of the functional impact of protein sequence variations on the dynamics of signalling pathways. This is of particular interest when the SNP or mutation is known to be associated to disease. We expect that this approach will help in the study of the functional impact of disease-associated SNPs on the behaviour of cell signalling pathways, which ultimately will lead to a better understanding of the mechanisms underlying complex diseases.

Generalized linear and generalized additive models in studies of species distributions: setting the scene

An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001.We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling.

Towards robust network based complex systems : from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Preparation with fasting and acipimox increases myocardial glucose uptake in mice during cardiac 18F-FDG microPET

Purpose: Cardiac 18F-FDG PET is considered as the gold standard to assess myocardial metabolism and infarct size. The myocardial demand for glucose can be influenced by fasting and/or following pharmacological preparation. In the rat, it has been previously shown that fasting combined with preconditioning with acipimox, a nicotinic acid derivate and lipidlowering agent, increased dramatically 18F-FDG uptake in the myocardium. Strategies aimed at reducing infarct scar are evaluated in a variety of mouse models. PET would particularly useful for assessing cardiac viability in the mouse. However, prior knowledge of the best preparation protocol is a prerequisite for accurate measurement of glucose uptake in mice. Therefore, we studied the effect of different protocols on 18F-FDG uptake in the mouse heart.Methods: Mice (n = 15) were separated into three treatment groups according to preconditioning and underwent a 18FDG PET scan. Group 1: No preconditioning (n = 3); Group 2: Overnight fasting (n = 8); and Group 3: Overnight fasting and acipimox (25mg/kg SC) (n = 4). MicroPET images were processed with PMOD to determine 18F-FDG mean standard uptake value (SUV) at 30 min for the whole left ventricle (LV) and for each region of the 17-segments AHA model. For comparisons, we used Mann-Whitney test and multilevel mixed-effects linear regression (Stata 11.0).Results: In total, 27 microPET were performed successfully in 15 animals. Overnight fasting led to a dramatic increase in LV-SUV compared to mice without preconditioning (8.6±0.7g/mL vs. 3.7±1.1g/mL, P<0.001). In addition, LV-SUV was slightly but not significantly higher in animals treated with acipimox compared to animals with overnight fasting alone (10.2±0.5 g/mL, P = 0.06). Fastening increased segmental SUV by 5.1±0.5g/mL as compared to free-feeding mice (from 3.7±0.8g/mL to 8.8±0.4g/mL, P<0.001); segmental-SUV also significantly increased after administration of acipimox (from 8.8±0.4g/mL to 10.1±0.4g/mL, P<0.001).Conclusion: Overnight fasting led to myocardial glucose deprivation and increases 18F-FDG myocardial uptake. Additional administration of acipimox enhances myocardial 18F-FDG uptake, at least at the segmental level. Thus, preconditioning with acipimox may provide better image quality that may help for assessing segmental myocardial metabolism.