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Non-linear Mixed-effects Modeling Software
Nonlinear mixed-effects models are a special case of regression analysis for which a range of different software solutions are available. The statistical properties of nonlinear mixed-effects models make direct estimation by a BLUE estimator impossible. Nonlinear mixed effects models are therefore estimated according to Maximum Likelihood principles. Specific estimation methods are applied, such as linearization methods as first-order (FO), first-order conditional (FOCE) or the laplacian (LAPL), approximation methods such as iterative-two stage (ITS), importance sampling (IMP), stochastic approximation estimation (SAEM) or direct sampling. A special case is use of non-parametric approaches. Furthermore, estimation in limited or full Bayesian frameworks is performed using the Metropolis-Hastings or the NUTS algorithms. Some software solutions focus on a single estimation method, others cover a range of estimation methods and/or with interfaces for specific use cases. General-pur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Mixed-effects Model
Nonlinear mixed-effects models constitute a class of statistical models generalizing linear mixed-effects models. Like linear mixed-effects models, they are particularly useful in settings where there are multiple measurements within the same statistical units or when there are dependencies between measurements on related statistical units. Nonlinear mixed-effects models are applied in many fields including medicine, public health, pharmacology, and ecology. Definition While any statistical model containing both fixed effects and random effects is an example of a nonlinear mixed-effects model, the most commonly used models are members of the class of nonlinear mixed-effects models for repeated measures :_ = f(\phi_,_) + \epsilon_,\quad i =1,\ldots, M, \, j = 1,\ldots, n_i where *M is the number of groups/subjects, *n_i is the number of observations for the ith group/subject, *f is a real-valued differentiable function of a group-specific parameter vector \theta_ and a covariat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
WinBUGS
WinBUGS is statistical software for Bayesian analysis using Markov chain Monte Carlo (MCMC) methods. It is based on the BUGS ( Bayesian inference Using Gibbs Sampling) project started in 1989. It runs under Microsoft Windows, though it can also be run on Linux or Mac using Wine. It was developed by the BUGS Project, a team of British researchers at the MRC Biostatistics Unit, Cambridge, and Imperial College School of Medicine, London. Originally intended to solve problems encountered in medical statistics, it soon became widely used in other disciplines, such as ecology, sociology, and geology. The last version of WinBUGS was version 1.4.3, released in August 2007. Development is now focused on OpenBUGS, an open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized sof ... version of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Design
In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing exper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physiologically Based Pharmacokinetic Modelling
Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species. PBPK modeling is used in pharmaceutical research and drug development, and in health risk assessment for cosmetics or general chemicals. PBPK models strive to be mechanistic by mathematically transcribing anatomical, physiological, physical, and chemical descriptions of the phenomena involved in the complex ADME processes. A large degree of residual simplification and empiricism is still present in those models, but they have an extended domain of applicability compared to that of classical, empirical function based, pharmacokinetic models. PBPK models may have purely predictive uses, but other uses, such as statistical inference, have been made possible by the development of Bayesian statistical tools able to deal with complex models. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LAPACK
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines. LAPACK was designed as the successor to the linear equations and linear least-squares routines of LINPACK and the eigenvalue routines of EISPACK. LINPACK, written in the 1970s and 1980s, was designed to run on the then-modern vector computers with shared memory. LAPACK, in contrast, was designed to effectivel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Runge–Kutta Methods
In numerical analysis, the Runge–Kutta methods ( ) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. These methods were developed around 1900 by the German mathematicians Carl Runge and Wilhelm Kutta. The Runge–Kutta method The most widely known member of the Runge–Kutta family is generally referred to as "RK4", the "classic Runge–Kutta method" or simply as "the Runge–Kutta method". Let an initial value problem be specified as follows: : \frac = f(t, y), \quad y(t_0) = y_0. Here y is an unknown function (scalar or vector) of time t, which we would like to approximate; we are told that \frac, the rate at which y changes, is a function of t and of y itself. At the initial time t_0 the corresponding y value is y_0. The function f and the initial conditions t_0, y_0 are given. Now we pick a step-size ''h'' > 0 and define: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia (programming Language)
Julia is a high-level, dynamic programming language. Its features are well suited for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism in a dynamic programming language; with multiple dispatch as its core programming paradigm. Julia supports concurrent, (composable) parallel and distributed computing (with or without using MPI or the built-in corresponding to "OpenMP-style" threads), and direct calling of C and Fortran libraries without glue code. Julia uses a just-in-time (JIT) compiler that is referred to as "just- ahead-of-time" (JAOT) in the Julia community, as Julia compiles all code (by default) to machine code before running it. Julia is garbage-collected, uses eager evaluation, and includes efficient libraries for floating-point calculations, linear algebra, random number generation, and regular expression matching. Many libraries are available, including some (e.g., for fast Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NONMEM
NONMEM is a non-linear mixed-effects modeling software package developed by Stuart L. Beal and Lewis B. Sheiner in the late 1970s at University of California, San Francisco, and expanded by Robert Bauer at Icon PLC. Its name is an acronym for NON-linear mixed effects modeling but it is especially powerful in the context of population pharmacokinetics, pharmacometrics, and PK/PD models. NONMEM models are written in NMTRAN, a dedicated model specification language that is translated into FORTRAN, compiled on the fly and executed by a command-line script. Results are presented as text output files including tables. There are multiple interfaces to assist modelers with housekeeping of files, tracking of model development, goodness-of-fit evaluations and graphical output, such as PsN and xpose and Wings for NONMEM. Current version for NONMEM is 7.5. Model estimation NONMEM estimates its models according to principles of maximum likelihood estimation. nonlinear mixed-effects mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Differential Equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast with the term partial differential equation which may be with respect to ''more than'' one independent variable. Differential equations A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form :a_0(x)y +a_1(x)y' + a_2(x)y'' +\cdots +a_n(x)y^+b(x)=0, where , ..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of the unknown function of the variable . Among ordinary differential equations, linear differential equations play a prominent role for several reasons. Most elementary and special functions that are encountered in physics and applied mathematics are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pharmacometrics
Pharmacometrics is a field of study of the methodology and application of models for disease and pharmacological measurement. It uses mathematical models of biology, pharmacology, disease, and physiology to describe and quantify interactions between xenobiotics and patients (human and non-human), including beneficial effects and adverse effects. It is normally applied to quantify drug, disease and trial information to aid efficient drug development, regulatory decisions and rational drug treatment in patients. Pharmacometrics uses models based on pharmacology, physiology, and disease for quantitative analysis of interactions between drugs and patients. This involves Systems pharmacology, pharmacokinetics, pharmacodynamics and disease progression with a focus on populations and variability. Mould and Upton provide an overview of basic concepts in population modeling, simulation, and model-based drug development. A major focus of pharmacometrics is to understand variability in dru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stan (software)
Stan is a probabilistic programming language for statistical inference written in C++.Stan Development Team. 2015Stan Modeling Language User's Guide and Reference Manual, Version 2.9.0/ref> The Stan language is used to specify a (Bayesian) statistical model with an imperative program calculating the log probability density function. Stan is licensed under the New BSD License. Stan is named in honour of Stanislaw Ulam, pioneer of the Monte Carlo method. Stan was created by a development team consisting of 34 members that includes Andrew Gelman, Bob Carpenter, Matt Hoffman, and Daniel Lee. Interfaces The Stan language itself can be accessed through several interfaces: * CmdStan – a command-line executable for the shell, * CmdStanR and rstan – R software libraries, * CmdStanPy and PyStan – libraries for the Python programming language, * MatlabStan – integration with the MATLAB numerical computing environment, * Stan.jl – integration with the Julia programming langua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SPSS
SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. Current versions (post 2015) have the brand name: IBM SPSS Statistics. The software name originally stood for Statistical Package for the Social Sciences (SPSS), reflecting the original market, then later changed to Statistical Product and Service Solutions. Overview SPSS is a widely used program for statistical analysis in social science. It is also used by market researchers, health researchers, survey companies, government, education researchers, marketing organizations, data miners, and others. The original SPSS manual (Nie, Bent & Hull, 1970) has been described as one of "sociology's most influential books" for allowing ordinary researchers to do their own statistical analysis. In addition to statistical analysis, data management (ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
