Dealing with Uncertainty and Variability A Course on Physiologically Based Pharmacokinetic (PBPK) Modeling in Drug Development and Evaluation
|
|
- Angela Goodwin
- 7 years ago
- Views:
Transcription
1 Dealing with Uncertainty and Variability A Course on Physiologically Based Pharmacokinetic (PBPK) Modeling in Drug Development and Evaluation April 6-10, 2009 Center for Human Health Assessment Center for Drug Safety Sciences
2 Parameterizing the model: Parameter Estimation Issues Identifiability Colinearity (correlation) Sensitivity
3 Parameter optimization: Fitting the model to the data Issues: Multiple parameter fitting Colinearity Local Minima Weighting ObjectiveFunction = γ = heteroscedasticity parameter γ = 0 : absolute weighting constant variance linear plot follows mass γ = 2 : relative weighting constant coefficient of variance logarithmic plot follows rates ( Predicted - Observed ) Y Observed 2
4 Parameter colinearity (Correlation) Parameters in PBPK models are not always independent: VMaxC and KM VMaxC and KfC QCC and QPC Ignoring parameter interdependence can distort sensitivity analysis, uncertainty analysis and parameter optimization
5 Parameter sensitivity coefficient: (Log Normalized) Fractional Change in Model Output Fractional Change in Parameter If Normalized Coefficient >> 1, parameter error is amplified and model output may be highly uncertain
6 Monte Carlo uncertainty analysis Parameter A Parameter B PBPK Model Model Output Distribution Parameter X Parameter Distributions
7 Simple Monte Carlo analysis vs. Markov Chain Monte Carlo Simple Monte Carlo: parameters are repeatedly sampled from distributions provided by the investigator and distributions for outputs are generated with the model. Markov Chain Monte Carlo: information from prior distributions and fit of the model to selected data sets is combined in a hierarchical Bayesian framework to generate posterior distributions for parameters reflecting uncertainty and variability.
8 What is MCMC Analysis? Markov chain Monte Carlo (MCMC) analysis - an implementation of the hierarchical Bayesian statistical approach Monte Carlo analysis - drawing samples from distributions Markov chain - a series of random samples, each sample dependent only on the one before Heirarchy: population, study, individual
9 Hierarchical model Population Level M (mean) S 2 (variability) θ φ Subject Level PBPK Data σ 2 measurement/model error Figure adapted from Bois (2000) analysis of TCE model
10 Bayes Theorem P ( θ D ) = P ( θ ) P ( θ ) P ( D P ( D θ ) θ ) d θ Prior knowledge (parameter distributions) combined with new information (data) to obtain posterior distributions sample priors run model compute likelihoods MCMC algorithm (MCSim, developed by F. Bois) (
11 PBPK model calibration using hierarchical Bayesian analysis Prior Parameter Distributions Data MCMC Sampling PBPK Model Posterior Distributions Of Parameters MC Sampling Calibrated PBPK Model Posterior Distributions Of Dosemetrics
12 MCMC Samples drawn using a Markov chain The chain forgets starting position and converges to a stationary, posterior distribution
13 Re-estimation of distribution for Muscle:Blood partition coefficient lnpslw(1) Average Median 2 sd Prior Posterior lnpslw(1) Average = E+00 Stdev = E-01 Median = E
14 Distribution of Variance in Fractional Volume of the Fat Compartment 70 Prior 60 Posterior
15 Common MCMC problem: failure to converge logvmaxc(1.3) logvpr(1.14) iteration iteration
16 To MC or MCMC: That is the question Advantages of Markov Chain Monte Carlo: Combines parameter identification with variability analysis Allows estimation of variability distributions for selected parameters based on fit of model to multiple kinetic data sets Disadvantages of Markov Chain Monte Carlo: May give undue priority to kinetic data included in MCMC analysis (as opposed to other information regarding parameters) Parameter distributions may be inappropriately reestimated due to model error
17 Hattis s Laws of Uncertainty Analysis 1. Nearly all parameter distributions look lognormal, as long as you don t look too closely. 2. Any estimate of the uncertainty of a parameter value will always itself be more uncertain than the estimate of the parameter itself. 3. The application of standard statistical techniques to a single data set will nearly always reveal only a trivial proportion of the overall uncertainty in the parameter value.
18 Clewell s Law of Reciprocal Uncertainty The more important the parameter, the less certain will be its value.
19 Uncertainty/Variability analysis Maintaining mass balance During Monte Carlo sampling, the model code must assure that the selected blood flows to the tissues add up to the total blood flow, i.e.: ΣQ i = Q C
20 Uncertainty vs. Variability Definitions Uncertainty = limitation in estimating mean parameter value for population Variability = limitation in estimating extent to which individual parameter value may vary from population mean
21 Uncertainty vs. Variability Animal studies: Uncertainty dominates In-bred strains Multiple animals per dose group Human studies: Variability dominates Heterogeneous population Variability in exposure
22 PBPK model for Xenon exposure C I C X C V Alveolar Air Alveolar Blood Lung Tissue C A Venous Blood Arterial Blood Oral Dose Slowly Perfused Tissue C S ka Stomach Lumen ktssi Rapidly Perfused Tissue C R kasi Small Intestinal Lumen ktsli Fat Tissue C F kaui Upper Large Intestinal Lumen Gastrointestinal Tissue C G kali ktuli Lower Large Intestinal Lumen ktex Liver Tissue C L
23 Variability in G.I. uptake (Confidence intervals based on standard deviation) CT Hours
24 Uncertainty in G.I. uptake (Confidence intervals based on standard error of mean) CT Hours
25 Prediction of G.I. uptake across studies 3 log(atotp) Accuracy of extrapolation reflects low uncertainty (SEM) in spite of high variability (SD) of individual data Non-fasting Predicted Fasting Time (hours)
26 Variability in human P450 isozymes Isozyme Assay Variability (-fold) Inducible Evidence for Polymorphism Cancer Impact 1A yes no smoking 1A2 caffeine 50 yes no PAH 2C mephenytion yes (3% poor)? 2D6 debrisoquine yes? 2E1 chlorzoxazone 10 yes yes halogenated hydrocarbons 3A4 nifedipine 20 yes no aflatoxin-b1
27 Evaluating pharmacokinetic variability The pharmacokinetic variability across a population is a function of many chemical-specific, genetic, and physiological factors. Speculation regarding the overall variability in pharmacokinetic sensitivity based on the observed variability of individual pharmacokinetic factors can be highly misleading. Analysis using a PBPK model and Monte Carlo techniques provides a more reliable approach for estimating population pharmacokinetic variability.
28 Example: impact of CYP2C9 Polymorphism on Warfarin Internal Dose iv dose Plasma QC Kidney QKid Rapidly Perfused QRap Skin QSkn Slowly Perfused QSlw Liver QLiv oral dose VMax, KM, KMI PBPK Model for Warfarin (Gentry et al., 2002)
29 Metabolic Parameters for (S)-Warfarin for Three CYP2C9 Alleles Vmax (mg/hr/kg 3/4 ) Km (mg/l) Intrinsic Clearance Allele Reference Mean CV Mean CV (VmaxC/Km) CYP2C9*1 Haining et al., Takahashi et al., 1998b Sullivan-Klose et al., Rettie et al., Rettie et al., CYP2C9*2 Sullivan-Klose et al., Rettie et al., Rettie et al., Rettie et al., CYP2C9*3 Haining et al., Takahashi et al., 1998b Sullivan-Klose et al., baculovirus/insect cell system, purified enzyme 2 yeast expression, microsomes 3 Hep G2 cells, cell lysate 4 Hep G2 cells, particulate preparation 5 expressed in insect cells, purified enzymes (Haber et al., 2002)
30 Average Prevalence of CYP2C9 Alleles in the U.S. Population Prevalence S1 homozygous 78% S1/S2 heterozygous 12% S1/S3 heterozygous 9% S2 homozygous 1% S2/S3 heterozygous 1% S3 homozygous 0.5% (Haber et al., 2002)
31 Descriptive Statistics of the AUC Distribution for (S)-Warfarin Case 1 (CYP2C9*1) Case 1 (CYP2C9*2) Case 1 (CYP2C9*3) Case 2 (Normal Population) Case 3 (Total Population) Mean Standard Error Median Standard Deviation Sample Variance Kurtosis Skewness Range Minimum th Pctile th Pctile Maximum Count * Case 1 Varying only the metabolism parameters defining the polymorphism, using the allele indicated Case 2 Varying all parameter except those defining the polymorphism Case 3 Varying all parameters, using U.S. population frequencies of each allele (Gentry et al., 2002)
32 Simulation of impact of genetic polymorphism on Warfarin internal dose Plasma Concentration (mg/l) 5 A. C Y P 2 C 9 * 1 A lle le H o u rs Plasma Concentration (mg/l) 5 B. C Y P 2 C 9 * 2 A lle le H o u rs Plasma Concentration (mg/l) 5 C. C Y P 2 C 9 * 3 A lle le H o u rs
33 Simulation of impact of genetic polymorphism on Warfarin internal dose 250 Normal population Case Frequency of (S)-Warfarin AUC 1000 Total population Case 3 (S)-Warfarin AUC
PHAR 7633 Chapter 19 Multi-Compartment Pharmacokinetic Models
Student Objectives for this Chapter PHAR 7633 Chapter 19 Multi-Compartment Pharmacokinetic Models To draw the scheme and write the differential equations appropriate to a multi-compartment pharmacokinetic
More informationMore details on the inputs, functionality, and output can be found below.
Overview: The SMEEACT (Software for More Efficient, Ethical, and Affordable Clinical Trials) web interface (http://research.mdacc.tmc.edu/smeeactweb) implements a single analysis of a two-armed trial comparing
More informationConstructing PK Models
Constructing PK Models Interpretation of biomonitoring data using physiologically based pharmacokinetic modeling Center for Human Health Assessment September 25-29, 29, 2006 Pharmacokinetics Studies of
More informationModel-based Synthesis. Tony O Hagan
Model-based Synthesis Tony O Hagan Stochastic models Synthesising evidence through a statistical model 2 Evidence Synthesis (Session 3), Helsinki, 28/10/11 Graphical modelling The kinds of models that
More informationA Bayesian hierarchical surrogate outcome model for multiple sclerosis
A Bayesian hierarchical surrogate outcome model for multiple sclerosis 3 rd Annual ASA New Jersey Chapter / Bayer Statistics Workshop David Ohlssen (Novartis), Luca Pozzi and Heinz Schmidli (Novartis)
More informationCHAPTER 3 EXAMPLES: REGRESSION AND PATH ANALYSIS
Examples: Regression And Path Analysis CHAPTER 3 EXAMPLES: REGRESSION AND PATH ANALYSIS Regression analysis with univariate or multivariate dependent variables is a standard procedure for modeling relationships
More informationAbsorption of Drugs. Transport of a drug from the GI tract
Absorption of Drugs Absorption is the transfer of a drug from its site of administration to the bloodstream. The rate and efficiency of absorption depend on the route of administration. For IV delivery,
More informationStatistics and Pharmacokinetics in Clinical Pharmacology Studies
Paper ST03 Statistics and Pharmacokinetics in Clinical Pharmacology Studies ABSTRACT Amy Newlands, GlaxoSmithKline, Greenford UK The aim of this presentation is to show how we use statistics and pharmacokinetics
More informationApplications of R Software in Bayesian Data Analysis
Article International Journal of Information Science and System, 2012, 1(1): 7-23 International Journal of Information Science and System Journal homepage: www.modernscientificpress.com/journals/ijinfosci.aspx
More informationQuantitative Methods for Finance
Quantitative Methods for Finance Module 1: The Time Value of Money 1 Learning how to interpret interest rates as required rates of return, discount rates, or opportunity costs. 2 Learning how to explain
More informationIV solutions may be given either as a bolus dose or infused slowly through a vein into the plasma at a constant or zero-order rate.
د.شيماء Biopharmaceutics INTRAVENOUS INFUSION: IV solutions may be given either as a bolus dose or infused slowly through a vein into the plasma at a constant or zero-order rate. The main advantage for
More informationA spreadsheet Approach to Business Quantitative Methods
A spreadsheet Approach to Business Quantitative Methods by John Flaherty Ric Lombardo Paul Morgan Basil desilva David Wilson with contributions by: William McCluskey Richard Borst Lloyd Williams Hugh Williams
More informationGLMs: Gompertz s Law. GLMs in R. Gompertz s famous graduation formula is. or log µ x is linear in age, x,
Computing: an indispensable tool or an insurmountable hurdle? Iain Currie Heriot Watt University, Scotland ATRC, University College Dublin July 2006 Plan of talk General remarks The professional syllabus
More informationSTA 4273H: Statistical Machine Learning
STA 4273H: Statistical Machine Learning Russ Salakhutdinov Department of Statistics! rsalakhu@utstat.toronto.edu! http://www.cs.toronto.edu/~rsalakhu/ Lecture 6 Three Approaches to Classification Construct
More informationBIOAVAILABILITY & BIOEQUIVALENCE TRIALS
BIOAVAILABILITY & BIOEQUIVALENCE TRIALS Shubha Rani,, Ph.D. Technical Director & Head-Biometrics and Data Management Synchron Research Services Pvt. Ltd. Ahmedabad 380 054 drshubha@synchronresearch.com
More informationImputing Missing Data using SAS
ABSTRACT Paper 3295-2015 Imputing Missing Data using SAS Christopher Yim, California Polytechnic State University, San Luis Obispo Missing data is an unfortunate reality of statistics. However, there are
More informationModeling and Analysis of Call Center Arrival Data: A Bayesian Approach
Modeling and Analysis of Call Center Arrival Data: A Bayesian Approach Refik Soyer * Department of Management Science The George Washington University M. Murat Tarimcilar Department of Management Science
More informationStandard Deviation Estimator
CSS.com Chapter 905 Standard Deviation Estimator Introduction Even though it is not of primary interest, an estimate of the standard deviation (SD) is needed when calculating the power or sample size of
More informationStatistics Graduate Courses
Statistics Graduate Courses STAT 7002--Topics in Statistics-Biological/Physical/Mathematics (cr.arr.).organized study of selected topics. Subjects and earnable credit may vary from semester to semester.
More informationAPPLIED MISSING DATA ANALYSIS
APPLIED MISSING DATA ANALYSIS Craig K. Enders Series Editor's Note by Todd D. little THE GUILFORD PRESS New York London Contents 1 An Introduction to Missing Data 1 1.1 Introduction 1 1.2 Chapter Overview
More informationBayesian Phylogeny and Measures of Branch Support
Bayesian Phylogeny and Measures of Branch Support Bayesian Statistics Imagine we have a bag containing 100 dice of which we know that 90 are fair and 10 are biased. The
More informationTutorial on Markov Chain Monte Carlo
Tutorial on Markov Chain Monte Carlo Kenneth M. Hanson Los Alamos National Laboratory Presented at the 29 th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Technology,
More informationWeb-based Supplementary Materials for Bayesian Effect Estimation. Accounting for Adjustment Uncertainty by Chi Wang, Giovanni
1 Web-based Supplementary Materials for Bayesian Effect Estimation Accounting for Adjustment Uncertainty by Chi Wang, Giovanni Parmigiani, and Francesca Dominici In Web Appendix A, we provide detailed
More informationNM- Nuclear Medicine
NM- Nuclear Medicine CODE DESCRIPTION 78000 Thyroid uptake; single determination 78001 Thyroid uptake; multiple determinations 78003 Thyroid uptake; stimulation, suppression or discharge 78006 Thyroid
More informationDrug Excretion. Renal Drug Clearance. Drug Clearance and Half-Life. Glomerular Filtration II. Glomerular Filtration I. Drug Excretion and Clearance
t/.drugexcretion AINTRAVENOUSDOSE 36848765430TIME(hours) t/ Drug Excretion Dr. Robert G. Lamb Professor Pharmacology & Toxicology Drug Excretion and Clearance Drug Excretion: is the movement of drug from
More informationBayeScan v2.1 User Manual
BayeScan v2.1 User Manual Matthieu Foll January, 2012 1. Introduction This program, BayeScan aims at identifying candidate loci under natural selection from genetic data, using differences in allele frequencies
More informationBayesian Machine Learning (ML): Modeling And Inference in Big Data. Zhuhua Cai Google, Rice University caizhua@gmail.com
Bayesian Machine Learning (ML): Modeling And Inference in Big Data Zhuhua Cai Google Rice University caizhua@gmail.com 1 Syllabus Bayesian ML Concepts (Today) Bayesian ML on MapReduce (Next morning) Bayesian
More informationUsing SAS PROC MCMC to Estimate and Evaluate Item Response Theory Models
Using SAS PROC MCMC to Estimate and Evaluate Item Response Theory Models Clement A Stone Abstract Interest in estimating item response theory (IRT) models using Bayesian methods has grown tremendously
More informationInstitute of Actuaries of India Subject CT3 Probability and Mathematical Statistics
Institute of Actuaries of India Subject CT3 Probability and Mathematical Statistics For 2015 Examinations Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in
More informationExercise Day 3-13 A PBPK Model for Methyl Mercury
Exercise Day 3-13 A PBPK Model for Methyl Mercury Interpretation of biomonitoring data using physiologically based pharmacokinetic modeling Center for Human Health Assessment September 25-29, 29, 2006
More informationVolume of Distribution
1 Volume of Distribution Nick Holford Dept Pharmacology & Clinical Pharmacology University of Auckland, New Zealand 2 Objectives Learn the definition of volume of distribution Understand the physiological
More informationData Preparation and Statistical Displays
Reservoir Modeling with GSLIB Data Preparation and Statistical Displays Data Cleaning / Quality Control Statistics as Parameters for Random Function Models Univariate Statistics Histograms and Probability
More informationIntroduction to Markov Chain Monte Carlo
Introduction to Markov Chain Monte Carlo Monte Carlo: sample from a distribution to estimate the distribution to compute max, mean Markov Chain Monte Carlo: sampling using local information Generic problem
More informationExposure Modeling. Interpretation of biomonitoring data using physiologically based pharmacokinetic modeling. Centers for Human Health Assessment
Exposure Modeling Interpretation of biomonitoring data using physiologically based pharmacokinetic modeling Centers for Human Health Assessment September 25-29, 2006 Exposure assessment Emission Inhalation
More information1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96
1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years
More informationValidation and Calibration. Definitions and Terminology
Validation and Calibration Definitions and Terminology ACCEPTANCE CRITERIA: The specifications and acceptance/rejection criteria, such as acceptable quality level and unacceptable quality level, with an
More informationQSAR. The following lecture has drawn many examples from the online lectures by H. Kubinyi
QSAR The following lecture has drawn many examples from the online lectures by H. Kubinyi LMU Institut für Informatik, LFE Bioinformatik, Cheminformatics, Structure independent methods J. Apostolakis 1
More informationParallelization Strategies for Multicore Data Analysis
Parallelization Strategies for Multicore Data Analysis Wei-Chen Chen 1 Russell Zaretzki 2 1 University of Tennessee, Dept of EEB 2 University of Tennessee, Dept. Statistics, Operations, and Management
More informationImputing Values to Missing Data
Imputing Values to Missing Data In federated data, between 30%-70% of the data points will have at least one missing attribute - data wastage if we ignore all records with a missing value Remaining data
More informationA Bayesian Model to Enhance Domestic Energy Consumption Forecast
Proceedings of the 2012 International Conference on Industrial Engineering and Operations Management Istanbul, Turkey, July 3 6, 2012 A Bayesian Model to Enhance Domestic Energy Consumption Forecast Mohammad
More informationLinear regression methods for large n and streaming data
Linear regression methods for large n and streaming data Large n and small or moderate p is a fairly simple problem. The sufficient statistic for β in OLS (and ridge) is: The concept of sufficiency is
More information11. Time series and dynamic linear models
11. Time series and dynamic linear models Objective To introduce the Bayesian approach to the modeling and forecasting of time series. Recommended reading West, M. and Harrison, J. (1997). models, (2 nd
More informationConfidence Intervals for One Standard Deviation Using Standard Deviation
Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from
More informationMeans, standard deviations and. and standard errors
CHAPTER 4 Means, standard deviations and standard errors 4.1 Introduction Change of units 4.2 Mean, median and mode Coefficient of variation 4.3 Measures of variation 4.4 Calculating the mean and standard
More informationApplying Statistics Recommended by Regulatory Documents
Applying Statistics Recommended by Regulatory Documents Steven Walfish President, Statistical Outsourcing Services steven@statisticaloutsourcingservices.com 301-325 325-31293129 About the Speaker Mr. Steven
More informationTowards running complex models on big data
Towards running complex models on big data Working with all the genomes in the world without changing the model (too much) Daniel Lawson Heilbronn Institute, University of Bristol 2013 1 / 17 Motivation
More information2. Filling Data Gaps, Data validation & Descriptive Statistics
2. Filling Data Gaps, Data validation & Descriptive Statistics Dr. Prasad Modak Background Data collected from field may suffer from these problems Data may contain gaps ( = no readings during this period)
More informationDATA INTERPRETATION AND STATISTICS
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
More informationA Basic Introduction to Missing Data
John Fox Sociology 740 Winter 2014 Outline Why Missing Data Arise Why Missing Data Arise Global or unit non-response. In a survey, certain respondents may be unreachable or may refuse to participate. Item
More informationA Latent Variable Approach to Validate Credit Rating Systems using R
A Latent Variable Approach to Validate Credit Rating Systems using R Chicago, April 24, 2009 Bettina Grün a, Paul Hofmarcher a, Kurt Hornik a, Christoph Leitner a, Stefan Pichler a a WU Wien Grün/Hofmarcher/Hornik/Leitner/Pichler
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More informationBayesian Statistical Analysis in Medical Research
Bayesian Statistical Analysis in Medical Research David Draper Department of Applied Mathematics and Statistics University of California, Santa Cruz draper@ams.ucsc.edu www.ams.ucsc.edu/ draper ROLE Steering
More informationProbabilistic Risk Assessment Methodology for Criteria Calculation Versus the Standard (Deterministic) Methodology
Probabilistic Risk Assessment Methodology for Criteria Calculation Versus the Standard (Deterministic) Methodology State of Idaho Department of Environmental Quality March 2014 Background The equation
More informationShort title: Measurement error in binary regression. T. Fearn 1, D.C. Hill 2 and S.C. Darby 2. of Oxford, Oxford, U.K.
Measurement error in the explanatory variable of a binary regression: regression calibration and integrated conditional likelihood in studies of residential radon and lung cancer Short title: Measurement
More informationDeterminants of Blood Oxygen Content Instructor s Guide
Determinants of Blood Oxygen Content Instructor s Guide Time to Complete This activity will take approximately 75 minutes, but can be shortened depending on how much time the instructor takes to review
More informationStatistical Rules of Thumb
Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN
More informationBusiness Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.
Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing
More information> plot(exp.btgpllm, main = "treed GP LLM,", proj = c(1)) > plot(exp.btgpllm, main = "treed GP LLM,", proj = c(2)) quantile diff (error)
> plot(exp.btgpllm, main = "treed GP LLM,", proj = c(1)) > plot(exp.btgpllm, main = "treed GP LLM,", proj = c(2)) 0.4 0.2 0.0 0.2 0.4 treed GP LLM, mean treed GP LLM, 0.00 0.05 0.10 0.15 0.20 x1 x1 0.4
More informationPHAR 7633 Chapter 22 Non-Linear Regression Analysis of Pharmacokinetic Data Individual Data and Population Analysis
PHAR 7633 Chapter 22 Non-Linear Regression Analysis of Pharmacokinetic Data Individual Data and Population Analysis Student Objectives for this Chapter Understand the use of computer programs such as Boomer
More information1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
More informationNon Linear Dependence Structures: a Copula Opinion Approach in Portfolio Optimization
Non Linear Dependence Structures: a Copula Opinion Approach in Portfolio Optimization Jean- Damien Villiers ESSEC Business School Master of Sciences in Management Grande Ecole September 2013 1 Non Linear
More informationLogistic Regression (a type of Generalized Linear Model)
Logistic Regression (a type of Generalized Linear Model) 1/36 Today Review of GLMs Logistic Regression 2/36 How do we find patterns in data? We begin with a model of how the world works We use our knowledge
More informationJava Modules for Time Series Analysis
Java Modules for Time Series Analysis Agenda Clustering Non-normal distributions Multifactor modeling Implied ratings Time series prediction 1. Clustering + Cluster 1 Synthetic Clustering + Time series
More informationFunctional Data Analysis of MALDI TOF Protein Spectra
Functional Data Analysis of MALDI TOF Protein Spectra Dean Billheimer dean.billheimer@vanderbilt.edu. Department of Biostatistics Vanderbilt University Vanderbilt Ingram Cancer Center FDA for MALDI TOF
More informationEstimation and comparison of multiple change-point models
Journal of Econometrics 86 (1998) 221 241 Estimation and comparison of multiple change-point models Siddhartha Chib* John M. Olin School of Business, Washington University, 1 Brookings Drive, Campus Box
More informationExample: Credit card default, we may be more interested in predicting the probabilty of a default than classifying individuals as default or not.
Statistical Learning: Chapter 4 Classification 4.1 Introduction Supervised learning with a categorical (Qualitative) response Notation: - Feature vector X, - qualitative response Y, taking values in C
More informationNew anticoagulants: Monitoring or not Monitoring? Not Monitoring
The 2 nd World Congress on CONTROVERSIES IN HEMATOLOGY (COHEM) Barcelona, Spain September 6 8, 2012 New anticoagulants: Monitoring or not Monitoring? Not Monitoring Anna Falanga, MD Immunohematology and
More informationCHM333 LECTURE 13 14: 2/13 15/13 SPRING 2013 Professor Christine Hrycyna
INTRODUCTION TO ENZYMES Enzymes are usually proteins (some RNA) In general, names end with suffix ase Enzymes are catalysts increase the rate of a reaction not consumed by the reaction act repeatedly to
More information1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2
PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand
More informationProfit Forecast Model Using Monte Carlo Simulation in Excel
Profit Forecast Model Using Monte Carlo Simulation in Excel Petru BALOGH Pompiliu GOLEA Valentin INCEU Dimitrie Cantemir Christian University Abstract Profit forecast is very important for any company.
More informationBasic research methods. Basic research methods. Question: BRM.2. Question: BRM.1
BRM.1 The proportion of individuals with a particular disease who die from that condition is called... BRM.2 This study design examines factors that may contribute to a condition by comparing subjects
More informationA Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data
A Bootstrap Metropolis-Hastings Algorithm for Bayesian Analysis of Big Data Faming Liang University of Florida August 9, 2015 Abstract MCMC methods have proven to be a very powerful tool for analyzing
More informationGENOMIC SELECTION: THE FUTURE OF MARKER ASSISTED SELECTION AND ANIMAL BREEDING
GENOMIC SELECTION: THE FUTURE OF MARKER ASSISTED SELECTION AND ANIMAL BREEDING Theo Meuwissen Institute for Animal Science and Aquaculture, Box 5025, 1432 Ås, Norway, theo.meuwissen@ihf.nlh.no Summary
More informationTail-Dependence an Essential Factor for Correctly Measuring the Benefits of Diversification
Tail-Dependence an Essential Factor for Correctly Measuring the Benefits of Diversification Presented by Work done with Roland Bürgi and Roger Iles New Views on Extreme Events: Coupled Networks, Dragon
More informationEstimating Industry Multiples
Estimating Industry Multiples Malcolm Baker * Harvard University Richard S. Ruback Harvard University First Draft: May 1999 Rev. June 11, 1999 Abstract We analyze industry multiples for the S&P 500 in
More informationSENSITIVITY ANALYSIS AND INFERENCE. Lecture 12
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. Your use of this material constitutes acceptance of that license and the conditions of use of materials on this
More informationCALCULATIONS & STATISTICS
CALCULATIONS & STATISTICS CALCULATION OF SCORES Conversion of 1-5 scale to 0-100 scores When you look at your report, you will notice that the scores are reported on a 0-100 scale, even though respondents
More informationPharmacokinetics: Do we know what we are doing? Prof Dana Niehaus Department of Psychiatry University of Stellenbosch
Pharmacokinetics: Do we know what we are doing? Prof Dana Niehaus Department of Psychiatry University of Stellenbosch Content Pharmacokinetics (What the body does to the drug) Absorption Distribution Metabolism
More informationModel Calibration with Open Source Software: R and Friends. Dr. Heiko Frings Mathematical Risk Consulting
Model with Open Source Software: and Friends Dr. Heiko Frings Mathematical isk Consulting Bern, 01.09.2011 Agenda in a Friends Model with & Friends o o o Overview First instance: An Extreme Value Example
More informationP (B) In statistics, the Bayes theorem is often used in the following way: P (Data Unknown)P (Unknown) P (Data)
22S:101 Biostatistics: J. Huang 1 Bayes Theorem For two events A and B, if we know the conditional probability P (B A) and the probability P (A), then the Bayes theorem tells that we can compute the conditional
More informationBayesian Statistics in One Hour. Patrick Lam
Bayesian Statistics in One Hour Patrick Lam Outline Introduction Bayesian Models Applications Missing Data Hierarchical Models Outline Introduction Bayesian Models Applications Missing Data Hierarchical
More informationName Date Period. Keystone Review Enzymes
Name Date Period Keystone Review Enzymes 1. In order for cells to function properly, the enzymes that they contain must also function properly. What can be inferred using the above information? A. Cells
More informationTRINITY COLLEGE. Faculty of Engineering, Mathematics and Science. School of Computer Science & Statistics
UNIVERSITY OF DUBLIN TRINITY COLLEGE Faculty of Engineering, Mathematics and Science School of Computer Science & Statistics BA (Mod) Enter Course Title Trinity Term 2013 Junior/Senior Sophister ST7002
More informationCourse Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics
Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This
More informationBioavailability / Bioequivalence
Selection of CROs Selection of a Reference Product Metrics (AUC, C max /t max, Shape of Profile) Acceptance Ranges (0.80 1.25 and beyond) Sample Size Planning (Literature References, Pilot Studies) Steps
More informationDealing with large datasets
Dealing with large datasets (by throwing away most of the data) Alan Heavens Institute for Astronomy, University of Edinburgh with Ben Panter, Rob Tweedie, Mark Bastin, Will Hossack, Keith McKellar, Trevor
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationPHAR 7633 Chapter 21 Non-Linear Pharmacokinetic Models
Student Objectives for this Chapter PHAR 7633 Chapter 21 Non-Linear Pharmacokinetic Models To draw the scheme and write the differential equations for compartmental pharmacokinetic models with non-linear
More informationBiomedical Optics Theory
Introduction Biomedical Optics Theory Diffuse reflectance spectroscopy (DRS) and Laser Doppler Flowmetry (LDF) are booth optical techniques that can quantify a number of microcirculatory parameters. Prof
More informationChenfeng Xiong (corresponding), University of Maryland, College Park (cxiong@umd.edu)
Paper Author (s) Chenfeng Xiong (corresponding), University of Maryland, College Park (cxiong@umd.edu) Lei Zhang, University of Maryland, College Park (lei@umd.edu) Paper Title & Number Dynamic Travel
More informationMethods for Meta-analysis in Medical Research
Methods for Meta-analysis in Medical Research Alex J. Sutton University of Leicester, UK Keith R. Abrams University of Leicester, UK David R. Jones University of Leicester, UK Trevor A. Sheldon University
More informationOne-year reserve risk including a tail factor : closed formula and bootstrap approaches
One-year reserve risk including a tail factor : closed formula and bootstrap approaches Alexandre Boumezoued R&D Consultant Milliman Paris alexandre.boumezoued@milliman.com Yoboua Angoua Non-Life Consultant
More informationThe HB. How Bayesian methods have changed the face of marketing research. Summer 2004
The HB How Bayesian methods have changed the face of marketing research. 20 Summer 2004 Reprinted with permission from Marketing Research, Summer 2004, published by the American Marketing Association.
More informationEthyl Glucuronide. Where is the Drug? Detection Windows. Urine. Blood. Absorption and Distribution. Metabolism. Excretion
Where is the Drug? Ethyl Absorption and Distribution A Biomarker for Ethanol Use Metabolism Excretion Anthony G. Costantino, Ph.D. D-ABFT NMS Labs,Willow Grove, PA John J. Treuting, Ph.D. Treuting & Assoc.
More informationExperiment #1, Analyze Data using Excel, Calculator and Graphs.
Physics 182 - Fall 2014 - Experiment #1 1 Experiment #1, Analyze Data using Excel, Calculator and Graphs. 1 Purpose (5 Points, Including Title. Points apply to your lab report.) Before we start measuring
More informationDeterministic and Stochastic Modeling of Insulin Sensitivity
Deterministic and Stochastic Modeling of Insulin Sensitivity Master s Thesis in Engineering Mathematics and Computational Science ELÍN ÖSP VILHJÁLMSDÓTTIR Department of Mathematical Science Chalmers University
More informationGT-020 Phase 1 Clinical Trial: Results of Second Cohort
GT-020 Phase 1 Clinical Trial: Results of Second Cohort July 29, 2014 NASDAQ: GALT www.galectintherapeutics.com 2014 Galectin Therapeutics inc. Forward-Looking Statement This presentation contains, in
More informationSimple linear regression
Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between
More informationNonparametric statistics and model selection
Chapter 5 Nonparametric statistics and model selection In Chapter, we learned about the t-test and its variations. These were designed to compare sample means, and relied heavily on assumptions of normality.
More information