ASCA: analysis of multivariate data from an experimental design, Biosystems Data Analysis group Universiteit van Amsterdam.

Slides:

Advertisements

Similar presentations

Institute on Research and Statistics, Sacramento 04/08/04

Advertisements

Step three: statistical analyses to test biological hypotheses General protocol continued.

PCA for analysis of complex multivariate data. Interpretation of large data tables by PCA In industry, research and finance the amount of data is often.

Regression analysis Relating two data matrices/tables to each other Purpose: prediction and interpretation Y-data X-data.

Regression Bivariate Multivariate. Simple Regression line – line of best fit Ŷ = a + bX The mean point is always on the line Y is the criterion variable.

i) Two way ANOVA without replication

The General Linear Model Or, What the Hell’s Going on During Estimation?

Linear Regression and Binary Variables The independent variable does not necessarily need to be continuous. If the independent variable is binary (e.g.,

Chapter 17 Making Sense of Advanced Statistical Procedures in Research Articles.

Lecture 7: Principal component analysis (PCA)

Principal Components Analysis Babak Rasolzadeh Tuesday, 5th December 2006.

An introduction to Principal Component Analysis (PCA)

LINEAR REGRESSION: Evaluating Regression Models. Overview Standard Error of the Estimate Goodness of Fit Coefficient of Determination Regression Coefficients.

LISA Short Course Series Multivariate Analysis in R Liang (Sally) Shan March 3, 2015 LISA: Multivariate Analysis in RMar. 3, 2015.

© 2005 The McGraw-Hill Companies, Inc., All Rights Reserved. Chapter 14 Using Multivariate Design and Analysis.

CALIBRATION Prof.Dr.Cevdet Demir

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

Experimental Design Terminology  An Experimental Unit is the entity on which measurement or an observation is made. For example, subjects are experimental.

PATTERN RECOGNITION : PRINCIPAL COMPONENTS ANALYSIS Prof.Dr.Cevdet Demir

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

Analysis of Variance & Multivariate Analysis of Variance

Analysis of Covariance The function of Experimental design is to explain the effect of a IV or DV while controlling for the confounding effect of extraneous.

Structural Equation Modeling Intro to SEM Psy 524 Ainsworth.

Principal Component Analysis. Philosophy of PCA Introduced by Pearson (1901) and Hotelling (1933) to describe the variation in a set of multivariate data.

Advantages of Multivariate Analysis Close resemblance to how the researcher thinks. Close resemblance to how the researcher thinks. Easy visualisation.

Fundamentals of Data Analysis Lecture 7 ANOVA. Program for today F Analysis of variance; F One factor design; F Many factors design; F Latin square scheme.

Analysis of Covariance David Markham

 Combines linear regression and ANOVA  Can be used to compare g treatments, after controlling for quantitative factor believed to be related to response.

Canonical Correlation Analysis and Related Techniques Simon Mason International Research Institute for Climate Prediction The Earth Institute of Columbia.

INTRODUCTION TO ANALYSIS OF VARIANCE (ANOVA). COURSE CONTENT WHAT IS ANOVA DIFFERENT TYPES OF ANOVA ANOVA THEORY WORKED EXAMPLE IN EXCEL –GENERATING THE.

Metabolomics Metabolome Reflects the State of the Cell, Organ or Organism Change in the metabolome is a direct consequence of protein activity changes.

1 Statistical Analysis Professor Lynne Stokes Department of Statistical Science Lecture 8 Analysis of Variance.

CHAPTER 4 Analysis of Variance One-way ANOVA

Math 5364/66 Notes Principal Components and Factor Analysis in SAS Jesse Crawford Department of Mathematics Tarleton State University.

Principal Components Analysis. Principal Components Analysis (PCA) A multivariate technique with the central aim of reducing the dimensionality of a multivariate.

CPE 619 One Factor Experiments Aleksandar Milenković The LaCASA Laboratory Electrical and Computer Engineering Department The University of Alabama in.

Innovative Paths to Better Medicines Design Considerations in Molecular Biomarker Discovery Studies Doris Damian and Robert McBurney June 6, 2007.

Module III Multivariate Analysis Techniques- Framework, Factor Analysis, Cluster Analysis and Conjoint Analysis Research Report.

PATTERN RECOGNITION : PRINCIPAL COMPONENTS ANALYSIS Richard Brereton

Regression Analysis. 1. To comprehend the nature of correlation analysis. 2. To understand bivariate regression analysis. 3. To become aware of the coefficient.

Principal Component Analysis (PCA)

Principal Component Analysis Zelin Jia Shengbin Lin 10/20/2015.

1 Statistical Analysis Professor Lynne Stokes Department of Statistical Science Lecture 9 Review.

Advanced Statistics Factor Analysis, I. Introduction Factor analysis is a statistical technique about the relation between: (a)observed variables (X i.

Finding Answers. Steps of Sci Method 1.Purpose 2.Hypothesis 3.Experiment 4.Results 5.Conclusion.

Applying MetaboAnalyst

Université d’Ottawa / University of Ottawa 2001 Bio 8100s Applied Multivariate Biostatistics L11.1 Lecture 11: Canonical correlation analysis (CANCOR)

Multivariate statistical methods. Multivariate methods multivariate dataset – group of n objects, m variables (as a rule n>m, if possible). confirmation.

Chapter 14 EXPLORATORY FACTOR ANALYSIS. Exploratory Factor Analysis  Statistical technique for dealing with multiple variables  Many variables are reduced.

Strategies for Metabolomic Data Analysis Dmitry Grapov, PhD.

Advanced Strategies for Metabolomic Data Analysis Dmitry Grapov, PhD.

Univariate Statistics PSYC*6060 Class 11 Peter Hausdorf University of Guelph.

Principal Component Analysis

Metabolomics Research & Consultancy CJ Alexander, CA Hackett & JW McNicol With collaborations below as indicated from: 1The James Hutton Institute, UK.

Projection on Latent Variables

i) Two way ANOVA without replication

Principal Component Analysis (PCA)

Measuring latent variables

LEARNING OUTCOMES After studying this chapter, you should be able to

Chapter 13 Group Differences

Principal Components Analysis

PCA of Waimea Wave Climate

Solving Equations 3x+7 –7 13 –7 =.

Principal Component Analysis

Lecture 8: Factor analysis (FA)

Factor Analysis.

Measuring latent variables

One-way Analysis of Variance

Structural Equation Modeling

Presentation transcript:

ASCA: analysis of multivariate data from an experimental design, Biosystems Data Analysis group Universiteit van Amsterdam

Contents ANOVA SCA ASCA Conclusions

ANOVA different design factors contribute to the variation For two treatments A and B the total sum of squares can be split into several contributions

Example Experiment: Time: 6, 24 and 48 hours Experimental Design: Rats are given Bromobenzene that affects the liver Groups: 3 doses of BB Animals: 3 rats per dose per time point Vehicle group, Control group Rat 1 11 Rat 2 11 Rat 3 11 Rat 1 12 Rat 2 12 Rat 3 12 Rat 1 13 Rat 2 13 Rat 3 13 Rats 6 hours 24 hours 48 hours chemical shift (ppm) Measurements: NMR spectroscopy of urine

NMR Spectroscopy -Each type of H-atom has a specific Chemical shift -The peak height is number of H-atoms at this chemical shift = metabolite concentration -NMR measures ‘concentrations’ of different types of H- atoms

Different contributions time Time Animal time Dose time Trajectories Experimental Design

The Method I: ANOVA Constraints: time time time Data Individualihih Dose grouph Timek MeaningSymbol Estimates of these factors:

The Method II ANOVA is a Univariate technique x X Structured !

Multivariate Data NMR Spectroscopy Covariance between the variables ppm 6.01 ppm Or: Relationship between the columns of X X

The Method III: Principal Component Analysis 3D  2D … Imagine! 350D  2D !!! x x x 3 X Loading PC 1 Loading PC 2 loadingsscores residuals PC 1 PC 2 Scores

The Method IV: ANOVA and PCA  ASCA Column spaces are Orthogonal E Parts of the data not explained by the component models

In Words: ASCA models the different contributions to the variation in the data ASCA takes the covariance between the variables into account ASCA gives a solution for the problem at hand.

Results I 40 % Time (Hours) Scores control vehicle low medium high

Results II Quantitative effect! No effect of vehicle Scores are in agreement with visual inspection Time (Hours) Scores control vehicle low medium high

Results III  biomarkers chemical shift (ppm) Differences between submodels Interesting for Biology Interesting for Diagnostics Unique to the α submodel

Conclusions Metabolomics (and other –omics) techniques give multivariate datasets with an underlying experimental design For this type of data, ASCA can be used The results observed for this experiment are in accordance with clinical observations The metabolites that are responsible for this variation can be found using ASCA  BIOMARKERS

Discussion 1.How can I perform statistics on the ASCA model? (e.g. Significance testing) 2.Are there other constraints possible for this model? (e.g. stochastic independence) 3.Are there alternative methods for solving this problem?