Statistical Analysis. NBAF-B Metabolomics Masterclass. Mark Viant

Transcription

1 Statistical Analysis NBAF-B Metabolomics Masterclass Mark Viant

2 1. Introduction 2. Univariate analysis Overview of lecture 3. Unsupervised multivariate analysis Principal components analysis (PCA) Interpreting scores and loadings plots Statistical tests on PCA scores data 4. Supervised multivariate analysis Partial least squares discriminant analysis (PLS-DA) Partial least squares regression (PLS-R) 5. Data standards, databases, and NBAF-B data analysis workflow

3 1. Introduction

4 peak 1 peak 2 peak 3 n bin 1 bin 2 bin 3 n Output from spectral processing (Jon & Ulf) sample 1 sample 2 sample 3 m X matrix of NMR signal intensities sample 1 sample 2 sample 3 X matrix of MS signal intensities m

5 peak 1 peak 2 peak 3 Output from spectral processing: X and Y matrices sample label X matrix of signal intensities EITHER Y matrix = treatment group labels = discrete variable OR Y matrix = separate non-metabolic measurement for each sample = continuous variable

6 2. Univariate statistical analysis

7 peak 1 peak 2 peak 3 Univariate statistical analysis sample label X matrix of signal intensities Y matrix = treatment group labels = discrete variable t-test or ANOVA t-test or ANOVA with false discovery rate (FDR) correction

8 But what p-value is significant? Yes, this is possible, but it must be done with caution! Typically if we conduct a single univariate statistical test then p<0.05 is considered a significant result. But this is associated with an error rate of 5% (1 in every 20 tests gives false result). Imagine we dataset contains 1000 metabolites; so we conduct 1000 univariate tests - if p<0.05 is significant, we will incorrectly say that 50 metabolites are significantly different when they are not Unacceptable error rate! Correction for multiple testing Adjustment for multiple testing False discovery rate (FDR) by Benjamini and Hochberg, Journal of the Royal Statistical Society, Series B 57: (1995). Controls the expected proportion of incorrectly rejected null hypotheses (type I errors)

9 Typical output for NBAF-B MS dataset

10 peak 1 peak 2 peak 3 Multivariate statistical analysis sample label X matrix of signal intensities Y matrix = treatment group labels = discrete variable Analyse data in its entirety --- unsupervised and supervised analyses

11 3. Unsupervised multivariate statistical analysis What is principal components analysis (PCA)? Scores plots and their interpretation Loadings plots and their interpretation Statistical tests on scores data

12 What is unsupervised multivariate statistics? Multivariate statistical analyses deals with large numbers of variables (e.g. metabolites) simultaneously Unsupervised means that the analysis algorithm has no knowledge of the identities of the samples; the algorithm looks at the innate variation in the dataset Many unsupervised methods; we focus on principal components analysis Widely used in omics analyses, including metabolomics, proteomics and transcriptomics

13 Multivariate data and PCA Common to find correlated variables in multivariate data redundancy in the information provided by these variables PCA exploits this redundancy enabling us to: - pick out patterns (relationships) in the variables - reduce the dimensionality of a data set without a significant loss of information PCA is a projection technique

14 Concept behind principal components analysis: Consider 50 different fish For each fish, measure length and breadth

15 breadth Principal components analysis - continued Plotting length vs. breadth shows clear relationship between these two variables Multivariate!!! Fish Length Breadth : : : : : : length

16 breadth Principal components analysis - continued Plotting length vs. breadth shows clear relationship between these two variables PC1 Create new axis (PC1) that accounts for the largest proportion of the data s variance PC1 = p1.length + p2.breadth length PC1 = principal component 1 For each data point, project the two original variables (length, breadth) onto the one new variable (PC1)

17 breadth Principal components analysis - continued Plotting length vs. breadth shows clear relationship between these two variables Simpler dataset!!! Fish PC1 PC : : length : : 50 6

18 Sample From dataset to variable space PCA step by step var. 3 (i) One sample in variable space var. 2 var. 1 The dataset (many samples) yields a swarm of points in "variable space"

19 var. 3 PCA step by step Mean centering move centre of swarm of points to the origin of variable space (0,0,0) var. 3 original mean (i) var. 2 new mean var. 2 var. 1 (i) var. 1

20 PCA step by step PC1 score var. 3 PC1 axis var. 2 (i) var. 1 The first principal component (PC1) is set to describe the largest variation in the data, which is the same as the direction in which the points spread most in the variable space. The Score value for point i is the distance from the projection of the point on the 1st component to the origin. PC1 is the first variable in a new coordinate system that describes the variation in the data.

21 PCA step by step var. 3 PC1 axis PC2 axis (i) var. 2 PC2 scores var. 1 The second principal component (PC2) is set to describe the largest variation in the data, perpendicular (orthogonal) to PC1. The Score value for point i is the distance from the projection of the point on the 2nd component to the origin.

22 GENDER DIFFERENCE PC2 axis PCA scores plot: Analysis of LC-MS metabolomics data 100 Female Night 50 Female Day 0-50 Male Night Male Day PC1 axis DIURNAL DIFFERENCE The relative distances among individual samples in the scores plot represent the similarities/differences between those samples

23 PCA scores plots of 1 H NMR spectra of foot muscle Metabolic changes??? PC1 loadings

24 Loadings on PC 1 PCA loadings plot 0.03 Peaks/metabolites with positive PC1 loadings are diseased abalone ELEVATED in diseased abalone healthy abalone Peaks/metabolites with negative PC1 loadings are ELEVATED in healthy abalone Variable number (e.g. metabolites) Identify which metabolites (or peaks) are responsible for the pattern of samples in the scores plot

25 Loadings on PC 1 PCA loadings plot 0.03 homarine (p<0.001) diseased abalone formate (p<0.001) healthy abalone ATP (p<0.001) tryptophan (p<0.001) tyrosine (p<0.001) Variable number (e.g. metabolites) Identify which metabolites (or peaks) are responsible for the pattern of samples in the scores plot

26 Typical output for NBAF-B MS dataset

27 Summary of PCA scores and loadings plots PCA scores plot shows relationship between samples shows major underlying unbiased structures in your data PCA loadings plot identifies which metabolites (or peaks) are responsible for the structures in the scores plot

28 Significance testing on PCA scores data (1) PC1 scores for healthy PC1 scores for diseased

29 Significance testing on PCA scores data (2) Sample PC1 score Healthy Healthy Healthy Healthy Healthy Healthy Diseased Diseased Diseased Diseased t-test on scores data (p<0.001 for abalone) Unsupervised analysis found significant separation of groups Diseased 5 7.3

30 Summary of Principal Components Analysis 1. PCA is a common unsupervised method for analysing metabolomics datasets. 2. Aim is to identify the metabolic similarities and differences between the samples. 3. Excellent initial approach for screening dataset, identifying outliers, and getting a feel of the structure of your data. 4. Can be used to determine which metabolites discriminate between different groups of samples (although not as powerful as supervised methods)

31 4. Supervised multivariate statistical analysis Partial least squares discriminant analysis (PLS-DA) Partial least squares regression (PLS-R)

32 What is supervised multivariate statistics? Supervised means that the analysis algorithm has prior knowledge of the identities (classification) or some other continuous property (regression) of the samples Used to build multivariate models that can predict identity of an unknown sample (classification) or predict continuous variable of that unknown sample (regression) Powerful tool for discovering biomarkers Many supervised methods exist; we focus on partial least squares (PLS) based methods Widely used in metabolomics

33 peak 1 peak 2 peak 3 Partial least squares discriminant analysis (PLS-DA) sample label X matrix of signal intensities Y matrix = treatment group labels PLS-DA seeks to discriminate different groups of samples (classification), and to discover the relevant biomarkers

34 Example of PLS-DA Miniature Schnauzer (MS) dogs Labrador dogs known Labrador dogs Predict dog breed from urine known MS dogs

35 What are urinary metabolic differences between two dog breeds? Determined using partial least squares discriminant analysis (PLS-DA)

36 peak 1 peak 2 peak 3 Partial least squares regression (PLS-R) sample label X matrix of signal intensities Y matrix = separate non-metabolic measurement for each sample = continuous variable PLS-R seeks to discover relevant biomarkers that can predict the continuous variable (regression)

37 Total no. of neonates produced per daphnid Example dataset for PLS-R (continuous variable = neonate production) 38 individual adult daphnids (in 5 treatment groups)

38 Example of PLS-R (continuous variable = neonate production) r 2 (CV) = Optimal PLS model: 107 peaks in mass spectra (out of ca total)

39 5. Data standards, databases, and NBAF-B data analysis workflow

40 Data standards in omics science Transcriptomics MIAME: Minimum information about a microarray experiment MAGE: Microarray gene expression - data exchange format Proteomics PSI-OM: Proteomics standards initiative - object model Metabolomics

41 Transcriptomics Databases in omics science Proteomics Metabolomics? - no publically available databases to store metabolomics measurements (yet)

42 Median Relative Standard Deviation for QC No. of peaks RSD from 3 analytical reps (%) Median RSD is a simple measure of reproducibility

43 Typical NBAF-B data analysis workflow NMR or MS spectral processing Initial PCA of dataset with QC samples is data of high technical quality? Initial PCA of dataset without QC samples are there biological outliers? Further multivariate statistics (PLS-DA or PLS-R, depending on biological question) Univariate statistics on NMR or MS data (with FDR) Metabolite identification using software tools (MI-Pack, Chenomx, etc.) Metabolite identification via further MS and/or NMR experiments