Dmitry Grapov, PhD

Multivariate Analysis and Visualization of ProteOmic Data

State of the art facility producing massive amounts of biological data…

>20-30K samples/yr>200 studies

Analysis at the ProteOmic Scale and Beyond

Genomic

Proteomic

MetabolomicMulti-OmicOmic

integration

Sam

ple

Variable

Data Analysis and Visualization

Quality Assessment• use replicated mesurements

and/or internal standards to estimate analytical variance

Statistical and Multivariate• use the experimental design

to test hypotheses and/or identify trends in analytes

Functional• use statistical and multivariate

results to identify impacted biochemical domains

Network• integrate statistical and

multivariate results with the experimental design and analyte metadata

experimental design

- organism, sex, age etc.

analyte description and metadata

- biochemical class, mass spectra, etc.

VariableSample

Sam

ple

Variable

Data Analysis and Visualization

Quality Assessment• use replicated mesurements

and/or internal standards to estimate analytical variance

Statistical and Multivariate• use the experimental design

to test hypotheses and/or identify trends in analytes

Functional• use statistical and multivariate

results to identify impacted biochemical domains

Network• integrate statistical and

multivariate results with the experimental design and analyte metadata

Network Mapping

experimental design

- organism, sex, age etc.

analyte description and metadata

- biochemical class, mass spectra, etc.

VariableSample

Data Quality AssessmentQuality metrics•Precision (replicated measurements)

•Accuracy (reference samples)

Common tasks•normalization •outlier detection •missing values imputation

Principal Component Analysis (PCA) of all analytes, showing QC sample scores

Batch EffectsDrift in >400 replicated measurements across >100 analytical batches for a single analyte

Acquisition batch

Abun

danc

e QCs embedded among >5,5000 samples (1:10) collected over 1.5 yrs

If the biological effect size is less than the analytical variance

then the experiment will incorrectly yield insignificant results

Analyte specific data quality overview

Sample specific normalization can be used to estimate and remove analytical variance

Raw Data Normalized Data

Normalizations need to be numerically and visually validated

log mean

low precision

%RS

D

high precision

SamplesQCs

Batch Effects

Outlier Detection

• 1 variable (univariate)

• 2 variables (bivariate)

• >2 variables (multivariate)

bivariate vs.

multivariate

mixed up samplesoutliers?

(scatter plot)

(PCA scores plot)

Outlier Detection

Network Mapping

Ranked statistically significant differences within a a biochemical

context

Statistics

Multivariate

Context

++=

Statistical and Multivariate AnalysesGroup 1

Group 2

What analytes are different between the

two groups of samples?

Statistical

significant differences lacking rank and

context

t-Test

Multivariate

ranked differences lacking significance

and context

O-PLS-DA

Network Mapping

Statistics

Multivariate

Context

++=

Statistical and Multivariate AnalysesGroup 1

Group 2

What analytes are different between the

two groups of samples?

Statistical

t-Test

Multivariate

O-PLS-DA

To see the big picture it is necessary too view the data from multiple different angles

Statistical Analysis: achieving ‘significance’

significance level (α) and power (1-β )

effect size (standardized difference in means)

sample size (n) Power analyses can be used to optimize future experiments given preliminary data

Example: use experimentally derived (or literature estimated) effect sizes, desired p-value (alpha) and power (beta) to calculate the optimal number of samples per group

Statistical Tests

• Should be chosen based on the distribution (shape, type) of the (e.g. normal, negative binomial, Poisson)

• Can be optimized based on data pre-treatment (e.g. NSAF, Power Law Global Error Model, PLGEM)

Poisson normal

False Discovery Rate (FDR)

Type I Error: False Positives (α)

•Type II Error: False Negatives (β)

•Type I risk =

•1-(1-p.value)m

m = number of variables tested

False Discovery Rate AdjustmentFD

R ad

just

ed p

-val

ue

p-value

Benjamini & Hochberg (1995) (“BH”)•Accepted standard

Bonferroni•Very conservative•adjusted p-value = p-value x # of tests (e.g. 0.005 x 148 = 0.74 )

Functional Analysis

Nucl. Acids Res. (2008) 36 (suppl 2): W423-W426.doi: 10.1093/nar/gkn282

Identify changes or enrichment in biochemical domains

• decrease• increase

Functional Analysis: Enrichment

Biochemical Pathway Biochemical Ontology

Common Multivariate Methods

Clustering

Projection

Networks

Artist: Chuck Close

Cluster AnalysisUseful for

•pattern recognition

•complexity reduction

Common Methods

•Hierarchical

•Model based

•Other (k-means, k-NN, PAM, fuzzy)

Linkage k-means

Distribution Density

Hierarchical Clustering

Sim

ilarit

y

x

xx

x

Dendrogram

How does my metadata match my data structure?

Projection Methods

The algorithm defines the position of the light sourcePrincipal Components Analysis (PCA)

• unsupervised• maximize variance (X)

Partial Least Squares Projection to Latent Structures (PLS)

• supervised• maximize covariance (Y ~ X)

James X. Li, 2009, VisuMap Tech.

single analyte all analytes

Interpreting scores and loadings

variables with the highest loadings have the greatest contribution to sample scores

loadings represent how variables contribute to sample scores

loadings

Scores represent dis/similarities in samples

based on all variables

scores

Networks

Biochemical•interaction• enrichment•etc

Empirical (dependency)•correlation•partial-correlation•clustering

variable 2

variable 1

variable 3

Enrichment NetworkMapping of parents through children

Interaction Networks

Empirical Networks

• Correlation based networks (CN) (simple, tendency to hairball)

• GGM or partial correlation based networks (advanced, preference of direct over indirect relationships

• *Increase in robustness with sample size

10.1007/978-1-4614-1689-0_17

Proteomic Case Study: Diabetes Markers• Small sample size (control =12, GDM =6); covariates (time of sample collection)• >600 measured colostrum proteins; ~ 300 NSAF normalized proteins retained • Multivariate classification with O-PLS-DA used to identify variables to test using

PLGEM with correction for FDR• Partial-correlation protein-protein interaction network analysis

DeviumWebhttps://github.com/dgrapov/DeviumWeb

• visualization• statistics• clustering • PCA• O-PLS

DeviumWeb

• visualization• statistics• clustering • PCA• O-PLS

https://github.com/dgrapov/DeviumWeb

Software and Resources•DeviumWeb- Dynamic multivariate data analysis and visualization platformurl: https://github.com/dgrapov/DeviumWeb

•imDEV- Microsoft Excel add-in for multivariate analysisurl: http://sourceforge.net/projects/imdev/

•MetaMapR- Network analysis tools for metabolomicsurl: https://github.com/dgrapov/MetaMapR

•TeachingDemos- Tutorials and demonstrations•url: http://sourceforge.net/projects/teachingdemos/?source=directory•url: https://github.com/dgrapov/TeachingDemos

•Data analysis case studies and Examplesurl: http://imdevsoftware.wordpress.com/

Questions?

dgrapov@ucdavis.edu

This research was supported in part by NIH 1 U24 DK097154