Introductory lecture to multivariate analysis of proteomic data. Material from the UC Davis 2014 Proteomics Workshop. See more at: http://sourceforge.net/projects/teachingdemos/files/2014%20UC%20Davis%20Proteomics%20Workshop/

1. Dmitry Grapov, PhD
Multivariate Analysis and
Visualization of ProteOmic Data

2. State of the art facility producing massive
amounts of biological data…
>20-30K samples/yr
>200 studies

3. Analysis at the ProteOmic Scale and Beyond
Genomic
Proteomic
Metabolomic
Multi-OmicOmic
integration

4. Sample
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

5. Sample
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

6. Data Quality Assessment
Quality metrics
•Precision (replicated
measurements)
•Accuracy (reference
samples)
Common tasks
•normalization
•outlier detection
•missing values
imputation

7. Principal Component
Analysis (PCA) of all
analytes, showing QC
sample scores
Batch Effects
Drift in >400 replicated measurements across >100 analytical batches for a single analyte
Acquisition batch
Abundance
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

8. 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
%RSD
high precision
Samples
QCs
Batch Effects

9. Outlier Detection
• 1 variable
(univariate)
• 2 variables
(bivariate)
• >2 variables
(multivariate)

10. bivariate vs.
multivariate
mixed up samples
outliers?
(scatter plot)
(PCA scores plot)
Outlier Detection

11. Network Mapping
Ranked statistically
significant differences
within a a biochemical
context
Statistics
Multivariate
Context
+
+
=
Statistical and Multivariate Analyses
Group 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

12. Network Mapping
Statistics
Multivariate
Context
+
+
=
Statistical and Multivariate Analyses
Group 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

13. 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

14. 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

15. 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

16. False Discovery Rate Adjustment
FDRadjustedp-value
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 )

17. 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

18. Functional Analysis: Enrichment
Biochemical Pathway Biochemical Ontology

19. Common Multivariate Methods
Clustering
Projection
Networks

20. Artist: Chuck Close
Cluster Analysis
Useful for
•pattern recognition
•complexity reduction
Common Methods
•Hierarchical
•Model based
•Other (k-means, k-NN, PAM,
fuzzy)
Linkage k-means
Distribution Density

21. Hierarchical Clustering
Similarity
x
x
x
x
Dendrogram
How does my metadata
match my data structure?

22. Projection Methods
The algorithm defines the position of the light source
Principal 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

23. 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

24. Networks
Biochemical
•interaction
• enrichment
•etc
Empirical (dependency)
•correlation
•partial-correlation
•clustering
variable 2
variable 1
variable 3

25. Enrichment Network
Mapping of parents through children

26. Interaction Networks

27. 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

28. 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

29. DeviumWeb
https://github.com/dgrapov/DeviumWeb
• visualization
• statistics
• clustering
• PCA
• O-PLS

30. DeviumWeb
• visualization
• statistics
• clustering
• PCA
• O-PLS
https://github.com/dgrapov/DeviumWeb

31. Software and Resources
•DeviumWeb- Dynamic multivariate data analysis and
visualization platform
url: https://github.com/dgrapov/DeviumWeb
•imDEV- Microsoft Excel add-in for multivariate analysis
url: http://sourceforge.net/projects/imdev/
•MetaMapR- Network analysis tools for metabolomics
url: 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 Examples
url: http://imdevsoftware.wordpress.com/

32. Questions?
dgrapov@ucdavis.edu
This research was supported in part by NIH 1 U24 DK097154