Unravelling `omics' data with the mixomics R package

Transcription

1 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Unravelling `omics' data with the R package Illustration on several studies Queensland Facility for Advanced Bioinformatics The University of Queensland

2 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Challenges The issue with integrative systems biology Unlimited quantity of data (n << p problem) Data from multiple sources Ecient and biologically relevant statistical methodologies are needed to combine the information in these heterogeneous data sets.

3 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio The biological questions Single Omics analysis Do we observe a `natural' separation between the dierent groups of patients? Can we identify potential biomarker candidates predicting the status of the patients? Integrative Omics analysis Can we identify a subset of correlated genes and proteins from matching data sets? Can we predict the abundance of a protein given the expression of a small subset of genes? Do two matching omics data set contain the same information?

4 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio The data The data n = number of patients p, q = number of biological features (genes, proteins..) Single Omics analysis one omic data set X(n x p) for a supervised analysis, Y vector indicating the class of the patients Integrative Omics analysis two matching omics data sets (measured on the same patients) X (n x p) and Z (n x q)

5 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Multivariate analysis Linear multivariate approaches enable: Dimension reduction project the data in a smaller subspace To handle multicollinear, irrelevant, missing variables To capture experimental annd biological variation In particular, in, focus is on: Data integration Variable selection Computationally ecient methodologies for large biological data sets Interpretable graphical outputs

6 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio is an R package dedicated to the exploration and the integrative analyses of high dimensional biological data sets. Website - R tutorials - Newsletter Web Interface - User friendly interface - Comprehensive results page -Lê Cao et al. (2009) integromics/: an R package to unravel relationships between two omics data sets, Bioinformatics

7 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Data Multivariate approach Internal variable selection Graphical outputs PCA IPCA spca sipca Sample plots One data set (n x p) PLS-DA spls-da Two matching data sets (n x p) & (n x q) PLS rcca PLS spls canonical spls regression Variable plots Missing values (n x p) imputation NIPALS

8 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Introduction with PCA Principal Component Analysis: PCA Seek the best directions in the data that account for most of the variability principal components: articial variables that are linear combinations of the original variables: c = X v (n) (nxp) (p) c is a linear function of the elements of X having maximal variance v is called the associated loading vector x2 x1

9 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Introduction with PCA Principal components cont. The new PCs form a vectorial subspace of dimension < p Project the data on these new axes. z z1 approximate representation of the data points in a lower dimensional space Problem: Interpretation dicult with very large number of (possibly) irrelevant variables

10 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Introduction with PCA sparse Principal Component Analysis: spca loading vectors sparse loading vectors Principal components (PCA) (spca) x x1 loading 1 loading loading 1 loading The principal components are linear combinations of the original variables, variables weights are dened in the associated loading vectors. sparse PCA computes the sparse loading vectors to remove irrelevant variables using lasso penalizations (Shen & Huang 2008, J. Multivariate Analysis).

11 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Independent Principal Component Analysis IPCA is based on Independent Component Analysis (ICA): assumes non Gaussian data distribution ( PCA). `blind source' signal separation. seeks for a set of independent components ( PCA). Combines the advantages of both PCA and ICA. The PCA loadings are transformed via ICA to obtain independent loading vectors and independent principal components. sparse IPCA also developed to select the variable contributing to the independent loading vectors Yao, F. Coquery, J. and Lê Cao, K-A Independent Principal Component Analysis for biologically meaningful dimension reduction of large biological data sets, BMC Bioinformatics.

12 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Independent Principal Component Analysis Illustration of PCA and IPCA Sample representation for the kidney transplant study (3 groups of rejection status patients)

13 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Discriminant Analysis PLS - Discriminant Analysis Similarly to Linear Discriminant Analysis, classical PLS-DA looks for the best components to separate the sample groups. As opposed to PCA/IPCA methods, it is a supervised approach. In addition to this, spls-da searches for discriminative variables that can help separating the sample groups. Evaluation of the discriminative power of the selected variables using external data sets or cross-validation. Lê Cao K-A., Boitard S. and Besse P. (2011) Sparse PLS Discriminant Analysis: biologically relevant feature selection and graphical displays for multiclass problems, BMC Bioinformatics, 12:253.

14 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Discriminant Analysis Illustration of spls-da Genomics training data Genomics error rate comp 1 comp 1:2 comp 1:3 Comp Train AR NR Test AR NR number of selected genes Comp 1 Figure: Tuning the number of var. to select with cross-validation Figure: Predicting the class of the test set samples

15 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Motivation Aims: unravel the correlation stucture between two data sets select co-regulated biological entities across samples select and integrate in a one step procedure the dierent types of data Partial Least Squares regression maximises the covariance between each linear combination (components) associated to each data set sparse PLS has been developed to include variable selection from both data sets Two modes are proposed to model the relationship between the two data sets ('regression' and 'canonical') Lê Cao et al. (2008), SAGMB, Lê Cao et al. (2009), BMC Bioinformatics

16 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Integrating genomics and proteomics Illustration of sparse PLS: sample plot spls aims at selecting correlated variables (genes, proteins) across the same samples by performing a multivariate regression. Regression: explain the protein abundance w.r.t the gene expression relationship. The latent variables (components) are determined based on the selected genes and proteins give more insight into the samples similarities. Unsupervised approach

17 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Probe set Protein group Dimension 1 Integrating genomics and proteomics Illustration of sparsepls: variable plot Relevance networks are bipartite graphs directly inferred from the spls components. Some other insightful graphical outputs: correlation circle plots clustered image maps Dimension González I., Lê Cao K.-A., Davis, M.D. and Déjean S. Visualising association between paired `omics' data sets. In revision.

18 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio H460 Comparing two proteomics platforms Illustration of spls canonical mode Selects correlated variables across the same samples and highlights the correlation structure between the two data sets. Canonical mode: relationship LEU RE BR COL LEU COL NS BR LEU LEU CNS COL OVNSRE COL COL BR OV BR RE REOV NS NS CNS OVPR RE BR NS MEL OV COL LEU RE COL RE CNS PR NS NS CNS RE NS OV CNS LEU MEL MEL MEL MEL MEL BR MEL BR MEL BR CNS COL LE MEL NS OV PR RE Figure: Arrow plot to highlight the similarties between 2 data sets

19 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Multilevel analysis Cross-over design Data Multivariate approach Internal variable selection Graphical outputs Sample plots One data set repeated measurements (n x p) supervised multilevel PLS-DA multilevel spls-da Two matching data sets repetated measurements (n x p) & (n x q) canonical, 1 level multilevel PLS multilevel spls Variable plots A novel approach for cross-over designs (repeated measurements up to 2 cross factors)

20 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Multilevel analysis Illustration of multilevel spls-da X variate 1 X variate 2 GAG+ GAG LIPO5 NS t1 t2 gene517 gene541 gene589 gene550 gene567 gene551 gene579 gene506 gene540 gene557 gene527 gene534 gene509 gene564 gene528 gene518 gene553 gene531 gene502 gene537 gene546 gene504 gene524 gene591 gene519 gene583 gene585 gene503 gene521 gene520 gene582 gene552 gene568 gene549 gene576 gene563 gene539 gene555 gene588 gene571 gene529 gene525 gene511 gene587 gene515 gene584 gene526 gene570 gene594 gene505 gene574 gene535 gene566 gene510 gene580 gene577 gene538 gene554 gene569 gene572 gene530 gene599 gene507 gene575 gene560 gene542 gene501 gene543 gene597 gene513 gene547 gene562 gene595 gene598 gene516 gene561 gene578 gene508 gene558 gene593 gene536 gene556 gene532 gene559 gene573 gene512 gene592 gene533 gene586 gene565 gene522 gene514 gene600 gene523 gene544 gene548 gene581 gene590 gene545 gene596 gene19 gene82 gene85 gene27 gene92 gene13 gene99 gene38 gene81 gene88 gene4 gene9 gene28 gene98 gene37 gene75 gene76 gene45 gene83 gene32 gene55 gene78 gene39 gene51 gene20 gene71 gene30 gene96 gene63 gene14 gene18 gene53 gene73 gene87 gene2 gene91 gene25 gene69 gene23 gene48 gene43 gene56 gene22 gene47 gene59 gene84 gene15 gene65 gene1 gene3 gene34 gene58 gene80 gene86 gene24 gene36 gene49 gene90 gene7 gene44 gene67 gene12 gene29 gene95 gene17 gene50 gene66 gene26 gene64 gene31 gene21 gene61 gene5 gene11 gene40 gene89 gene97 gene74 gene77 gene94 gene100 gene54 gene35 gene33 gene62 gene46 gene93 gene10 gene52 gene79 gene8 gene57 gene16 gene72 gene6 gene60 gene68 gene70 gene41 gene42 gene613 gene674 gene673 gene694 gene603 gene692 gene671 gene655 gene606 gene647 gene621 gene622 gene654 gene637 gene662 gene699 gene635 gene663 gene665 gene653 gene664 gene628 gene641 gene678 gene632 gene634 gene642 gene630 gene616 gene681 gene614 gene685 gene652 gene688 gene644 gene689 gene672 gene700 gene617 gene677 gene650 gene633 gene640 gene625 gene631 gene626 gene660 gene612 gene636 gene675 gene618 gene624 gene697 gene698 gene646 gene676 gene607 gene683 gene696 gene619 gene656 gene645 gene651 gene684 gene680 gene623 gene668 gene610 gene679 gene643 gene670 gene611 gene686 gene608 gene602 gene609 gene620 gene639 gene695 gene629 gene666 gene627 gene605 gene649 gene669 gene657 gene604 gene661 gene658 gene691 gene667 gene601 gene659 gene638 gene648 gene682 gene687 gene693 gene615 gene690 gene160 gene104 gene200 gene149 gene190 gene138 gene151 gene165 gene132 gene199 gene120 gene121 gene179 gene194 gene177 gene129 gene123 gene131 gene148 gene158 gene171 gene146 gene192 gene106 gene124 gene168 gene170 gene188 gene162 gene108 gene118 gene155 gene173 gene134 gene139 gene143 gene150 gene175 gene145 gene195 gene122 gene166 gene140 gene182 gene187 gene102 gene128 gene110 gene147 gene159 gene164 gene191 gene105 gene136 gene111 gene107 gene135 gene176 gene153 gene193 gene183 gene184 gene125 gene197 gene185 gene117 gene161 gene172 gene101 gene180 gene144 gene126 gene156 gene154 gene109 gene167 gene137 gene169 gene133 gene186 gene103 gene174 gene115 gene141 gene130 gene127 gene198 gene119 gene142 gene112 gene181 gene152 gene157 gene163 gene196 gene114 gene116 gene189 gene113 gene178 gene837 gene865 gene812 gene870 gene817 gene883 gene805 gene856 gene839 gene841 gene871 gene885 gene802 gene873 gene808 gene843 gene851 gene823 gene828 gene831 gene818 gene878 gene844 gene891 gene824 gene860 gene880 gene807 gene884 gene835 gene834 gene832 gene866 gene874 gene894 gene801 gene819 gene869 gene889 gene857 gene863 gene809 gene872 gene877 gene836 gene826 gene876 gene850 gene868 gene806 gene820 gene867 gene887 gene811 gene845 gene859 gene846 gene848 gene886 gene840 gene861 gene879 gene897 gene888 gene892 gene825 gene890 gene862 gene875 gene833 gene881 gene816 gene827 gene895 gene830 gene858 gene810 gene852 gene900 gene803 gene849 gene340 gene381 gene392 gene309 gene308 gene350 gene346 gene366 gene321 gene373 gene303 gene329 gene304 gene400 gene313 gene367 gene377 gene398 gene368 gene355 gene384 gene347 gene333 gene361 gene375 gene383 gene317 gene343 gene386 gene306 gene319 gene348 gene318 gene349 gene387 gene332 gene327 gene363 gene372 gene396 gene335 gene388 gene359 gene378 gene399 gene311 gene324 gene315 gene334 gene330 gene364 gene357 gene314 gene316 gene345 gene322 gene337 gene344 gene360 gene353 gene312 gene385 gene325 gene382 gene389 gene354 gene379 gene352 gene393 gene358 gene331 gene391 gene380 gene390 gene336 gene310 gene365 gene339 gene376 gene301 gene371 gene320 gene362 gene394 gene338 gene307 gene374 gene326 gene305 gene328 gene323 gene351 gene302 gene370 gene397 gene342 gene395 gene341 gene356 Sample Stimulation GAG+ GAG LIPO5 NS

21 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Conclusions Conclusions The exploratory and integrative approaches are: exible and can answer various types of questions. can highlight the potential of the data. enable to generate new hypotheses to be further investigated. Future work includes: Cross-platform comparison Integration of multiple data sets (unsupervised and supervised) Time-course experiments

22 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Conclusions Acknowledgements Sébastien Déjean Ignacio González Xin Yi Chua team Univ. Tlse Univ. Tlse QFAB Je Coquery Benoit Liquet Eric Fangzhou Yao Pierre Monget Other contributors to QFAB, Sup'Biotech Univ. Bordeaux QFAB, Shanghai Univ of Finance and Economics QFAB, CESI

23 Introduction Concept of Single Omics Analysis Integrative Omics Analysis Recent developments Conclusio Questions? Questions?