1 High Throughput Target Identification Stan Young, NISS Doug Hawkins, U Minnesota Christophe Lambert, Golden Helix Machine Learning, Statistics, and Discovery 25 June 03

2 Micro Array Literature

3 Guilt by Association : You are known by the company you keep.

4 Data Matrix Goal: Associations over the genes. Guilty Gene Genes Tissues

5 Goals 1.Associations. 2.Deep associations – beyond 1 st level correlations. 3. Uncover multiple mechanisms.

6 Problems 1.n < < p 2.Strong correlations. 3.Missing values. 4.Non-normal distributions. 5.Outliers. 6.Multiple testing.

7 Technical Approach 1.Recursive partitioning. 2.Resampling-based, adjusted p-values. 3.Multiple trees.

8 Recursive Partitioning Tasks 1.Create classes. 2.How to split. 3.How to stop.

9 Differences: Recursive Partitioning Top-down analysis Can use any type of descriptor. Uses biological activities to determine which features matter. Produces a classification tree for interpretation and prediction. Big N is not a problem! Missing values are ok. Multiple trees, big p is ok. Clustering Often bottom-up Uses “gestalt” matching. Requires an external method for determining the right feature set. Difficult to interpret or use for prediction. Big N is a severe problem!!

10 Forming Classes, Categories, Groups Profession Av. Income Baseball Players 1.5M Football Players 1.2M Doctors.8M Dentists.5M Lawyers.23M Professors.09M.....

11 Forming Classes from “Continuous” Descriptor How many “cuts” and where to make them?

12 Splitting : t-test n = 1650 ave = 0.34 sd = 0.81 n = 1614 ave = 0.29 sd = 0.73 n = 36 ave = 2.60 sd = 0.9 Signal t = = = Noise NN-CC TT: NN-CC rP = 2.03E-70 aP = 1.30E-66

13 Splitting : F-test n = 1650 ave = 0.34 sd = 0.81 n = 1553 ave = 0.21 sd = 0.73 n = 36 ave = 2.60 sd = 0.9 n = 61 ave = 1.29 sd = 0.83 n = 61 ave = 1.29 sd = 0.83 Signal Among Var  (Xi. - X..) 2 /df1 F = = = Noise Within Var  (Xij - Xi.) 2 /df2

14 How to Stop Examine each current terminal node. Stop if no variable/class has a significant split, multiplicity adjusted.

15 Levels of Multiple Testing 1.Raw p-value. 2.Adjust for class formation, segmentation. 3.Adjust for multiple predictors. 4.Adjust for multiple splits in the tree. 5.Adjust for multiple trees.

16 Understanding observations NB: Splitting variables govern the process, linked to response variable. linked to response variable. Multiple Mechanisms Conditionally important descriptors.

17 Multiple Mechanisms

18 Reality: Example Data 60 Tissues 1453 Genes Gene 510 is the “guilty” gene, the Y.

19 1 st Split of Gene 510 (Guilty Gene)

20 Split Selection 14 spliters with adjusted p-value < 0.05

21 Histogram Non-normal, hence resampling p-values make sense.

22 Resampling-based Adjusted p-value

23 Single Tree RP Drawbacks Data greedy. Only one view of the data. May miss other mechanisms. Highly correlated variables may be obscured. Higher order interactions may be masked. No formal mechanisms for follow-up experimental design. Disposition of outliers is difficult.

24 Etc. Multiple Trees, how and why?

25 How do you get multiple trees? 1.Bootstrap the sample, one tree per sample. 2.Randomize over valid splitters. Etc.

26 Random Tree Browsing, 1000 Trees.

27 Example Tree

28 1 st Split

29 Example Tree, 2 nd Split

30 Conclusion for Gene G510 If G518 < and G790 < then G510 = /- 0.30

31 Using Multiple Trees to Understand variables Which variables matter? How to rank variables in importance. Correlations. Synergistic variables.

32 Correlation Interaction Matrix Red=Syn.

33 Summary Review recursive partitioning. Demonstrated multiple tree RP’s capabilities –Find associated genes –Group correlated predictors (genes) –Synergistic predictors (genes that predict together) Used to understand a complex data set.

34 Needed research Real data sets with known answers. Benchmarking. Linking to gene annotations. Scale (1,000*10,000). Multiple testing in complex data sets. Good visualization methods. Outlier detection for large data sets. Missing values. (see NISS paper 123)

35 Teams NC State University : Jacqueline Hughes-Oliver Katja Rimlinger U Waterloo : Will Welch Hugh Chipman Marcia Wang Yan Yuan U. Minnesota : Douglas Hawkins NISS : Alan Karr (Consider post docs) GSK : Lei Zhu Ray Lam

36 References/Contact papers 122 and GSK patent.

37 Questions