1. Model-based analysis of oligonucleotide arrays, dChip software Statistics and Genomics – Lecture 4 Department of Biostatistics Harvard School of Public Health January 23-25, 2002 Cheng Li (Joint work with Wing Wong)

2. Source: Affymetrix website

3. Custom software: raw image

4. Custom software: getting representative value of a probe cell

5. Normalization is needed to minimize non-biological variation between arrays

6. Normalization methods Current software uses linear normalization Nonlinear curve fitting based on scatter plot is still inadequate because 1) effects of differentially expressed genes may be “normalized” 2) regression phenomenon and asymmetry

7. Regression phenomenon and asymmetry

8. Invariant set normalization method A set of points (x i, y i ) is said to be order-preserving if y i < y j whenever x i < x j The maximal order-preserving subset can be obtained by dynamic programming If a gene is really differentially expressed, it’s cells tend not to be included into an large order- preserving subset Our method is based on an approximately order preserving subset, called “Invariant set”

9. Fig. 2.9 Normalization of a pair of replicated arrays

10. Figure 2.10. Two different samples. The smoothing spline in (A) is affected by several points at the lower-right corner, which might belong to differentially expressed genes. Whereas the “invariant set” does not include these points when determining normalization curve, leading to a different normalization relationship at the high end.

11. A pair of split-sample replicate arrays

12. Source: Affymetrix website

13. PM/MM differences eliminate background and cross- hybridization signals Data for one probe set, one array

14. Lockhart et al. (1996) Nature Genetics, Vol 14: 1675-1680 Validation experiments suggest Average Differences are linear to mRNA concentrations at certain dynamic range

15. Data for one gene in many arrays

16. Box plot showing array and probe effects

17. Modeling probe effects 1) Probes sequence has different hybridization efficiency 2) cross hybridization, SNP, alternative splicing 3) Probe position effect, 3’ bias Probe effects can dominate biological variation of interest Previous method : use multiple probes, average to reduce “noise” Our methods: statistical models for probe effects, “meta- analysis”, learning algorithms, estimation of expression level conditional on knowledge of probe effect

18. Principal component analysis (42 points in 20-space) suggests the data matrix has approx. rank 1

19. Model for one gene in multiple arrays

20. Figure 1.1. Black curves are the PM and MM data of gene A in the first 6 arrays. Light curves are the fitted values to model (1). Probe pairs are labeled 1 to 20 on the horizontal axis.

21. Using PM/MM Differences PM/MM differences eliminate most background and cross-hybridization signals Affyemtrix’s GeneChip software is using average differences as basis for determining fold changes, and their validation showed average differences are linear to mRNA concentrations at certain dynamic range

22. Model for PM/MM differences (1.2)

23. Figure 1.2. Black curves are the PM-MM difference data of gene A in the first 6 arrays. Light curves are the fitted values to model (2).

25. Residuals of the fitting

26. Model fitting amounts to fixing  ’s and regress to estimate 

27. Fig 1.5 Array outlier: large standard errors of  4

28. Fig. 1.6 Probe outlier: large standard errors of  17 Also see gene 6898

29. Fig. 1.4 Array outlier image shows that the model automatically handles image contamination

30. Compare Model-based expression with Average Difference The array set 5 has 29 pair of arrays replicated at split-mRNA level The differences between the replicated arrays provides a opportunity to assess different expression calculation method

31. Figure 2.5. Log (base 10) expression indexes of a pair of replicate arrays (array 1 and 2 of array set 5) for MBEI method (A) and AD method (B). The center line is y=x, and the flanking lines indicate the difference of a factor of two.

32. (A)(B) Figure 2.6. Boxplots of average absolute log (base 10) ratios between replicate arrays stratified by presence proportion for (A) MBEI method, (B) AD method.

33. Source: Affymetrix website

34. Finding Confidence Interval of Fold Change

35. Table 2.1 Using expression levels and associated standard errors to determine confidence intervals of fold changes

36. Resampling hierarchical clustering using standard errors of model-based expression

37. Incorporate biological knowledge and database when analyzing microarray data Right picture: Gene Ontology: tool for the unification of biology, Nature Genetics, 25, p25

38. Found 13 structural protein genes out of a 49-cluster (all: 198/2622, PValue: 1.00e+000) Functional significant clusters

39. Problems with LWR model: LWR model: The expression index can still be negative. Genes with negative index can still be classified as present. Statistical analysis of high-density oligonucleotide arrays: a multiplicative noise model R. Sasik and J. Corbeil (UCSF) Slides prepared by Xuemin Fang

40. Statistical model: Based on the same assumption as the LW model, that PM intensity is directly proportional to the concentration c i of the transcript,. Write the relation in the form Our model is where Least squared estimation of the parameters. Constraint:

41. Algorithm -- When analyzing a batch of n s samples: Normalize all samples to the first one on the list by requiring the sum of all PM intensities be the same as that of the first sample. Select the background probes using Naef’s method (MM is used in this step). Subtract the median of the background probe intensity from every PM probe in the array. Probes that become negative are eliminated. Fit the model and probes contributes most to the sum of squares are eliminated. Normalize again and repeat 1-5, until the distribution of residuals is Gaussian.

42. Bias, variance and fit for three measures of expression: AvDiff, Li & Wong's, AvLog (PM -bg) Rafael Irizarry, Terry Speed (Johns Hopkins) Slides prepared by Xuemin Fang

43. A background plus signal model: Here represents background signal caused by optical noise and non-specific binding. The mean background level is represented with and the random component with. The transcript signal contains a probe affinity effect, the log expression measures, and an error term. Both error terms and are independent standard normal.

44. Expression index: A naïve estimate of is given by with the mode of the log 2 (MM) distribution. An estimate of this distribution is obtained using a density kernel estimate.

45. Acknowledgement Data source: Stan Nelson (UCLA) Sven de Vos (UCLA) Dan Tang (DFCI) Andy Bhattacharjee (DFCI) Richardson Andresa (DFCI) Allen Fienberg (Rockefeller)