Batch effects. 8 normal samples color: processing date. Expression. Sample

Transcription

1 Unwanted variation We have seen that microarray expression data suffers from unwanted variation. We have discussed a number of preprocessing algorithms intended to increase the signal-to-noise in such data. But sometimes (unwanted) variation remains.

2 Batch effects a 16 b Expression 10 Expression Sample Sample 8 normal samples color: processing date

3 Batch effects c 10 Batch 1 Batch 2 d 9 Expression Normal Normal Normal Normal Normal Normal Normal Normal Sample One gene Clustering

4 Batch effects Batch effects: unwanted variation remaining after normalization. Often associated with processing date or processing batch. Often thought to be technical, but can be biological (later). Two extreme situations: (1) Batch effect is orthogonal to comparison of interest. This will increase noise and dilute signal, but otherwise ok. (2) Batch effect is confounded with comparison of interest. This will make any conclusion highly circumspect (and likely wrong).

5 Sources of Heterogeneity

6 The Effect of Heterogeneity Color = Environment (Idaghdour et al. 2008) Color = Processing Year (Cheung et al. 2008) Color = Allele (Brem et al. 2005)

7 A Simple Simulated Example Independent E Dependent E Genes Genes Arrays Arrays

8 Gene by Gene Model expression = b 0 + b 1 group + noise Test whether b 1 = 0 <=> T test for gene I Calculate a P value

9 Null P Value Distribu$ons Independent E P value P value P value P value Dependent E P value P value P value P value

10 Null P Value Distribu$ons Correla$on ρ = 0.40 ρ = 0.31 ρ = 0.10 ρ = 0.00 Independent E P value P value P value P value Dependent E P value P value P value P value

11 False Discovery Rate Es$mates Independent E Dependent E

12 Ranking Es$mates Independent E Dependent E

13 Principal Components Analysis / Singular Value Decomposi$on A method to iden$fy paterns in the data that explain a large percentage of the varia$on PCA and SVD have different mathema$cal goals but end up es$ma$ng the same thing First proposed for genomics by Alter et al. (2000) PNAS

14 Singular Value Decomposi$on samples U D V T genes = Data eigenarrays/ leu singular vectors/ loadings singular values eigengenes/ right singular vectors/ principal components

15 Proper$es of SVD samples U D V T genes = Columns of V T /rows of U are orthogonal and calculated one at a $me Columns of V T describe paterns across genes Columns of U describe paterns across arrays n d 2 2 i / d is the percent of varia$on explained by the ith column of V i i=1

16 1 Patern 1 st SV 1 st Column of U 1 st Column of V T = +

17 2 Paterns, 1 st SV 1 st Column of U 1 st Column of V T = +

18 Surrogate Variable Analysis The Data Pr(!Group & Batch) Es$mate of Batch True Batch

19 Surrogate Variable Analysis The Data Pr(!Group & Batch) Es$mate of Batch True Batch

20 Surrogate Variable Analysis The Data Pr(!Group & Batch) Es$mate of Batch True Batch

21 Surrogate Variable Analysis The Data Pr(!Group & Batch) Es$mate of Batch True Batch

22 Surrogate Variable Analysis The Data Pr(!Group & Batch) Es$mate of Batch True Batch

23 Surrogate Variable Analysis The Data Pr(!Group & Batch) Es$mate of Batch True Batch

24 SVA Adjusted Gene by Gene Model expression = b 0 + b 1 group + surrogates + noise Test whether b 1 = 0 Calculate a P value

25 Ranking Estimates Independent E Dependent E Dependent E + IRW SVA Average Ranking by T Sta$s$c Average Ranking by T Sta$s$c Average Ranking by T Sta$s$c Ranking by True Signal to Noise Ranking by True Signal to Noise Ranking by True Signal to Noise

26 Methods (IRW-) SVA by Leek and Storey. RUV by Gagnon-Bartsch and Speed Many methods are small modifications of SVA. The idea behind RUV is to use control (genes / probes) to estimate batch effects. Controls could be probes unaffected by biology (negative controls) or genes known to be differentially expressed.

27 An example of biological batch effect Changes in cell type composition. Expression changes associated with Age or Cell cycle.