# Presentation: 379409

## Combining copy numbersacross TCGA centers

**Combining copy numbers****across TCGA centers**

- Henrik Bengtsson1, Amrita Ray2,
- Paul Spellman2, Terry Speed1,3
- 1) Department of Statistics, University of California, Berkeley, USA
- 2) Life Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, USA
- 3) Walter & Eliza Hall Institute of Medical Research, Parkville, Australia

## BACKGROUND
For each sample, the 4 TCGA centers produce raw copy-number (CN) estimates independently of each others. 3 platforms are used.

Each center identifies CNV regions based on their own CN data. Currently, there is no integration      of data or results.  This approach will miss some CN regions and produce unnecessary false positives. It is also not cost effective.

If done appropriately, combining          CN estimates across centers        should increase the precision and      the resolution of identified CN regions.  More regions will be    found and fewer false positives     will be reported.

**BACKGROUND**
- For each sample, the 4 TCGA centers produce raw copy-number (CN) estimates independently of each others. 3 platforms are used.
- Each center identifies CNV regions based on their own CN data. Currently, there is no integration      of data or results.  This approach will miss some CN regions and produce unnecessary false positives. It is also not cost effective.
- If done appropriately, combining          CN estimates across centers        should increase the precision and      the resolution of identified CN regions.  More regions will be    found and fewer false positives     will be reported.

- (A) **Broad, Affymetrix GWS6**, n=1800K, 1.59kb/locus, 25-mers

- (B) **Stanford, Illumina 550K**, n=550K, 5.53kb/locus, 50-mers

- (C) **MSKCC, Agilent 244K**, n=236K, 12.7kb/locus, 60-mers

*Tumor/normal CNs by four TCGA centers *
*(“sources”) in a 60Mb region on Chr3 in sample TCGA-02-104. (The combined set would consist of 2,822K loci with average distance 0.95kb/locus.)*

- (D) **Harvard, Agilent 244K**, n=236K, 12.7kb/locus, 60-mers

## PROBLEM
CN estimates from different centers show different degrees of attenuation of the true CN changes.
That is, their mean levels differ.
(Noise levels differ too; more later).

For this reason, it is not a straightforward matter to combine    CN estimates from different centers.

If combined as is, the signal-to-noise ratio will be unnecessarily low.  In the worst case, regions found by the individual centers are no longer found.

**PROBLEM**
- CN estimates from different centers show different degrees of attenuation of the true CN changes.
- That is, their mean levels differ.
- (Noise levels differ too; more later).
- For this reason, it is not a straightforward matter to combine    CN estimates from different centers.
- If combined as is, the signal-to-noise ratio will be unnecessarily low.  In the worst case, regions found by the individual centers are no longer found.

## OBJECTIVES
To normalize the data at the full resolution such that CN estimates from different centers are on the same scale.

The relationship between centers should be linear (proportional).

CN estimates across centers should agree on the mean level for all CN aberrations.

Normalization should be done on individual estimates - not after segmentation or similar.

Normalize each sample separately
(computationally favorable).

Heteroscedasticity:  Leave it to downstream methods to deal with the differences in noise levels.

**OBJECTIVES**
- To normalize the data at the full resolution such that CN estimates from different centers are on the same scale.
- The relationship between centers should be linear (proportional).
- CN estimates across centers should agree on the mean level for all CN aberrations.
- Normalization should be done on individual estimates - not after segmentation or similar.
- Normalize each sample separately
- (computationally favorable).
- Heteroscedasticity:  Leave it to downstream methods to deal with the differences in noise levels.

*The smoothed raw CNs from the four centers have similar CN profiles but different mean levels.*

*The smoothed normalized CNs from the four centers have similar CN profiles and same mean levels.  They now agree.*

## METHOD
Step 1 From a large set of common loci, we estimate relationships between CN estimates produced by the different TCGA centers.

Since different platforms measure CNs at different loci, we use kernel estimators to obtain estimates at a common set of loci.

We use principal component curves to estimate the non-linear relationships.  We can do this robustly in 4 dimensions at once.

Step 2 We then normalize the full-resolution data such that these relationships becomes linear (proportional) and on the same scale.

**METHOD**
- Step 1 From a large set of common loci, we estimate relationships between CN estimates produced by the different TCGA centers.
- Since different platforms measure CNs at different loci, we use kernel estimators to obtain estimates at a common set of loci.
- We use principal component curves to estimate the non-linear relationships.  We can do this robustly in 4 dimensions at once.
- Step 2 We then normalize the full-resolution data such that these relationships becomes linear (proportional) and on the same scale.

*Before normalization:*
***Non-linearity between pairs***

*After normalization: *
***Linearity between pairs***

- Center A

- Center B

- Center C

- Center D

## Multi-source

**Multi-source**
**copy-number**
**normalization**

## EVALUATION (inspired by segmentation methods)
Data set
(1) Pick a random sample, and find a change point that clearly separates two CN states.
(2) Excluding loci within 250kb of the change point, let  the loci to the left and the right represent the two CN states.

Test
(4) For a give bin-size (“resolution”), generate smoothed CNs by binning the existing estimates in consecutive bins and average within each bin.
(5) Use ROC analysis to assess how well the smoothed CNs can separate the two CN states.  There is a trade off between the number of true and false positives.
(6) Compare the ROC curves for the different data sets by keeping resolution fixed.

To account for heteroscedasticity 
in the combined data sets, we bin
using weighted averaging so that 
noisier platforms have less impact.

**EVALUATION** (inspired by segmentation methods)
**Data set**
- (1) Pick a random sample, and find a change point that clearly separates two CN states.
- (2) Excluding loci within 250kb of the change point, let  the loci to the left and the right represent the two CN states.
**Test**
- (4) For a give bin-size (“resolution”), generate smoothed CNs by binning the existing estimates in consecutive bins and average within each bin.
- (5) Use ROC analysis to assess how well the smoothed CNs can separate the two CN states.  There is a trade off between the number of true and false positives.
- (6) Compare the ROC curves for the different data sets by keeping resolution fixed.
- To account for heteroscedasticity
- in the combined data sets, we bin
- using weighted averaging so that
- noisier platforms have less impact.

*At any given resolution (amount of smoothing), with combined normalized CNs** (****solid red****) **one can separate two CN states ****better**** than with combined raw CNs** (****dot-dashed red****), **and with each of the individuals sources** (****gray dotted****).*

- (**A**)
- (**B**)
- (**C**)
- (**D**)
- (**raw+comb**)
- (**norm+comb**)

- bin size: 25kb

## RESULTS

We find that after normalization

(i) the mean levels of randomly selected CN aberrations are the same across platforms.

With combined normalized data

(ii) there is more power to detect a CN aberration at any given resolution,

(iii) the resolution increases, i.e. the locations of change points are estimated with greater precision, and

(iv) the genome coverage increases, as the different platforms complement each other in different regions.

**RESULTS**
- We find that after normalization
- (i) the mean levels of randomly selected CN aberrations are the same across platforms.
- With combined normalized data
- (ii) there is more power to detect a CN aberration at any given resolution,
- (iii) the resolution increases, i.e. the locations of change points are estimated with greater precision, and
- (iv) the genome coverage increases, as the different platforms complement each other in different regions.

*With **combined normalized** CNs, there is more power to detect change points and their locations are more precise.*

*A 400kb region in TCGA-02-104 on Chr 3: CNs from** different **sources give **different **segmentation results at **different** precisions.*

## WHAT still NEEDS TO BE DONE:

Down-stream methods need to accomodate heteroscedasticity
Segmentation methods (sample by sample):
The multi-source segmentation method developed by Nancy Zhang (Stanford) and Jun Li (Univ of Michigan) is promising.
Extend CBS to accommodate weights if possible
Existing methods (e.g. CBS) can still be used, but are sub-optimal.

Methods for identifying CN polymorphic regions (across samples).

ONGOING/FUTURE WORK
    Assess performances of the available copy-number estimates originating from the different TCGA centers:
This will depend on platform, assay, lab, algorithm and objective.
Objectives for what is good have to be well defined.
Evaluation methods for each objective need to be developed.
There may or may not be a clear “winner”.
This is work for the members of the TCGA CN Group.

**WHAT still NEEDS TO BE DONE:**
**Down-stream methods need to accomodate heteroscedasticity**
- Segmentation methods (sample by sample):
- The multi-source segmentation method developed by Nancy Zhang (Stanford) and Jun Li (Univ of Michigan) is promising.
- Extend CBS to accommodate weights if possible
- Existing methods (e.g. CBS) can still be used, but are sub-optimal.
- Methods for identifying CN polymorphic regions (across samples).
**ONGOING/FUTURE WORK**
-     Assess performances of the available copy-number estimates originating from the different TCGA centers:
- This will depend on platform, assay, lab, algorithm and objective.
- Objectives for what is good have to be well defined.
- Evaluation methods for each objective need to be developed.
- There may or may not be a clear “winner”.
- This is work for the members of the TCGA CN Group.

## Appendix

## Combining copy numbers “as is”

- Platform #1

- Platform #2

- Combined

- Combining copy numbers “as is”

## Combining normalized copy numbers

- Platform #1

- Platform #2

- Normalized & Combined

- Combining normalized copy numbers

## A second region; resolution 15 bk

**A second region; resolution 15 bk**