Tutorial: Copy Number Variation (CNV) Analysis

6. DISCRETIZING COPY NUMBER SEGMENT COVARIATES

Outlined below is a procedure for discretizing the logR copy number segment covariates as two state (0,1) or three state (-1,0,1) covariates based on defined thresholds. Discretizing the covariates has the following benefits:

• Approximate copy number calls (potential: deletion, neutral, duplication, not a deletion, or not a duplication) can be made based on thresholds denoting transitions between copy number states.
• Discretizing can magnify small, statistically significant differences between cases and controls.
• Using discretized values does not let outliers (extremely small or large logR values) have any more influence on a p-value than those close to the threshold.

To complete this step you first need to download the following scripts:

Create Spreadsheet for Segmentation.py
Discretize CN Segment Covariates.py

• Save these scripts to your *..\Application Data\Golden Helix SVS\UserScripts\Spreadsheet\Scripts folder.

Note: The Application Data folder is a hidden folder on Windows operating systems and its location varies between XP and Vista. The easiest way to locate this directory on your computer is to click on the AppData shortcut in your C:\Program Files\Golden Helix SVS\ directory or wherever you installed Golden Helix SVS.

If saved to the proper folder, these scripts should show up in the Scripts menu from any spreadsheet.

Determining Appropriate Thresholds Between Copy Number States

In addition to detecting copy number segments, CNAM optimal segmenting can be used to define thresholds between the three copy number states: copy number loss, copy number neutral and copy number gain. First, create a histogram of segment means for an understanding of what the segmenting algorithm is doing.

• Open the Segment List spreadsheet.
• Right-click on the Segment Mean column header and select Plot Histogram.

A histogram is displayed with an apparent normal distribution. With copy number data you expect to see at least three "hills" or distributions of logRs, representing copy number loss (left hill), copy number neutral (middle hill), and copy number gain (right hill). This becomes visible when you change the Bin Size on the histogram. To do this:

• Click on Graph 1 in the Graph Control Interface.
• Change the Bin Count to 128.

The histogram should now match that in Figure 13 with the three hills.

IMPORTANT: If you observe a uni-modal distribution (only one hill) regardless of Bin Count and/or a large number of outliers in your data, discretizing is not recommended. In this case using the PCA corrected segments as covariates for association testing is recommended.

The objective is to now determine the boundaries between the three hills. This is difficult to do, especially visually, as the three distributions overlap. Rather than approximate these boundaries, CNAM optimal segmenting offers a more exact approach as it minimizes the sum of squared errors between each of the distributions.

• Open the Segment List spreadsheet again, right-click the Segment Mean column header and select Sort Ascending.
• From the resulting Segment List – Sheet 2 spreadsheet, select Scripts >Create Spreadsheet for Segmentation.

You will be prompted to select a column number to index. You want to index the Segment Means column or column #4.

• Enter 4 for Select the column number: and click OK.

This will create a new spreadsheet in the Project Navigator called Index Segment Mean – Mapped Sheet 1, with 1 row and 2,437 columns. The smallest value should be at the beginning of the spreadsheet and the largest value at the end of the spreadsheet.

• Open Index Segment Mean – Mapped Sheet 1 and select Analysis >CNAM Optimal Segmenting.
• Set the parameters to those of Figure 14 and click Run.

Two new spreadsheets and a run log appear. The Segment List spreadsheet is all you need for this step.

• Delete the new Segmentation Run Log and the Segmentation Covariates First Column spreadsheet.

Notice in the Segment List spreadsheet (Figure 15) that CNAM found three segments as indicated by the number of rows in the spreadsheet.

The End Index column denotes the boundaries between the three distributions. For the threshold values you need to locate their respective columns in the Index Segment Mean - Mapped Sheet 1 spreadsheet.

• Open the Index Segment Mean - Mapped Sheet 1 spreadsheet and select Edit >Go To. Enter Column: 407 and click OK.

This takes you to column 407, which has a value of -0.113927878439426 denoting the boundary between copy number loss and copy number neutral.

• Select Edit >Go To, enter Column: 1988 and click OK.

The value at this column is 0.0986386612057686 denoting the boundary between copy number neutral and copy number gain.

NOTE: CNAM bases its calculations on the mean of each distribution and therefore its results can be affected by large outliers. This may result in discrepancies with visual inspection. What are considered outliers and how outliers are handled differs from study-to-study, array-to-array, and researcher-to-researcher. Even though visually there appear to be negative outliers in the left-most distribution, for the purpose of this tutorial they will not be treated as such and the calculated thresholds will be used for discretizing.

B. Three-State Discretization

Now that appropriate thresholds have been determined, you can use these to discretize the copy number segment covariates (continuous logR values) as two-state (0,1) or three-state (-1,0,1) covariates. This tutorial will cover three-state discretization, though the same process can be applied to two-state discretization.

• Open the Segmentation Covariates Every Column spreadsheet under the PCA-Corrected Data spreadsheet (unless you imported this spreadsheet separately) and select Scripts >Discretize CN Segment Covariates.

You will be prompted to choose a Three State Model or one of two Two State Models.

• Choose Three State Model (-1,0,1) and click OK.
• On the next dialog enter -0.113927878439426 as the Lower Threshold Level and 0.0986386612057686 as the Upper Tolerance Level and click OK.

This will create a new spreadsheet, Three State Covariates, with -1s for potential losses, 0s for potential neutrals, and 1s for potential gains (Figure 16).

You will need to reapply the marker map.

• Open the Three State Covariates spreadsheet and select File >Apply Genetic Marker Map.
• Choose the Affymetrix 500K marker map as before and click OK.
• It will ask you which columns to show by default. Uncheck the last three: Flank, Strand Versus dbSNP, and Probe Count.

A final spreadsheet, Three State Covariates - Mapped Sheet 1, is created, which you can use to perform association tests on discretized copy number segments.