CNV PCA Search Tutorial

Transcription

1 CNV PCA Search Tutorial Release 8.1 Golden Helix, Inc. March 18, 2014

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3 Contents 1. Data Preparation 2 A. Join Log Ratio Data with Phenotype Information B. Activate only Autosome Columns C. Set the Case/Control Column as the Dependent Variable Calculate Principal Components and Eigenvalues 3 A. Run Numeric Principal Component Analysis B. Generate Scree Plot of PC Eigenvalues C. Determine Min and Max Number of PCs Run CNV PCA Search Script 6 A. Download the CNV PCA Search Script B. Run the Script Interpret Results 8 A. Determine Number of PCs with Slope Closest to One Verify Solution with Q-Q Plots 10 A. Generate Q-Q Plot i

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5 CNV PCA Search Tutorial, Release 8.1 Updated: March 1st, 2014 Level: Advanced Packages: CNV Analysis, Power Seat For both microarray and acgh data, significant bias can be introduced by batch effects (plate, machine, and site variation), genomics waves, and population stratification. Other sources of variation include sample extraction and procedures, cell types, temperature fluctuation, and even ambient ozone levels in a lab. These can lead to complications ranging from poorly defined copy number segments to false and non-replicable findings. Utilizing SVS 8 s powerful principal component analysis methods enables you to simultaneously correct for all these variations, while significantly improving signal-to-noise ratios. But the question is, How many principal components should you correct for to remove the batch effects without also removing the signal? This tutorial leads you through a holistic approach to determine the optimal number of principal components to correct for with copy number data by utilizing both PCA and association analysis techniques. Requirements To complete this tutorial you will need: A marker mapped spreadsheet containing a case/control affection status column and log ratio data. If the phenotype of interest is quantitative, you will need to transform this variable into a dichotomous trait by using a cut-off value. Note: The dataset used in this tutorial is the phenotype and log ratio data that is provided in the CNV Quality Assurance tutorial. We hope you enjoy the experience and look forward to your feedback. Contents 1

6 1. Data Preparation Using all chromosomes in PCA analysis can cause an erroneous shift of the data. This is due to autosomes having, on average, three distributions (one for loss, one for gain, and one for a normal number of copies), whereas there are only two expected distributions for the X chromosome (one for males and one for females). Therefore, X chromosome log ratios are less than zero for males and greater than zero for females. If there is an imbalance in the number of males and females in your sample set, this will undoubtedly skew the distribution. We therefore recommend calculating principal components using only autosomes and then applying them to all chromosomes when PCA correcting the data. A. Join Log Ratio Data with Phenotype Information If you have not already done so you need to join the case/control status with the log ratio data. Note: Make sure your log ratio spreadsheet is marker mapped before completing this step. Open your spreadsheet containing phenotype information and select File >Join or Merge Spreadsheets. Select your spreadsheet containing log ratio data and click OK. Set the New dataset name: to Pheno + LogRs. Select the appropriate join parameters for your data and click OK when finished. This will create a new spreadsheet, Pheno + LogRs - Sheet 1, with phenotype information at the beginning of the spreadsheet followed by log ratio data. B. Activate only Autosome Columns From the Pheno + LogRs - Sheet 1 spreadsheet, select Select >Activate by Chromosomes. Uncheck the X box (and Y and M if applicable) and click OK. IMPORTANT If you have other phenotype data in your spreadsheet you will need to inactivate these columns as well. To do this, left-click twice on each column to turn it grey denoting it as inactive. C. Set the Case/Control Column as the Dependent Variable Left-click the Case/Control column header once to turn it magenta. This sets it as the dependent variable. 2

7 2. Calculate Principal Components and Eigenvalues Now that your data is in the correct orientation, the next step is to calculate as many principal components as possible (the limit is the number of samples less 1) and the eigenvalues for only the autosomes. A. Run Numeric Principal Component Analysis Open Pheno + LogRs - Sheet 1 and select Numeric >Numeric Principal Component Analysis. Set the parameters in the Numeric Principal Component Analysis window as shown in Figure 2a where Find up to to components is equal to your total number of samples minus 1. Make sure Center data by marker is checked and click Run. Figure 2a. Numeric PC parameters. 3

8 CNV PCA Search Tutorial, Release 8.1 Upon completion, two spreadsheets are created Principal Components (Center by Marker), and Eigenvalues (Center by Marker). B. Generate Scree Plot of PC Eigenvalues From the PC Eigenvalues (Center by Marker) spreadsheet, right-click on the Eigenvalue column header and select Plot Variable. This generates a scree plot of the PC eigenvalues (Figure 2b). There should be an apparent bend in the plot, referred to as the elbow. Figure 2b. Zoomed scree plot with potential elbow highlighted. C. Determine Min and Max Number of PCs Rather than examine all possible number of principal components to find the ideal number, you can usually, by visual inspection, narrow the search by selecting a range to search through that covers the elbow Calculate Principal Components and Eigenvalues

9 CNV PCA Search Tutorial, Release 8.1 Determine the minimum number of principal components and the maximum number of principal components. For this example, the minimum number of components will be set to 1 and the maximum number of components set to 20 in order to ensure that the optimum number of components is not missed. C. Determine Min and Max Number of PCs 5

10 3. Run CNV PCA Search Script The search for the optimum number of principal components involves correcting log ratios using each possible number of principal components within the range determined in the previous step, performing association tests on the case/control status using the corrected data, running regression analysis on the top 90% least significant results, and then evaluating the respective Q-Q Plots to determine which number gives the best results. A script is available that will automatically peform the first three procedures for each number of principal components within the range. A. Download the CNV PCA Search Script Download the script: CNV PCA Search.py Save this script to your *..\AppData\Golden Helix SVS\UserScripts\Spreadsheet\Scripts folder. Note: The AppData folder is a hidden folder on Windows operating systems and its location varies between OS Versions. The easiest way to locate this directory on your computer is to open SVS and go to Tools >Open Folder >User Scripts Folder. If saved to the proper folder, this script should show up in the Scripts menu from any spreadsheet. B. Run the Script Open the Pheno + LogRs - Sheet 1 spreadsheet and select Scripts >CNV PCA Search. Click on Select Sheet and select the Principal Components (Center by Marker) spreadsheet. Set the Minimum components and Maximum components as determined in the previous step. In this example it would be 1 and 20. Set the Step size to 1 and make sure Center data by marker is selected. Click OK. Using the min and max components considered in this example, the script will generate 20 different Principal Components spreadsheets, as well as 20 different Association Test Result spreadsheets. In the background a regression analysis will also be computed for the top 90% least significant results. From the regression analysis, the slope, and F statistic will be stored and log10(f statistic) will be computed. These values will be output in the PCA Search Results spreadsheet (see Figure 3). For each number of principal components the slope and F statistic will be output in the node annotations log for each association results spreadsheet. 6

11 CNV PCA Search Tutorial, Release 8.1 Figure 3. PCA Search results for 1 through 20 principal components. B. Run the Script 7

12 4. Interpret Results The next step is to interpret the results from the CNV PCA Search script and determine the number of principal components to use for the principal component analysis. A. Determine Number of PCs with Slope Closest to One From the PCA Search Results spreadsheet, right-click the Slope column header and select Sort Ascending. Scroll to the number of components that has a Slope closest to one. In this example, the slope is closest to one for 7 principal components. Figure 4a. PCA Search Results displaying slope closest to one and the smallest -log10(f) value. 8

13 CNV PCA Search Tutorial, Release 8.1 Note: A slope of one indicates that the observed values are in line with the expected values, thus indicating that the observed p-values that are not significant are no more or no less significant than expected. You can also look for the number of components that has the smallest -log10(f) value. In most cases, this will be consistent with the number that has a slope closest to one. In the case of this data this is true A. Determine Number of PCs with Slope Closest to One 9

14 5. Verify Solution with Q-Q Plots Finally, by plotting Q-Q plots of the observed log10 p-values versus the expected -log10 rank p-values you can confirm an ideal solution. A. Generate Q-Q Plot Open the Association Tests results spreadsheet that was generated using the optimum number of principal components as determined in the previous step. In this example it would be the Association Tests PCA on predictors (Center by Marker) PCA 7. Activate all rows by selecting Select >Row >Activate All Rows. Next, generate the plot by going to Plot >XY Scatter Plots. For the independent axis (in the left box) select Corr/Trend expected log10 P, and for the dependent axis (in the right box) select Corr/Trend log10 P. Click Plot. This will generate a Q-Q Plot of the observed vs. expected values. See Figure 5a. When the plot viewer opens, click on Graph1 in the Graph Control Interface on the left. The Graph control panel will become visible. Click on the Add Item tab and select f(x) = m(x) + b from the list, then click Add. By examining the Q-Q plots after correcting for 7 and 10 components respectively, it is clear that 7 components yields a better result as the observed p-values more closely follow the y=x line. See Figure 5b, Figure 5c and Figure 5d. It is recommended that you examine the Q-Q plots to verify that the optimal number of principal components selected yields a good solution. Thus, 7 components should be used for correcting this dataset. The first 7 principal components can now be applied to all markers including markers from non-autosomal chromosomes as long as Center data by marker is used. 10

15 CNV PCA Search Tutorial, Release 8.1 Figure 5a. Plot Viewer Q-Q plot of observed versus expected -log 10 P values. A. Generate Q-Q Plot 11

16 CNV PCA Search Tutorial, Release 8.1 Figure 5b. Good correction, the p-values are near the line between 0 and 4 along the X axis Verify Solution with Q-Q Plots

17 CNV PCA Search Tutorial, Release 8.1 Figure 5c.Over correction, the p-values are below the line between 0 and 4 along the X axis. A. Generate Q-Q Plot 13

18 CNV PCA Search Tutorial, Release 8.1 Figure 5d. Under correction, the p-values are above the line between 0 and 4 along the X axis Verify Solution with Q-Q Plots