Regression with Covariates Tutorial

Transcription

1 Regression with Covariates Tutorial Release 8.1 Golden Helix, Inc. March 18, 2014

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3 Contents 1. Overview of the Project 2 A. Data preparation Controlling For Confounding Variables 3 A. Full Model Only B. Full vs. Reduced Model Accounting for SNP Correlation 8 A. Using a Moving Window Using the Regression Module for Model Comparison 10 i

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5 Regression with Covariates Tutorial, Release 8.1 Updated: March 6th, 2014 Level: Intermediate Packages: SNP Analysis, CNV Analysis, RNA-Seq Analysis, Power Seat This tutorial provides an in-depth look at the SVS 8 Regression Module. It will cover controlling for confounding variables, model comparison, and stepwise regression. The genotype spreadsheet included in the project file contains PCA-corrected numeric SNP columns for an additive model. The phenotype information is simulated. If you are interested in learning how to set up a linear regression model, please read our blog post on the topic. Requirements To complete this tutorial you will need to download and unzip the following file, which includes a Golden Helix Project File. Download Regression_Tutorial.zip File included in the above ZIP file: Regression_Tutorial - SVS Project file containing mapped genotype information and a phenotype spreadsheet. We hope you enjoy the experience and look forward to your feedback. Contents 1

6 1. Overview of the Project Regression analysis is a useful and necessary tool in any researcher s toolbox. This tutorial provides several workflows to showcase different ways to use regression analysis in a genotypic model assessment setting. Also included is an overview of how to interpret the Regression Results output. A. Data preparation Open the SVS Project available for download on the first page of this tutorial. You should see two spreadsheets: a phenotype spreadsheet (HM_Sim_Pheno... ) and a marker-mapped genotype spreadsheet (PCA-Corrected HM_500K_Geno... ). The genotype spreadsheet contains numeric values from chromosome 1 that have been corrected for 3 principle components. This data comes from HapMap samples and is thus tainted by population stratification. Open the HM_Sim_Pheno Dataset - Sheet 1. You will need to join this spreadsheet with the genotype spreadsheet in order to perform regression. Choose File >Join or Merge Spreadsheets. Select the PCA_Corrected HM_500K_Geno - Sheet 1 and click OK. After New dataset name: type Pheno + Geno and under Spreadsheet as Child of choose Current spreadsheet. Click OK. Now you should have the phenotypic and genotypic information in the same spreadsheet. First we will use the phenotypic and genotypic information to predict case/control status in the full model. SVS will recognize case/control status as a binary dependent variable and automatically perform logistic regression. Using a continuous dependent variable does not change the model building steps; you would perform linear regression instead of logistic regression and the output would change accordingly. Note: To perform regression analysis in SVS the genotype data must be encoded numerically. If necessary you can recode your data by going to Edit >Recode >Recode Genotypes and selecting the radio button Encode genotypes numerically based on genetic model: and choosing one of the provided numeric models. Currently, multivariate regression (more than one dependent variable in the model) is not supported. A single dependent column must be indicated and must contain real-, integer-, or binary-values. If you are interested in building a model to predict more than one variable, performing several simple regressions is recommended. A categorical variable must be converted into a binary- or integer-valued variable if you wish make it dependent in the model. 2

7 2. Controlling For Confounding Variables If you build a model and the response is highly correlated with one or more of the predictors (or confounded by one or more variables), these predictors can suppress possible real associations. For the regression model, the additive genetic model covariates will predict the case/control status which is known to be correlated with blood pressure. You will see that the log10 P-values when testing the relationship between the two blood pressure phenotypes (sbp and dbp) and case status are very high and could explain other possible significant associations. A. Full Model Only First we will perform regression on every column using a model with an intercept and one predictor, or covariate, represented by each column other than the column assigned as the dependent variable. This technique computes the significance of that predictor using the full model and a reduced model with just an intercept. This technique will individually assess the relationship between the dependent variable and the covariate (predictor). Open the Pheno + Geno - Sheet 1 spreadsheet. First you must indicate a dependent variable. To do this, leftclick once on the Case/Control column header (the column should turn magenta). Choose Numeric >Numeric Regression Analysis. Select Regress on each of the numeric columns. Open the Output Parameters tab and check Output data for P-P/Q-Q plots. This option includes several extra columns in the resulting spreadsheet, including a log10 P column which is useful for plotting. Confirm your options with Figure 1 and Figure 2 and click Run. After the regression runs, a Regression Results spreadsheet will appear. Because we will be doing several regression analyses, we will rename each node appropriately. From the Project Navigator, right click on the Regression Results node and select Rename Node. Rename Regression Results to Regression Results - All Columns. Open the Regression Results - All Columns spreadsheet again and take a look at the log10 Full-Model P column. The first row represents the blood pressure covariate (SBP) and as you can see, it has a very large log10 P value. Scroll over to the Odds Ratio column (column 10) and you will see that the odds of a case after an increase in 1 unit of SBP or DBP is about 1.1 times the odds before the increase. A 5 unit increase in blood pressure would correspond to a five-fold increase in the odds of that individual being a case. On closer inspection high blood pressure is very common among cases and is confounding the results A plot of the results will allow for comparison with the model that accounts for SBP, as we will see later. In the Regression Results - All Columns spreadsheet, right-click on the log10 Full-Model P column (column 2) and choose Plot Variable in GenomeBrowse. Zoom into chromosome 1 by double clicking on the cytoband track and the following plot (Figure 3) appears. 3

8 Regression with Covariates Tutorial, Release 8.1 Figure 1. Regression window A Figure 2. Regression window B 4 2. Controlling For Confounding Variables

9 Regression with Covariates Tutorial, Release 8.1 Figure 3. P-value plot all columns Notice that there are two areas of possible interest. Keep these in mind when we look at the p-values, after correcting for SBP. B. Full vs. Reduced Model The next step is to correct for the confounding variables and compare to the results from the Full Model. Correcting for a confounding variable adds this covariate to both the reduced and full models. Then for all of the other covariates, the full model contains an intercept, the SBP predictor and that covariate. The reduced model contains only the intercept and SBP. The comparison between the full and reduced models allows for individual assessment of each covariate after accounting for SBP. Open the Pheno + Geno - Sheet 1 spreadsheet. The Case/Control column should still be selected as the dependent variable. Select Numeric >Numeric Regression Analysis to bring up the Regression Analysis window. This time choose Correct for covariate(s) underneath Regress on each of the numeric columns. The Reduced Model Covariates section should activate. Next to the Reduced Model Covariates box, click Add Covariate. From the resulting list check SBP and click Add and then Close to close this window. The rest of the options should have remained the same from the last analysis. Confirm that your parameters match those in Figure 4 and click Run. From the Project Navigator rename the Regression Results to Regression Results Corrected for SBP. Notice in the resulting spreadsheet that since SBP has been corrected for, it is no longer listed in the results spreadsheet as a covariate. Next, add these results to our first plot to compare the two analyses. Open the Plot of Column -log10 Full-Model P from Regression Results - All Columns plot. B. Full vs. Reduced Model 5

10 Regression with Covariates Tutorial, Release 8.1 Figure 4. Regression window Click the top -log10 Full-Model P node in the Plot Tree, then under the Controls window on the Add tab click Add Item. From the Add Data Sources dialog, click the Project button and select the Regression Results - Corrected for SBP spreadsheet and click -log10 FvR Model P. It should look like Figure 5 then press Plot & Close. Now change the color of the new data points by clicking the -log10 FvR Model P node and under the Display tab click the blue box under Style* and change it to green. Now we only see one area of interest in green compared to the two blue regions that showed high log10 P values. The genetic region that was significant in the previous analysis is probably also associated with high blood pressure and was thus confounding the results. The region that shows an association has even larger log10 P values after correcting for this confounding variable Controlling For Confounding Variables

11 Regression with Covariates Tutorial, Release 8.1 Figure 5. Add Data Sources window Figure 6. P-value plot comparison B. Full vs. Reduced Model 7

12 3. Accounting for SNP Correlation If the regression analysis uses the entire genome as predictors, then it is recommended that the Use a moving window of regressors option is selected. A moving window tries to incorporate consecutive SNPs, which might be in high linkage disequilibrium, providing information not captured with single variable regression. This can also be accomplished by detecting Haplotype blocks to use for regression. For this analysis, we will use a dynamic moving window size with a fixed number of base pairs. A. Using a Moving Window As SBP is a known confounding variable, it is included as a reduced model regressor for this analysis. Open the Pheno + Geno - Sheet 1 spreadsheet. The Case/Control column should still be selected as the dependent variable. Select Numeric >Numeric Regression Analysis to bring up the Regression window. This time choose Regress on a moving window with parameters: radio button under Selection Parameters. Then choose Dynamic window over mapped numeric columns with size kb and with max markers: 20. Add SBP as a Reduced Model Regressor in the same manner as before. Confirm that your parameters match those in Figure 7 and click Run. From the Project Navigator rename the Regression Results to Regression Results Moving Window as before. In the Regression Results Moving Window spreadsheet, right-click on the log10 FvR Model P column (column 2) and choose Plot Variable in GenomeBrowse. Then once again zoom into chromosome 1. As you can see from Figure 8, this plot is similar to the previously corrected regression, however the peak around 1q32.2 has a maximum log10 P-value of around 8 on the y-axis, compared to before when it had a maximum of around 10. 8

13 Regression with Covariates Tutorial, Release 8.1 Figure 7. Regression Options (Moving Window) Figure 8. P-value plot (Moving Window) A. Using a Moving Window 9

14 4. Using the Regression Module for Model Comparison The SVS 8 regression module can also be used for model selection. This is a more classical way of thinking about regression, comparing the added effect of full model regressors with a full vs. reduced model test. For this demonstration we will subset out the non-genetic information and only use the phenotypes as covariates. Open the Pheno + Geno - Sheet 1 spreadsheet and choose Select >Activate by Chromosomes, then uncheck 1 and click OK. This will create Pheno + Geno Sheet 2. Select Numeric >Numeric Regression Analysis to bring up the Regression window. This time choose Perform single regression with selected covariates under Selection Parameters. The covariates that are added as reduced model covariates are automatically included in the full model. Therefore to test for the effect of a regressor after correcting for the covariates selected for the reduced model, add the additional full model regressors to the Full model covariates: box. Check Correct for Covariate(s) and then under Reduced Model Covariates choose Add Covariate. Check both SBP and Previous Event and then click Add. Click Close to close the window. Next, add Chng in Dbp in the same manner under Full Model Covariates. Make sure the window looks like Figure 9 and click Run. This will test whether Chng in Dbp improves the fit of the model by explaining more of the dependent variable response after accounting for SBP and Previous Event. More specifically, the following models are used in the test: Full Model: Reduced Model: Case/Control i β 0 + β 1 * (SBP) + β 2 * (Previous Event) + β 3 * (Chng in Dbp) + ε i Case/Control i β 0 + β 1 * (SBP) + β 2 * (Previous Event) + ε i And the hypotheses are: H0: β 3 = 0 and Ha: β 3 0 The Regression Statistics Viewer shows a P-value of about for the full vs. reduced model (Figure 10). This means that Chng in Dbp is useful in predicting Case/Control status after accounting for SBP and Previous Event. For more information about the additional outputs in the Regression Statistics Viewer, see the Regression Analysis chapter in the SVS manual. 10

15 Regression with Covariates Tutorial, Release 8.1 Figure 9. Regression Options (perform regression with selected covariates only) 11

16 Regression with Covariates Tutorial, Release 8.1 Figure 10. Regression Statistics Viewer Using the Regression Module for Model Comparison