BioinformaticsBioinformaticsR for BioinformaticsR for Bioinformatics

PART IIPART II

Kristel Van Steen, PhD, ScDKristel Van Steen, PhD, ScD

(kristel.vansteen@ulg.ac.be)(kristel.vansteen@ulg.ac.be)

Université de Liege - Institut MontefioreUniversité de Liege - Institut Montefiore

2008-20092008-2009

Simplified Epistasis TestingSimplified Epistasis Testing

We shall now use logistic regression in R to test for epistatic interactions between We shall now use logistic regression in R to test for epistatic interactions between locus 3 and another unlinked locus (locus 5). An epistatic interaction means that locus 3 and another unlinked locus (locus 5). An epistatic interaction means that the combined effect of locus 3 and 5 is greater than the product (on the odds scale) the combined effect of locus 3 and 5 is greater than the product (on the odds scale) or the sum (on the log odds scale) of the locus 3 and locus 5 individual effects. or the sum (on the log odds scale) of the locus 3 and locus 5 individual effects.

First get rid of the data in the memory and read in the new data. This data is the First get rid of the data in the memory and read in the new data. This data is the same as the original pedfile, but with an additional column giving genotype at same as the original pedfile, but with an additional column giving genotype at (unlinked) locus 5: (unlinked) locus 5:

detach(casecon) detach(casecon) newcasecon <- read.table("newcasecondata.txt", header=T)newcasecon <- read.table("newcasecondata.txt", header=T)attach(newcasecon) attach(newcasecon)

You can look at the data by typing You can look at the data by typing

fix(newcasecon) fix(newcasecon)

Cordell practical Cordell practical (see statistical genetics (see statistical genetics

class)class) Next create appropriate genotype and case variables: Next create appropriate genotype and case variables:

case <- affected-1 case <- affected-1

g3 <- genotype(loc3_1, loc3_2) g3 <- genotype(loc3_1, loc3_2) g5 <- genotype(loc5_1, loc5_2) g5 <- genotype(loc5_1, loc5_2)

The individual effects at locus 3 and 5 are now coded by the variables g3 The individual effects at locus 3 and 5 are now coded by the variables g3 and g5. We can test for association at each locus separately: and g5. We can test for association at each locus separately:

gcontrasts(g3) <- "genotype" gcontrasts(g3) <- "genotype" logit (case ~ g3) logit (case ~ g3) anova(logit (case ~ g3)) anova(logit (case ~ g3))

gcontrasts(g5) <- "genotype" gcontrasts(g5) <- "genotype" logit (case ~ g5) logit (case ~ g5) anova(logit (case ~ g5))anova(logit (case ~ g5))

In order to investigate epistasis, it is more convenient to create new In order to investigate epistasis, it is more convenient to create new variables that code numerically for the number of copies of allele 2 in each variables that code numerically for the number of copies of allele 2 in each genotypes genotypes

count3<-allele.count(g3,2) count3<-allele.count(g3,2) count5<-allele.count(g5,2) count5<-allele.count(g5,2)

Check you understand how variables count3 and count5 relate to g3 and Check you understand how variables count3 and count5 relate to g3 and g5 by typing g5 by typing

g3 g3 count3 count3

g5 g5 count5 count5

We then create a variable that codes for the combined effect of locus 3 and 5 as We then create a variable that codes for the combined effect of locus 3 and 5 as follows: follows:

combo<-10*count3+count5 combo<-10*count3+count5

Check you understand how the 'combo' variable relates to g3 and g5 by typing Check you understand how the 'combo' variable relates to g3 and g5 by typing

g3 g3 g5 g5 combo combo

Now we need to code each of these variables as 'factors' which means we simply Now we need to code each of these variables as 'factors' which means we simply consider the numeric codes to act as labels for the different categories rather than consider the numeric codes to act as labels for the different categories rather than having numeric meaning: having numeric meaning:

fact3<-factor(count3) fact3<-factor(count3) fact5<-factor(count5) fact5<-factor(count5) factcombo<-factor(combo) factcombo<-factor(combo)

Check that the analysis with the 'factors' gives the same results as you found previously with the Check that the analysis with the 'factors' gives the same results as you found previously with the genotype variables: genotype variables:

anova(logit (case ~ fact3)) anova(logit (case ~ fact3)) anova(logit (case ~ fact5)) anova(logit (case ~ fact5))

Now test whether there is significant epistasis by typing Now test whether there is significant epistasis by typing

anova(logit(case ~ fact3 + fact5 + factcombo)) anova(logit(case ~ fact3 + fact5 + factcombo)) 1-pchisq(9.59,4) 1-pchisq(9.59,4)

This first fits the individual locus factors, and then adds in the extra effect of looking at the model with This first fits the individual locus factors, and then adds in the extra effect of looking at the model with epistasis included (i.e. a model with 9 estimated parameters corresponding to the 9 genotype epistasis included (i.e. a model with 9 estimated parameters corresponding to the 9 genotype combinations), and tests the difference between the models. You should get a chi-squared of 9.59 on combinations), and tests the difference between the models. You should get a chi-squared of 9.59 on 4 df with p value 0.048 i.e. there is marginal evidence of epistasis. 4 df with p value 0.048 i.e. there is marginal evidence of epistasis.

The above test is valid for testing for epistasis between linked or unlinked loci, although it does not The above test is valid for testing for epistasis between linked or unlinked loci, although it does not allow for haplotype (phase) effects between linked loci. A more powerful test for epistasis between allow for haplotype (phase) effects between linked loci. A more powerful test for epistasis between UNLINKED LOCI ONLY UNLINKED LOCI ONLY is to use 'case-only' analysis and test whether the genotypes at one locus is to use 'case-only' analysis and test whether the genotypes at one locus predict those at the other, in the cases alone. This is only valid at unlinked loci, because at linked loci predict those at the other, in the cases alone. This is only valid at unlinked loci, because at linked loci we expect genotypes at one locus to predict those at the other (even in controls) due to linkage we expect genotypes at one locus to predict those at the other (even in controls) due to linkage disequilibrium. disequilibrium.

To do this, we can use a chi squared test to look for correlation (association) between the loci To do this, we can use a chi squared test to look for correlation (association) between the loci within the case and control groups separately. within the case and control groups separately.

First we need to set up 2 new vectors of genotypes for loci 3 and 5, using only the cases. To do First we need to set up 2 new vectors of genotypes for loci 3 and 5, using only the cases. To do this, we can take advantage of the fact that the data has been ordered in such a way that cases this, we can take advantage of the fact that the data has been ordered in such a way that cases are the first 384 observations. (Check this by typing case or fix(newcasecon) ). So we can create are the first 384 observations. (Check this by typing case or fix(newcasecon) ). So we can create genotype vectors just for the cases using the following commands genotype vectors just for the cases using the following commands

caseg3<-g3[1:384] caseg3<-g3[1:384] caseg5<-g5[1:384] caseg5<-g5[1:384]

Take a look at the vectors you have created by typing Take a look at the vectors you have created by typing

caseg3 caseg3 caseg5 caseg5

Now do a chi-squared test on the genotype variables to see if they are correlated with each other: Now do a chi-squared test on the genotype variables to see if they are correlated with each other:

table(caseg3,caseg5) table(caseg3,caseg5) chisq.test(caseg3,caseg5) chisq.test(caseg3,caseg5)

You should find much more significant evidence of epistasis (p value 0.0018) than you did You should find much more significant evidence of epistasis (p value 0.0018) than you did using logistic regression. This is not surprising as the case-only test of interaction is a more using logistic regression. This is not surprising as the case-only test of interaction is a more powerful test. However, the case-only test does rely on the assumption that the two powerful test. However, the case-only test does rely on the assumption that the two genotype variables g3 and g5 are uncorrelated in the general population. Strictly speaking, genotype variables g3 and g5 are uncorrelated in the general population. Strictly speaking, we cannot test this assumption as we do not have a population-based control sample (our we cannot test this assumption as we do not have a population-based control sample (our controls are all unaffected). However, if the disease is rare, our controls should be controls are all unaffected). However, if the disease is rare, our controls should be reasonably close to an unselected sample. So we can use them to see if the genotype reasonably close to an unselected sample. So we can use them to see if the genotype variables g3 and g5 are uncorrelated in the control population: variables g3 and g5 are uncorrelated in the control population:

contg3<-g3[385:1056] contg3<-g3[385:1056] contg5<-g5[385:1056] contg5<-g5[385:1056]

contg3 contg3 contg5 contg5

table(contg3,contg5) table(contg3,contg5) chisq.test(contg3,contg5) chisq.test(contg3,contg5)

You should find a non-significant p value (p=0.99). This suggests that the case-only analysis You should find a non-significant p value (p=0.99). This suggests that the case-only analysis we did is valid, so there is indeed some reasonable (p=0.002) evidence for statistical we did is valid, so there is indeed some reasonable (p=0.002) evidence for statistical interaction between these loci. interaction between these loci.

Running the command lines in RRunning the command lines in R

to test for epistasisto test for epistasis

ResourcesResources

for microarray analysis:for microarray analysis:

http://www.nslij-genetics.org/microarray/http://www.nslij-genetics.org/microarray/

Review Paper: Review Paper:

gene expression analysisgene expression analysis

(Slonim et al 2002)(Slonim et al 2002)