SNPassoc 2.0.2

The `SNPassoc`

package contains facilities for data manipulation, tools for exploratory data analysis, convenient graphical facilities, and tools for assessing genetic association for both quantitative and categorial (case-control) traits in whole genome approaches. Genome-based studies are normally analyzed using a multistage approach. In the first step researchers are interested in assessing association between the outcome and thousands of SNPs. In a second and possibly third step, medium/large scale studies are performed in which only a few hundred of SNPs, those with a putative association found in the first step, are genotyped. `SNPassoc`

is specially designed for analyzing this kind of designs. In addition, a convenience-based approach (select variants on the basis of logistical considerations such as the ease and cost of genotyping) can also be analyzed using `SNPassoc`

. Different genetic models are
also implemented in the package. Analysis of multiple SNPs can be analyzed using either haplotype or gene-gene interaction approaches.

This document is an updated version of the initial vignette that was published with the SNPassoc paper González et al. (2007). It contains a more realistic example belonging to a real dataset. The original vignette is still available here.

SNP data are typically available in text format or Excel spreadsheets which are easily uploaded in `R`

as a data frame. Here, as an illustrative example, we are analyzing a dataset containing epidemiological information and 51 SNPs from a case-control study on asthma. The data is available within `SNPassoc`

and can be loaded by

Then, the data is loaded into the R session by

```
data(asthma, package = "SNPassoc")
str(asthma, list.len=9)
```

```
'data.frame': 1578 obs. of 57 variables:
$ country : Factor w/ 10 levels "Australia","Belgium",..: 5 5 5 5 5 5 5 5 5 5 ...
$ gender : Factor w/ 2 levels "Females","Males": 2 2 2 1 1 1 1 2 1 1 ...
$ age : num 42.8 50.2 46.7 47.9 48.4 ...
$ bmi : num 20.1 24.7 27.7 33.3 25.2 ...
$ smoke : int 1 0 0 0 0 1 0 0 0 0 ...
$ casecontrol: int 0 0 0 0 1 0 0 0 0 0 ...
$ rs4490198 : Factor w/ 3 levels "AA","AG","GG": 3 3 3 2 2 2 3 2 2 2 ...
$ rs4849332 : Factor w/ 3 levels "GG","GT","TT": 3 2 3 2 1 2 3 3 2 1 ...
$ rs1367179 : Factor w/ 3 levels "CC","GC","GG": 2 2 2 3 3 3 2 3 3 3 ...
[list output truncated]
```

`asthma[1:5, 1:8]`

```
country gender age bmi smoke casecontrol rs4490198 rs4849332
1 Germany Males 42.80630 20.14797 1 0 GG TT
2 Germany Males 50.22861 24.69136 0 0 GG GT
3 Germany Males 46.68857 27.73230 0 0 GG TT
4 Germany Females 47.86311 33.33187 0 0 AG GT
5 Germany Females 48.44079 25.23634 0 1 AG GG
```

We observe that we have case-control status (0: control, 1: asthma) and another 4 variables encoding the country of origin, gender, age, body mass index (bmi) and smoking status (0: no smoker, 1: ex-smoker, 2: current smoker). There are 51 SNPs whose genotypes are given by the alleles names.

To start the analysis, we must indicate which columns of the dataset `asthma`

contain the SNP data, using the `setupSNP`

function. In our example, SNPs start from column 7 onwards, which we specify in argument *colSNPs*

```
library(SNPassoc)
asthma.s <- setupSNP(data=asthma, colSNPs=7:ncol(asthma), sep="")
```

This is an alternative way of determining the columns containing the SNPs

```
idx <- grep("^rs", colnames(asthma))
asthma.s <- setupSNP(data=asthma, colSNPs=idx, sep="")
```

The argument *sep* indicates the character separating the alleles. The default value is ’‘/´´. In our case, there is no separating character, so that, we set *sep=""*. The argument *name.genotypes* can be used when genotypes are available in other formats, such as 0, 1, 2 or’‘norm´´,’‘het´´,’’mut´´. The purpose of the `setupSNP`

function is to assign the class *snp* to the SNPs variables, to which `SNPassoc`

methods will be applied. The function labels the most common genotype across subjects as the reference one. When numerous SNPs are available, the function can be parallelized through the argument *mc.cores* that indicates the number of processors to be used. We can verify that the SNP variables are given the new class *snp*

`head(asthma.s$rs1422993)`

```
[1] G/G G/T G/G G/T G/T G/G
Genotypes: G/G G/T T/T
Alleles: G T
```

`class(asthma.s$rs1422993)`

`[1] "snp" "factor"`

and summarize their content with `summary`

`summary(asthma.s$rs1422993)`

```
Genotypes:
frequency percentage
G/G 903 57.224335
G/T 570 36.121673
T/T 105 6.653992
Alleles:
frequency percentage
G 2376 75.28517
T 780 24.71483
HWE (p value): 0.250093
```

which shows the genotype and allele frequencies for a given SNP, testing for Hardy-Weinberg equilibrium (HWE). We can also visualize the results in a plot by

`plot(asthma.s$rs1422993)`

The argument *type* helps to get a pie chart

`plot(asthma.s$rs1422993, type=pie)`

The *summary* function can also be applied to the whole dataset

`summary(asthma.s, print=FALSE)`

```
alleles major.allele.freq HWE missing (%)
rs4490198 A/G 59.2 0.174133 0.6
rs4849332 G/T 61.8 0.522060 0.1
rs1367179 G/C 81.4 0.738153 1.0
rs11123242 C/T 81.7 0.932898 0.6
rs13014858 G/A 58.3 0.351116 0.1
rs1430094 G/A 66.9 0.305509 0.4
rs1430093 C/A 66.6 0.817701 3.5
rs746710 G/C 51.5 0.614368 0.0
rs1430090 T/G 70.0 0.025180 1.6
rs6737251 C/T 69.3 0.235996 0.3
rs11685217 C/T 80.1 0.009462 4.5
rs1430097 C/A 65.1 0.738166 1.0
rs10496465 A/G 85.8 0.917997 0.6
rs3756688 T/C 63.9 0.154632 0.6
rs2303063 A/G 53.0 0.722069 1.1
rs1422993 G/T 75.3 0.250093 0.0
rs2400478 G/A 62.6 0.256786 0.9
rs714588 A/G 54.9 0.838329 0.8
rs1023555 T/A 76.8 0.943443 0.5
rs898070 G/A 62.6 1.000000 0.6
rs963218 C/T 53.2 0.389387 0.3
rs1419835 C/T 78.2 0.505391 0.6
rs765023 T/C 64.5 0.030513 6.9
rs1345267 A/G 61.0 0.112183 0.1
rs324381 G/A 64.6 0.242223 11.6
rs184448 T/G 55.9 0.008446 2.2
rs324396 C/T 71.2 0.197291 0.3
rs324957 G/A 57.0 0.007417 0.4
rs324960 C/T 66.6 0.077777 1.1
rs10486657 C/T 81.3 0.672703 4.3
rs324981 A/T 53.2 0.048438 0.2
rs1419780 C/G 80.8 0.569652 0.2
rs325462 T/A 51.0 0.337862 0.3
rs727162 G/C 78.5 0.765708 0.0
rs10250709 G/A 65.4 0.266434 0.0
rs6958905 T/C 64.7 0.377472 0.4
rs10238983 T/C 75.7 0.216435 0.4
rs4941643 A/G 54.1 0.635887 7.2
rs3794381 C/G 71.7 0.652089 7.1
rs2031532 G/A 65.0 0.911918 0.0
rs2247119 T/C 71.5 0.457710 0.5
rs8000149 T/C 63.2 0.588077 0.4
rs2274276 G/C 57.0 0.571386 0.6
rs7332573 G/T 91.5 0.869947 1.5
rs3829366 T/A 51.6 0.722626 1.3
rs6084432 G/A 83.7 0.266716 0.6
rs512625 G/A 69.5 0.905395 0.4
rs3918395 G/T 86.8 0.508732 1.2
rs2787095 G/C 60.2 0.102053 0.8
rs2853215 G/A 73.0 0.249516 0.2
```

showing the SNP labels with minor/major allele format, the major allele frequency the HWE test and the percentage of missing genotypes. Missing values can be further explored plotting with

`plotMissing(asthma.s, print.labels.SNPs = FALSE)`

This plot can be used to inspect if missing values appear randomly across individuals and SNPs. In our case, we can see that the missing pattern may be considered random, except for three clusters in consecutive SNPs (large black squares). These individuals should be further checked for possible problems with genotyping.

Genotyping of SNPs needs to pass quality control measures. Aside from technical details that need to be considered for filtering SNPs with low quality, genotype calling error can be detected by a HWE test. The test compares the observed genotype frequencies with those expected under random mating, which follows when the SNPs are in the absence of selection, mutation, genetic drift, or other forces. Therefore, HWE must be checked only in controls. There are several tests described in the literature to verify HWE. In `SNPassoc`

HWE is tested for all the bi-allelic SNP markers using a fast exact test Wigginton, Cutler, and Abecasis (2005) implemented in the *tableHWE* function.

```
hwe <- tableHWE(asthma.s)
head(hwe)
```

```
HWE (p value)
rs4490198 0.1741325
rs4849332 0.5220596
rs1367179 0.7381531
rs11123242 0.9328981
rs13014858 0.3511162
rs1430094 0.3055089
```

We observe that the first SNPs in the dataset are under HWE since their P-values rejecting the HWE hypothesis (null hypothesis) are larger than 0.05. However, when tested in control samples only, by stratifying by cases and controls

```
hwe2 <- tableHWE(asthma.s, casecontrol)
#SNPs is HWE in the whole sample but not controls
snpNHWE <- hwe2[,1]>0.05 & hwe2[,2]<0.05
rownames(hwe2)[snpNHWE]
```

`[1] "rs1345267"`

`hwe2[snpNHWE,]`

```
all groups 0 1
0.11218285 0.04956349 0.81604706
```

We see that rs1345267 is not in HWE within controls because its P-value is <0.05. Notice that one is interested in keeping those SNPsthat do not reject the null hypothesis. As several SNPs are tested, multiple comparisons must be considered. In this particular setting, a threshold of 0.001 is normally considered. As a quality control measure, it is not necessary to be as conservative as in those situations where false discovery rates need to be controlled.

SNPs that do not pass the HWE test must be removed form further analyses. We can recall *setupSNP* and indicate the columns of the SNPs to be kept

```
snps.ok <- rownames(hwe2)[hwe2[,2]>=0.001]
pos <- which(colnames(asthma)%in%snps.ok, useNames = FALSE)
asthma.s <- setupSNP(asthma, pos, sep="")
```

Note that in the variable *pos* we redefine the SNP variables to be considered as class *snp*.

We are interested in finding those SNPs associated with asthma status that is encoded in the variable *casecontrol*. We first illustrate the association between case-control status and the SNP rs1422993. The association analysis for all genetic models is performed by the function *association* that regresses *casecontrol* on the variable rs1422993 from the dataset *asthma.s* that already contains the SNP variables of class *snp*.

`association(casecontrol ~ rs1422993, data = asthma.s)`

```
SNP: rs1422993 adjusted by:
0 % 1 % OR lower upper p-value AIC
Codominant
G/G 730 59.0 173 50.9 1.00 0.017768 1642
G/T 425 34.3 145 42.6 1.44 1.12 1.85
T/T 83 6.7 22 6.5 1.12 0.68 1.84
Dominant
G/G 730 59.0 173 50.9 1.00 0.007826 1642
G/T-T/T 508 41.0 167 49.1 1.39 1.09 1.77
Recessive
G/G-G/T 1155 93.3 318 93.5 1.00 0.877863 1649
T/T 83 6.7 22 6.5 0.96 0.59 1.57
Overdominant
G/G-T/T 813 65.7 195 57.4 1.00 0.005026 1641
G/T 425 34.3 145 42.6 1.42 1.11 1.82
log-Additive
0,1,2 1238 78.5 340 21.5 1.22 1.01 1.47 0.040151 1644
```

The function *association* follows the usual syntax of R modelling functions with the difference that the variables in the model that are of class *snp* are tested using different genetic models. In our example, we observe that all genetic models but the recessive one are statistically significant. *association* also fits the overdominant model, which compares the two homozygous genotypes versus the heterozygous one. This genetic model of inheritance is biologically rare although it has been linked to sickle cell anemia in humans. The result table describes the number of individuals in each genotype across cases and controls. The ORs and CI-95% are also computed. The last column describes the AIC (Akaike information criteria) that can be used to decide which is the best model of inheritance; the lower the better the model is.

In the example, one may conclude that rs1422993 is associated with asthma and that, for instance, the risk of being asthmatic is 39% higher in people having at least one alternative allele (T) with respect to individuals having none (dominant model). This risk is statistically significant since the CI-95% does not contain 1, the P-value is 0.0078<0.022, or the P-value of the max-statistics is 0.01

`maxstat(asthma.s$casecontrol, asthma.s$rs1422993)`

```
dominant recessive log-additive MAX-statistic Pr(>z)
[1,] 7.073 0.024 4.291 7.073 0.0142 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

If an expected model of inheritance is hypothesized, the association analysis for the model can be specified in the argument *model*, which by default test all models,

`association(casecontrol ~ rs1422993, asthma.s, model="dominant")`

```
SNP: rs1422993 adjusted by:
0 % 1 % OR lower upper p-value AIC
Dominant
G/G 730 59 173 50.9 1.00 0.007826 1642
G/T-T/T 508 41 167 49.1 1.39 1.09 1.77
```

Association tests are typically adjusted by covariates, which are incorporated in the model in the usual form

`association(casecontrol ~ rs1422993 + country + smoke, asthma.s)`

```
SNP: rs1422993 adjusted by: country smoke
0 % 1 % OR lower upper p-value AIC
Codominant
G/G 728 59.1 173 51.0 1.00 0.06940 1408
G/T 423 34.3 144 42.5 1.38 1.05 1.82
T/T 81 6.6 22 6.5 1.06 0.61 1.85
Dominant
G/G 728 59.1 173 51.0 1.00 0.03429 1407
G/T-T/T 504 40.9 166 49.0 1.33 1.02 1.73
Recessive
G/G-G/T 1151 93.4 317 93.5 1.00 0.79338 1411
T/T 81 6.6 22 6.5 0.93 0.54 1.60
Overdominant
G/G-T/T 809 65.7 195 57.5 1.00 0.02147 1406
G/T 423 34.3 144 42.5 1.37 1.05 1.80
log-Additive
0,1,2 1232 78.4 339 21.6 1.19 0.96 1.46 0.11191 1409
```

ORs for stratified analysis on given categorical covariates are used to verify whether the risk is constant across groups

`association(casecontrol ~ rs1422993 + survival::strata(gender), asthma.s)`

```
SNP: rs1422993 adjusted by: survival::strata(gender)
0 % 1 % OR lower upper p-value AIC
Codominant
G/G 730 59.0 173 50.9 1.00 0.022940 1634
G/T 425 34.3 145 42.6 1.42 1.11 1.83
T/T 83 6.7 22 6.5 1.09 0.66 1.80
Dominant
G/G 730 59.0 173 50.9 1.00 0.011144 1633
G/T-T/T 508 41.0 167 49.1 1.37 1.07 1.74
Recessive
G/G-G/T 1155 93.3 318 93.5 1.00 0.805330 1640
T/T 83 6.7 22 6.5 0.94 0.58 1.53
Overdominant
G/G-T/T 813 65.7 195 57.4 1.00 0.006378 1632
G/T 425 34.3 145 42.6 1.41 1.10 1.80
log-Additive
0,1,2 1238 78.5 340 21.5 1.21 1.00 1.46 0.055231 1636
```

We can see, for instance, that the dominant model is significant only in males. The subset argument allows fitting the model in a subgroup of individuals

```
association(casecontrol ~ rs1422993, asthma.s,
subset=country=="Spain")
```

```
SNP: rs1422993 adjusted by:
0 % 1 % OR lower upper p-value AIC
Codominant
G/G 179 54.6 22 44.9 1.00 0.3550 295.2
G/T 125 38.1 24 49.0 1.56 0.84 2.91
T/T 24 7.3 3 6.1 1.02 0.28 3.66
Dominant
G/G 179 54.6 22 44.9 1.00 0.2059 293.7
G/T-T/T 149 45.4 27 55.1 1.47 0.81 2.70
Recessive
G/G-G/T 304 92.7 46 93.9 1.00 0.7576 295.2
T/T 24 7.3 3 6.1 0.83 0.24 2.85
Overdominant
G/G-T/T 203 61.9 25 51.0 1.00 0.1502 293.2
G/T 125 38.1 24 49.0 1.56 0.85 2.85
log-Additive
0,1,2 328 87.0 49 13.0 1.23 0.77 1.96 0.3816 294.5
```

These analyses can be also be performed in quantitative traits, such as body mass index, since *association* function automatically selects the error distribution of the regression analysis (either Gaussian or binomial).

`association(bmi ~ rs1422993, asthma.s) `

```
SNP: rs1422993 adjusted by:
n me se dif lower upper p-value AIC
Codominant
G/G 896 25.53 0.1446 0.000000 0.9069 9069
G/T 565 25.50 0.1834 -0.027059 -0.4874 0.4332
T/T 105 25.71 0.4676 0.178076 -0.7057 1.0619
Dominant
G/G 896 25.53 0.1446 0.000000 0.9818 9067
G/T-T/T 670 25.54 0.1710 0.005089 -0.4324 0.4426
Recessive
G/G-G/T 1461 25.52 0.1135 0.000000 0.6694 9067
T/T 105 25.71 0.4676 0.188540 -0.6769 1.0540
Overdominant
G/G-T/T 1001 25.55 0.1383 0.000000 0.8424 9067
G/T 565 25.50 0.1834 -0.045739 -0.4965 0.4050
log-Additive
0,1,2 0.033951 -0.3153 0.3832 0.8489 9067
```

For BMI, *association* tests whether the difference between means is statistically significant, rather than computing an OR.

For multiple SNP data, our objective is to identify the variants that are significantly associated with the trait. The most basic strategy is, therefore, to fit an association test like the one described above for each of the SNPs in the dataset and determine which of those associations are significant. The massive univariate testing is the most widely used analysis method for *omic* data because of its simplicity. In *SNPassoc*, this type of analysis is done with the function *WGassociation*

```
ans <- WGassociation(casecontrol, data=asthma.s)
head(ans)
```

```
comments codominant dominant recessive overdominant log-additive
rs4490198 - 0.52765 0.29503 0.96400 0.29998 0.49506
rs4849332 - 0.96912 0.92986 0.84806 0.82327 0.97049
rs1367179 - 0.62775 0.59205 0.35786 0.86419 0.43994
rs11123242 - 0.68622 0.67596 0.39801 0.92878 0.52009
rs13014858 - 0.52578 0.26739 0.88011 0.34966 0.40897
rs1430094 - 0.13375 0.10569 0.54432 0.04490 0.36611
```

Here, only the outcome is required in the formula argument (first argument) since the function successively calls *association* on each of the variables of class *snp* within *data*. The function returns the P-values of association of each SNP under each genetic model. Covariates can also be introduced in the model

```
ans.adj <- WGassociation(casecontrol ~ country + smoke, asthma.s)
head(ans.adj)
```

`SNPassoc`

is computationally limited on large genomic data. The computing time can be reduced by parallelization, specifying in the argument *mc.cores* the number of computing cores to be used. Alternatively, the function *scanWGassociation*, a C compiled function, can be used to compute a predetermined genetic model across all SNPs, passed in the argument *model*, which by default is the additive model

`ans.fast <- scanWGassociation(casecontrol, asthma.s)`

**NOTE**: This function is not available on the `SNPassoc`

version available on CRAN. The user can install the development version available on GitHub to get access to this function just executing

`devtools::install_github("isglobal-brge/SNPassoc")`

The P-values obtained from massive univariate analyses are visualized with the generic *plot* function

`plot(ans)`

This produces a Manhattan plot of the -log10(P-values) for all the SNPs over all models. It shows the nominal level of significance and the Bonferroni level, which is the level corrected by the multiple testing across all SNPs. The overall hypothesis of massive univariate association tests is whether there is any SNP that is significantly associated with the phenotype. As multiple SNPs are tested, the probability of finding at least one significant finding increases if we do not lower the significance threshold. The Bonferroni correction lowers the threshold by the number of SNPs tested (0.0001=0.05/51). In the Manhattan plotof our analysis, we see that no SNP is significant at the Bonferroni level, and therefore there is no SNP that is significantly associated with asthma.

Maximum-statistic (see González et al. (2008)) can also be used to test association between asthma status and SNPs

```
ans.max <- maxstat(asthma.s, casecontrol)
ans.max
```

```
dominant recessive log-additive MAX-statistic Pr(>z)
rs4490198 1.097 0.002 0.466 1.097 0.5026
rs4849332 0.008 0.037 0.001 0.037 0.9764
rs1367179 0.287 0.845 0.602 0.845 0.5888
rs11123242 0.175 0.714 0.417 0.714 0.6388
rs13014858 1.230 0.023 0.683 1.230 0.4640
rs1430094 2.617 0.368 0.821 2.617 0.2070
rs1430093 1.051 0.042 0.743 1.051 0.5184
rs746710 0.728 0.679 1.051 1.051 0.5165
rs1430090 0.172 0.463 0.000 0.463 0.7428
rs6737251 0.143 0.156 0.217 0.217 0.8686
rs11685217 0.894 0.030 0.705 0.894 0.5682
rs1430097 0.003 0.183 0.029 0.183 0.8883
rs10496465 0.003 0.020 0.008 0.020 0.9872
rs3756688 0.016 0.738 0.266 0.738 0.6257
rs2303063 0.060 1.271 0.658 1.271 0.4527
rs1422993 7.073 0.024 4.291 7.073 0.0183 *
rs2400478 1.662 0.056 1.055 1.662 0.3591
rs714588 0.659 0.061 0.150 0.659 0.6582
rs1023555 0.221 0.104 0.261 0.261 0.8462
rs898070 0.020 1.794 0.346 1.794 0.3324
rs963218 0.165 0.190 0.263 0.263 0.8434
rs1419835 1.084 0.775 0.295 1.084 0.5107
rs765023 1.959 0.526 0.483 1.959 0.3033
rs1345267 2.582 0.003 1.383 2.582 0.2101
rs324381 0.175 0.402 0.377 0.402 0.7744
rs184448 9.710 2.026 8.253 9.710 0.0033 **
rs324396 2.312 0.188 1.051 2.312 0.2492
rs324957 7.598 2.134 7.157 7.598 0.0134 *
rs324960 2.901 7.928 6.443 7.928 0.0113 *
rs10486657 0.054 0.500 0.001 0.500 0.7303
rs324981 3.168 2.431 4.270 4.270 0.0839 .
rs1419780 0.123 1.193 0.005 1.193 0.4782
rs325462 1.545 1.645 2.412 2.412 0.2331
rs727162 3.022 0.643 3.074 3.074 0.1624
rs10250709 0.737 0.007 0.360 0.737 0.6284
rs6958905 0.490 0.099 0.447 0.490 0.7324
rs10238983 0.094 0.692 0.328 0.692 0.6478
rs4941643 1.294 0.006 0.465 1.294 0.4473
rs3794381 0.127 0.998 0.489 0.998 0.5357
rs2031532 0.025 0.240 0.127 0.240 0.8572
rs2247119 0.379 0.000 0.229 0.379 0.7843
rs8000149 0.020 0.043 0.043 0.043 0.9726
rs2274276 0.005 0.034 0.023 0.034 0.9781
rs7332573 1.247 1.703 1.825 1.825 0.3298
rs3829366 1.137 0.448 0.069 1.137 0.4909
rs6084432 2.999 0.848 3.279 3.279 0.1435
rs512625 2.180 0.030 1.119 2.180 0.2643
rs3918395 0.903 0.414 0.455 0.903 0.5714
rs2787095 0.178 0.069 0.184 0.184 0.8867
rs2853215 0.686 0.931 1.130 1.130 0.4931
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

We note that even under the max-statistics none of the SNPs tested is significant under the Bonferroni correction (<0.0001) for multiple SNP testing

```
#minimum P-value across SNPs
min(ans.max["Pr(>z)",])
```

`[1] 0.003304715`

Information for specific association models for given SNPs can also be retrieved with *WGstats*

`infoTable <- WGstats(ans)`

Therefore, we can have access to the results for a given SNP by

`infoTable$rs1422993`

```
SNP: rs1422993 adjusted by:
0 % 1 % OR lower upper p-value AIC
Codominant
G/G 730 59.0 173 50.9 1.00 0.017768 1642
G/T 425 34.3 145 42.6 1.44 1.12 1.85
T/T 83 6.7 22 6.5 1.12 0.68 1.84
Dominant
G/G 730 59.0 173 50.9 1.00 0.007826 1642
G/T-T/T 508 41.0 167 49.1 1.39 1.09 1.77
Recessive
G/G-G/T 1155 93.3 318 93.5 1.00 0.877863 1649
T/T 83 6.7 22 6.5 0.96 0.59 1.57
Overdominant
G/G-T/T 813 65.7 195 57.4 1.00 0.005026 1641
G/T 425 34.3 145 42.6 1.42 1.11 1.82
log-Additive
0,1,2 1238 78.5 340 21.5 1.22 1.01 1.47 0.040151 1644
```

recovering our previous results given by *association* function.

**NOTE**: The R output of specific association analyses can be exported into LaTeX by using *getNiceTable* function and *xtable* R package. The following code creates a table for the SNPs rs1422993 and rs184448

```
library(xtable)
out <- getNiceTable(ans[c("rs1422993", "rs184448")])
nlines <- attr(out, "nlines")
hlines <- c(-1, -1, 0, cumsum(nlines+1), nrow(out), nrow(out))
print(xtable(out, caption='Genetic association using
different genetic models from asthma
data example of rs1422993 and rs184448
SNPs obtained with SNPassoc.',
label = 'tab-2SNPs'),
tabular.enviroment="longtable", file="tableSNPs",
floating=FALSE, include.rownames = FALSE,
hline.after= hlines, sanitize.text.function=identity)
```

Gene-enviroment (GxE) analyses can be performed within `SNPassoc`

using *association* function. Assume that we are interested in testing whether the risk of rs1422993 for asthma under the dominant model is different among smokers (variable smoke; 0=never, 1=ever). This code fits a model with an interaction term where the environmental variable is required to be a factor factor variable.

```
association(casecontrol ~ dominant(rs1422993)*factor(smoke),
data=asthma.s)
```

```
SNP: dominant(rs1422993 adjusted by:
Interaction
---------------------
0 OR lower upper 1 OR lower upper
G/G 486 130 1.00 NA NA 242 43 0.66 0.46 0.97
G/T-T/T 354 128 1.35 1.02 1.79 150 38 0.95 0.63 1.42
p interaction: 0.8513
factor(smoke) within dominant(rs1422993
---------------------
G/G
0 1 OR lower upper
0 486 130 1.00 NA NA
1 242 43 0.66 0.46 0.97
G/T-T/T
0 1 OR lower upper
0 354 128 1.0 NA NA
1 150 38 0.7 0.47 1.06
p trend: 0.8513
dominant(rs1422993 within factor(smoke)
---------------------
0
0 1 OR lower upper
G/G 486 130 1.00 NA NA
G/T-T/T 354 128 1.35 1.02 1.79
1
0 1 OR lower upper
G/G 242 43 1.00 NA NA
G/T-T/T 150 38 1.43 0.88 2.31
p trend: 0.8513
```

The result is an interaction table showing that the risk of individuals carrying the T allele increases the risk of asthma in never smokers (OR=1.35; CI: 1.02-1.79) while it is not significant in ever smokers (OR=0.95; CI: 0.63-1.42). However, the interaction is not statistically significant (\(P\)-interaction=0.8513). The output also shows the stratified ORs that can help in interpreting the results.

In a similar way, gene-gene interaction (GxG) of a given SNP epistasis model can also be fitted using the same function. In that case, the genetic model of the interacting SNP must be indicated in the *model.inteaction* argument.

```
association(casecontrol ~ rs1422993*factor(rs184448),
data=asthma.s, model.interaction = "dominant" )
```

```
SNP: rs1422993 adjusted by:
Interaction
---------------------
T/T OR lower upper T/G OR lower upper 0 1 G/G lower upper
G/G 227 43 1.00 NA NA 359 96 1.41 0.95 2.10 128 30 1.24 0.74 2.07
G/T-T/T 154 33 1.13 0.69 1.86 265 93 1.85 1.24 2.77 78 38 2.57 1.55 4.27
p interaction: 0.24499
factor(rs184448) within rs1422993
---------------------
G/G
0 1 OR lower upper
T/T 227 43 1.00 NA NA
T/G 359 96 1.41 0.95 2.10
G/G 128 30 1.24 0.74 2.07
G/T-T/T
0 1 OR lower upper
T/T 154 33 1.00 NA NA
T/G 265 93 1.64 1.05 2.55
G/G 78 38 2.27 1.32 3.90
p trend: 0.24499
rs1422993 within factor(rs184448)
---------------------
T/T
0 1 OR lower upper
G/G 227 43 1.00 NA NA
G/T-T/T 154 33 1.13 0.69 1.86
T/G
0 1 OR lower upper
G/G 359 96 1.00 NA NA
G/T-T/T 265 93 1.31 0.95 1.82
G/G
0 1 OR lower upper
G/G 128 30 1.00 NA NA
G/T-T/T 78 38 2.08 1.19 3.62
p trend: 0.12743
```

We observe that the interaction between these two SNPs is not statistically significant (P-value=0.24). However, the OR of GG genotype of rs184448 differs across individuals between the GG and GT-TT genotypes of rs1422993 (see ORs for GG in the second table of the output).

The user also can perform GxG for a set of SNPs using this code. Let us assume we are interested in assessing interaction between the SNPs that are significant at 10% level

```
ans <- WGassociation(casecontrol, data=asthma.s)
mask <- apply(ans, 1, function(x) min(x, na.rm=TRUE)<0.1)
sig.snps <- names(mask[mask])
sig.snps
```

```
[1] "rs1430094" "rs1422993" "rs765023" "rs184448" "rs324396" "rs324957"
[7] "rs324960" "rs324981" "rs727162" "rs6084432"
```

```
idx <- which(colnames(asthma)%in%sig.snps)
asthma.s2 <- setupSNP(asthma, colSNPs = idx, sep="")
ans.int <- interactionPval(casecontrol ~ 1, data=asthma.s2)
ans.int
```

```
rs1430094 rs1422993 rs765023 rs184448 rs324396
rs1430094 0.132526514 0.653457029 0.816154586 0.787386835 0.694311497
rs1422993 0.140433948 0.016719949 0.133131712 0.375246182 0.683959376
rs765023 0.171993821 0.144029395 0.182805988 0.961405419 0.194520134
rs184448 0.100074594 0.019963426 0.034666219 0.007969948 0.036825613
rs324396 0.204742661 0.190583402 0.131945703 0.344952544 0.209589962
rs324957 0.103680541 0.019820456 0.034446832 0.696623215 0.318903026
rs324960 0.107216765 0.024180405 0.174801032 0.291457716 0.584132142
rs324981 0.128489057 0.144077239 0.153521356 0.646139555 0.301782199
rs727162 0.258828613 0.240900610 0.188971595 0.173341993 0.120240909
rs6084432 0.214413938 0.187372912 0.187830183 0.264160389 0.252965105
rs324957 rs324960 rs324981 rs727162 rs6084432
rs1430094 0.644661690 0.096913557 0.774083175 0.043758067 0.946641185
rs1422993 0.257661509 0.175946789 0.095251421 0.577504655 0.027437424
rs765023 0.437535350 0.614095008 0.117705086 0.217580773 0.896707843
rs184448 0.018290318 0.356124918 0.311031078 0.297592380 0.349332875
rs324396 0.232076552 0.747574191 0.064231657 0.361336095 0.388626207
rs324957 0.019578585 0.595796247 0.965290164 0.402781904 0.272919867
rs324960 0.404830873 0.017401694 0.168077057 0.406220478 0.725774374
rs324981 0.657378128 0.533095852 0.117043376 0.463436271 0.862291944
rs727162 0.174960014 0.500811687 0.167364803 0.206131411 0.885294485
rs6084432 0.174006927 0.146808311 0.210647392 0.203957720 0.193711884
```

we can visualize the results by

`plot(ans.int)`