Here we illustrate how to detect data linkage errors with the *omicsPrint* package using both artificially generated data and experimental data. Several additional vignettes are available that show the use of the package on further experimental data in different settings, i.e., 450k DNA methylation and imputed genotypes.

Here we generate a single vector with 100 randomly drawn integers from the set; 1, 2, 3, representing 100 SNP calls from a single individual. Three additional individuals are generated by randomly swapping a certain fraction of the SNPs. Swapping 5 SNPs will introduce a few mismatches mimicking a situation where the same individual was measured twice (replicate) but with measurement error. Swapping 50% of the SNPs will be similar to the difference in genotypes between parents and offspring. Swapping all SNPs will result in a situation similar to comparing two unrelated individuals.

```
swap <- function(x, frac=0.05) {
n <- length(x)
k <- floor(n*frac)
x1 <- sample(1:n,k)
x2 <- sample(1:n,k) ##could be overlapping
x[x2] <- x[x1]
x
}
x1 <- 1 + rbinom(100, size=2, prob=1/3)
x2 <- swap(x1, 0.05) ##strongly related e.g. replicate
x3 <- swap(x1, 0.5) ##related e.g. parent off spring
x4 <- swap(x1, 1) ##unrelated
x <- cbind(x1, x2, x3, x4)
```

Now `x`

contains the 100 SNPs for the four individuals using `head`

we can inspect the first six SNPs.

`head(x)`

```
## x1 x2 x3 x4
## [1,] 1 1 2 2
## [2,] 2 2 2 1
## [3,] 1 1 3 1
## [4,] 1 1 2 1
## [5,] 1 1 2 2
## [6,] 2 2 2 2
```

`allelesharing`

algorithmWe use Identity by State (IBS) for the set of SNPs to infer sample relations. See (**???**), for the description of this approach applied to genetic data. Briefly, between each sample pair, the IBS-vector is calculated, which is a measure of genetic distance between individuals. Next, the vector is summarized by its mean and variance. A mean of 2 and variance of 0 indicates that the samples are identical.

`data <- alleleSharing(x, verbose=TRUE)`

`## Hash relations`

`## Pruning 100 SNPs ...`

`## 0 SNPs removed because of low call rate!`

`## 0 samples removed because too few SNPs called!`

`## Using 100 polymorphic SNPs to determine allele sharing.`

`## Running `square` IBS algorithm!`

The set of SNPs may contain uninformative SNPs, SNPs of bad quality or even SNPs could be missing. The following pruning steps are implemented to yield the most informative set of SNPs (thresholds can be adjusted see `?alleleSharing`

):

- a SNP is remove if missing in >5% of the samples (
`callRate = 0.95`

) - a sample should have at least 2/3 of the SNPs called (
`coverageRate = 2/3`

) - a SNP is can be removed if it violates the Hardy-Weinberg equilibrium (
`alpha = 0`

). - a SNP is can be removed if the minor allele frequency is below the given threshold (
`maf = 0`

)

Hardy-Weinberg test-statistics is calculated using a \(\chi^2\)-test and Bonferonni multiple testing correction is performed.

`data`

```
## mean var colnames.x colnames.y relation
## 1 2.00 0.0000000 x1 x1 identical
## 2 1.96 0.0589899 x2 x1 unrelated
## 3 1.62 0.3187879 x3 x1 unrelated
## 4 1.40 0.3636364 x4 x1 unrelated
## 5 2.00 0.0000000 x2 x2 identical
## 6 1.60 0.3434343 x3 x2 unrelated
## 7 1.38 0.3793939 x4 x2 unrelated
## 8 2.00 0.0000000 x3 x3 identical
## 9 1.40 0.4242424 x4 x3 unrelated
## 10 2.00 0.0000000 x4 x4 identical
```

By default no relations are assumed except for the self-self relations.

The output is a `data.frame`

containing all pairwise comparisons with the mean and variance of the IBS over the set of SNPs and the reported sample relationship, including the identifiers.

Since we provided a list of known relations and assume that the majority is correct, we can build a classifier to discover misclassified relations. Linear discriminant analysis is used to generate a confusion-matrix, which is subsequently used to graphically represent the classification boundaries and generate an output file with misclassified sample pairs.

`mismatches <- inferRelations(data)`

`mismatches`

```
## mean var colnames.x colnames.y relation predicted
## 2 1.96 0.0589899 x2 x1 unrelated identical
```

There is one misclassified sample, namely the replicate that we introduced but was not a priori specified as an existing relationship. The true relationship with between sample `x1`

and sample `x2`

is an identical relation. Furthermore, we see two sample pairs with mean IBS of 1.96 and variance 0.06 which is an indication that also these pairs share a considerable number of alleles. If known, such relationships can be specified prior to analysis.

```
relations <- expand.grid(idx = colnames(x), idy= colnames(x))
relations$relation_type <- "unrelated"
relations$relation_type[relations$idx == relations$idy] <- "identical"
relations$relation_type[c(2,5)] <- "identical" ##replicate
relations$relation_type[c(3,7,9,10)] <- "parent offspring"
relations
```

```
## idx idy relation_type
## 1 x1 x1 identical
## 2 x2 x1 identical
## 3 x3 x1 parent offspring
## 4 x4 x1 unrelated
## 5 x1 x2 identical
## 6 x2 x2 identical
## 7 x3 x2 parent offspring
## 8 x4 x2 unrelated
## 9 x1 x3 parent offspring
## 10 x2 x3 parent offspring
## 11 x3 x3 identical
## 12 x4 x3 unrelated
## 13 x1 x4 unrelated
## 14 x2 x4 unrelated
## 15 x3 x4 unrelated
## 16 x4 x4 identical
```

Rerun the allelesharing algorithm now provided with the known relations.

`data <- alleleSharing(x, relations=relations)`

`## Hash relations`

`## Pruning 100 SNPs ...`

`## 0 SNPs removed because of low call rate!`

`## 0 samples removed because too few SNPs called!`

`## Using 100 polymorphic SNPs to determine allele sharing.`

`## Running `square` IBS algorithm!`

`data`

```
## mean var colnames.x colnames.y relation
## 1 2.00 0.0000000 x1 x1 identical
## 2 1.96 0.0589899 x2 x1 identical
## 3 1.62 0.3187879 x3 x1 parent offspring
## 4 1.40 0.3636364 x4 x1 unrelated
## 5 2.00 0.0000000 x2 x2 identical
## 6 1.60 0.3434343 x3 x2 parent offspring
## 7 1.38 0.3793939 x4 x2 unrelated
## 8 2.00 0.0000000 x3 x3 identical
## 9 1.40 0.4242424 x4 x3 unrelated
## 10 2.00 0.0000000 x4 x4 identical
```

`mismatches <- inferRelations(data)`

`mismatches`

```
## [1] mean var colnames.x colnames.y relation predicted
## <0 rows> (or 0-length row.names)
```

All misclassified relations were resolved.

The previous example showed how to perform sample relationship verification within a single omics data type. If a second set of SNPs is available obtained from a different omic data type (and the SNPs are partly overlapping), *omicsPrint* can be used to verify relationships between omics types, e.g. to establish whether two omics data types were indeed generated for the same individual in order to exclude or detect sample mix-ups.

In this artificial example a random subset of 80 SNPs is selected as the set of SNPs from a different omic type. First running without providing the known relations.

```
rownames(x) <- paste0("rs", 1:100)
y <- x[sample(1:100, 80),]
data <- alleleSharing(x, y)
```

`## Hash relations`

`## Pruning 100 SNPs ...`

`## 0 SNPs removed because of low call rate!`

`## 0 samples removed because too few SNPs called!`

`## Pruning 80 SNPs ...`

`## 0 SNPs removed because of low call rate!`

`## 0 samples removed because too few SNPs called!`

`## Using 80 polymophic SNPs to determine allele sharing.`

`## Running `rectangular` IBS algorithm!`

Note that pruning is performed on both data types and automatically a set of overlapping SNPs (80) is used provided that the rownames of `x`

and `y`

are identical (this also holds for sample relations where the relation identifiers `idx`

and `idy`

should match with the columnames of `x`

and `y`

).

`data`

```
## mean var colnames.x colnames.y relation
## 1 2.000 0.00000000 x1 x1 identical
## 2 1.950 0.07341772 x2 x1 unrelated
## 3 1.625 0.31329114 x3 x1 unrelated
## 4 1.425 0.34873418 x4 x1 unrelated
## 5 1.950 0.07341772 x1 x2 unrelated
## 6 2.000 0.00000000 x2 x2 identical
## 7 1.600 0.34430380 x3 x2 unrelated
## 8 1.400 0.36962025 x4 x2 unrelated
## 9 1.625 0.31329114 x1 x3 unrelated
## 10 1.600 0.34430380 x2 x3 unrelated
## 11 2.000 0.00000000 x3 x3 identical
## 12 1.375 0.41455696 x4 x3 unrelated
## 13 1.425 0.34873418 x1 x4 unrelated
## 14 1.400 0.36962025 x2 x4 unrelated
## 15 1.375 0.41455696 x3 x4 unrelated
## 16 2.000 0.00000000 x4 x4 identical
```

`mismatches <- inferRelations(data)`