sepscore {bapred} R Documentation

## Separation score as described in Hornung et al. (2016)

### Description

This metric described in Hornung et al. (2016) was derived from the mixture score presented in Lazar et al. (2012). In contrast to the mixture score the separation score does not measure the degree of mixing but the degree of separation between the batches. Moreover it is less dependent on the relative sizes of the involved batches.

### Usage

```sepscore(xba, batch, k = 10)
```

### Arguments

 `xba` matrix. The covariate matrix, raw or after batch effect adjustment. observations in rows, variables in columns. `batch` factor. Batch variable. Currently has to have levels: '1', '2', '3' and so on. `k` integer. Number of nearest neighbors.

### Details

For two batches j and j* (see next paragraph for the case with more batches): 1) for each observation in batch j its k nearest neighbours in both batches j and j* simultaneously with respect to the euclidean distance are determined. Here, the proportion of those of these nearest neighbours, which belong to batch j* is calculated; 2) the average - denoted as MS_j - is taken over the thus obtained n_j proportions. This value is the mixture score as in Lazar et al. (2012); 3) to obtain a measure for the separation of the two batches the absolute difference between MS_j and its value expected in the absence of batch effects is taken: |MS_j - n_j* /(n_j + n_j* - 1)|; 4) the separation score is defined as the simple average of the latter quantity and the corresponding quantity when the roles of j and j* are switched. If the supplied number `k` of nearest neighbours is larger than n_j + n_j*, `k` is set to n_j + n_j* - 1 internally.

For more than two batches: 1) for all possible pairs of batches: calculate the metric as described above; 2) calculate the weighted average of the values in 1) with weights proportional to the sum of the sample sizes in the two respective batches.

### Value

Value of the metric

### Note

The smaller the values of this metric, the better.

Roman Hornung

### References

Hornung, R., Boulesteix, A.-L., Causeur, D. (2016) Combining location-and-scale batch effect adjustment with data cleaning by latent factor adjustment. BMC Bioinformatics 17:27.

Lazar, C., Meganck, S., Taminau, J., Steenhoff, D., Coletta, A., Molter,C., Weiss-Solís, D. Y., Duque, R., Bersini, H., Nowé, A. (2012) Batch effect removal methods for microarray gene expression data integration: a survey. Briefings in Bioinformatics, 14(4), 469-490.

### Examples

```data(autism)

# Random subset of 150 variables:
set.seed(1234)
Xsub <- X[,sample(1:ncol(X), size=150)]

# In cases of batches with more than 20 observations
# select 20 observations at random:
subinds <- unlist(sapply(1:length(levels(batch)), function(x) {
indbatch <- which(batch==x)
if(length(indbatch) > 20)
indbatch <- sort(sample(indbatch, size=20))
indbatch
}))
Xsub <- Xsub[subinds,]
batchsub <- batch[subinds]
ysub <- y[subinds]

sepscore(xba=Xsub, batch=batchsub, k=5)

params <- ba(x=Xsub, y=ysub, batch=batchsub, method = "ratiog")