empiricalFDR {csaw} | R Documentation

## Control the empirical FDR

### Description

Control the empirical FDR across clusters for comparisons to negative controls, based on tests that are significant in the wrong direction.

### Usage

    empiricalFDR(ids, tab, weight=NULL, pval.col=NULL, fc.col=NULL, neg.down=TRUE)

### Arguments

`ids` | Integer vector containing the cluster ID for each test.
`tab` | A data.frame of results with `PValue` and at least one `logFC` field for each test.
`weight` | A numeric vector of weights for each window, defaults to 1 for each test.
`pval.col` | An integer scalar or string specifying the column of `tab` containing the p-values.
`fc.col` | An integer scalar or string specifying the column of `tab` containing the log-fold changes.
`neg.down` | A logical scalar indicating if negative log-fold changes correspond to the “wrong” direction.

### Details

Some experiments involve comparisons to negative controls where there should be no signal/binding. In such case, genuine differences should only occur in one direction, i.e., up in the non-control samples. Thus, the number of significant tests that change in the wrong direction can be used as an estimate of the number of false positives.

This function converts two-sided p-values in `tab[,pval.col]` to one-sided counterparts in the wrong direction. It combines the one-sided p-values for each cluster using `combineTests`. The number of significant clusters at some p-value threshold represents the estimated number of false positive clusters.

The same approach is applied for one-sided p-values in the right direction, where the number of detected clusters at the threshold represents the total number of discoveries. Dividing the number of false positives by the nmber of discoveries yields the empirical FDR at each p-value threshold. Monotonicity is enforced (i.e., the empirical FDR only decreases with decreasing p-value) as is the fact that the empirical FDR must be below unity.

The p-values specified in `pval.col` are assumed to be originally computed from some two-sided test, where the distribution of p-values is the same regardless of the direction of the log-fold change (under both the null and alternative hypothesis). This rules out p-values computed from ANODEV where multiple contrasts are tested at once; or from methods that yield asymmetric p-value distributions, e.g., GLM-based TREAT.

### Value

A DataFrame containing one row per cluster, with various fields:

- A numeric field containing the one-sided p-value for each cluster in the right direction. This field is named `PValue` if `pval.col=NULL`, otherwise its name is set to `colnames(tab[,pval.col])`.

- A numeric field containing the one-sided p-value for each cluster in the wrong direction. This has the same name as the previous field but with an additional `.neg` suffix, e.g., `PValue.neg`.

- A numeric field `FDR`, containing the empirical FDR corresponding to the p-value threshold equal to the value in `PValue`.

All other fields are the same as those returned by `combineTests`. The exception is the `direction` field, which is not returned as it is not informative for one-sided tests.

### Caution:

Control of the empirical FDR is best used for very noisy data sets where the BH method is not adequate. The BH method only protects against statistical false positives under the null hypothesis that the log-fold change is zero. However, the empirical FDR also protects against experimental false positives, caused by non-specific binding that yields uninteresting (but statistically significant) DB.

The downside is that the empirical FDR calculation relies on the availability of a good estimate of the number of false positives. It also assumes that the distribution of p-values is the same for non-specific binding events in both directions (i.e., known events with negative log-FCs and unknown events among those with positive log-FCs). Even if the log-fold changes are symmetric around zero, this does not mean that the p-value distributions will be the same, due to differences in library size and number between control and ChIP samples.

In summary, the BH method in `combineTests` is more statistically rigorous and should be preferred for routine analyses.

### Author(s)

Aaron Lun

### References

Zhang Y, Liu T, Meyer CA et al. (2008). Model-based Analysis of ChIP-Seq (MACS). Genome Biol. 9, R137.

### See Also

`combineTests`

### Examples

    ids <- round(runif(100, 1, 10))
    tab <- data.frame(logFC=rnorm(100), logCPM=rnorm(100), PValue=rbeta(100, 1, 2))
    empirical <- empiricalFDR(ids, tab)
    head(empirical)

[Package csaw version 1.16.1 Index]