qvalue {qvalue} | R Documentation

## Estimate the q-values for a given set of p-values

### Description

Estimate the q-values for a given set of p-values. The q-value of a test measures the proportion of false positives incurred (called the false discovery rate) when that particular test is called significant.

### Usage

    qvalue(p, fdr.level = NULL, pfdr = FALSE, lfdr.out = TRUE, pi0 = NULL,
      ...)

### Arguments

`p` | A vector of p-values (only necessary input).
`fdr.level` | A level at which to control the FDR. Must be in (0,1]. Optional; if this is selected, a vector of TRUE and FALSE is returned that specifies whether each q-value is less than fdr.level or not.
`pfdr` | An indicator of whether it is desired to make the estimate more robust for small p-values and a direct finite sample estimate of pFDR – optional.
`lfdr.out` | If TRUE then local false discovery rates are returned. Default is TRUE.
`pi0` | It is recommended to not input an estimate of pi0. Experienced users can use their own methodology to estimate the proportion of true nulls or set it equal to 1 for the BH procedure.
`...` | Additional arguments passed to `pi0est` and `lfdr`.

### Details

The function `pi0est` is called internally and calculates the estimate of pi_0, the proportion of true null hypotheses. The function `lfdr` is also called internally and calculates the estimated local FDR values. Arguments for these functions can be included via `...` and will be utilized in the internal calls made in `qvalue`. See http://genomine.org/papers/Storey_FDR_2011.pdf for a brief introduction to FDRs and q-values.

### Value

A list of object type "qvalue" containing:

`call` | Function call.
`pi0` | An estimate of the proportion of null p-values.
`qvalues` | A vector of the estimated q-values (the main quantity of interest).
`pvalues` | A vector of the original p-values.
`lfdr` | A vector of the estimated local FDR values.
`significant` | If fdr.level is specified, and indicator of whether the q-value fell below fdr.level (taking all such q-values to be significant controls FDR at level fdr.level).
`pi0.lambda` | An estimate of the proportion of null p-values at each lambda value (see vignette).
`lambda` | A vector of the lambda values utilized to obtain `pi0.lambda`.

### Author(s)

John D. Storey

### References

Storey JD. (2002) A direct approach to false discovery rates. Journal of the Royal Statistical Society, Series B, 64: 479-498.
http://onlinelibrary.wiley.com/doi/10.1111/1467-9868.00346/abstract Storey JD and Tibshirani R. (2003) Statistical significance for genome-wide experiments. Proceedings of the National Academy of Sciences, 100: 9440-9445.
http://www.pnas.org/content/100/16/9440.full

Storey JD. (2003) The positive false discovery rate: A Bayesian interpretation and the q-value. Annals of Statistics, 31: 2013-2035.
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aos/1074290335

Storey JD, Taylor JE, and Siegmund D. (2004) Strong control, conservative point estimation, and simultaneous conservative consistency of false discovery rates: A unified approach. Journal of the Royal Statistical Society, Series B, 66: 187-205.
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2004.00439.x/abstract

Storey JD. (2011) False discovery rates. In International Encyclopedia of Statistical Science.
http://genomine.org/papers/Storey_FDR_2011.pdf
http://www.springer.com/statistics/book/978-3-642-04897-5

### See Also

`pi0est`, `lfdr`, `summary.qvalue`, `plot.qvalue`, `hist.qvalue`, `write.qvalue`

### Examples

    # import data
    data(hedenfalk)
    p <- hedenfalk$p

    # get q-value object
    qobj <- qvalue(p)
    plot(qobj)
    hist(qobj)

    # options available
    qobj <- qvalue(p, lambda=0.5, pfdr=TRUE)
    qobj <- qvalue(p, fdr.level=0.05, pi0.method="bootstrap", adj=1.2)

[Package qvalue version 2.16.0 Index]