Bioinformatics Toolbox™

mafdr - Estimate false discovery rate (FDR) of differentially expressed genes from two experimental conditions or phenotypes

Syntax

FDR = mafdr(PValues) [FDR, Q] = mafdr(PValues) [FDR, Q, Pi0] = mafdr(PValues) [FDR, Q, Pi0, R2] = mafdr(PValues) ... = mafdr(PValues, ...'BHFDR', BHFDRValue, ...) ... = mafdr(PValues, ...'Lambda', LambdaValue, ...) ... = mafdr(PValues, ...'Method', MethodValue, ...) ... = mafdr(PValues, ...'Showplot', ShowplotValue, ...)

Arguments

PValues

Either of the following:

Column vector of p-values for each feature (for example, gene) in a data set, such as returned by mattest.
DataMatrix object containing p-values for each feature (for example, gene) in a data set, such as returned by mattest.

BHFDRValue

Property to control the use of the linear step-up (LSU) procedure originally introduced by Benjamini and Hochberg, 1995. Choices are true or false (default).

Note If BHFDRValue is set to true, the Lambda and Method properties are ignored.

LambdaValue

Input that specifies lambda, λ, the tuning parameter used to estimate the true null hypotheses,

. LambdaValue can be either:

A single value that is > 0 and < 1.

A series of values. Each value must be > 0 and < 1. There must be at least four values in the series.

Tip The series of values can be expressed by a colon operator with the form [first:incr:last], where first is the first value in the series, incr is the increment, and last is the last value in the series.

Default LambdaValue is the series of values [0.01:0.01:0.95].

Note If LambdaValue is set to a single value, the Method property is ignored.

MethodValue

String that specifies a method to calculate the true null hypothesis,

, from the tuning parameter, LambdaValue, when LambdaValue is a series of values. Choices are:

bootstrap (default)
polynomial

ShowplotValue

Property to display two plots:

Plot of the estimated true null hypotheses, , versus the tuning parameter, lambda, λ, with a cubic polynomial fitting curve
Plot of q-values versus p-values

Choices are true or false (default).

Return Values

`FDR`	One of the following: Column vector of positive FDR (pFDR) values (if `PValues` is a column vector). `DataMatrix object` containing positive FDR (pFDR) values and the same row names as `PValues` (if `PValues` is a DataMatrix object).
`Q`	Column vector of q-values.
`Pi0`	Estimated true null hypothesis, .
`R2`	Square of the correlation coefficient.

Description

FDR = mafdr(PValues) computes a positive FDR (pFDR) value for each value in PValues, a column vector or DataMatrix object containing p-values for each gene in two microarray data sets, using a procedure introduced by Storey, 2002. FDR is a column vector or a DataMatrix object containing positive FDR (pFDR) values.

[FDR, Q] = mafdr(PValues) also returns a q-value for each p-value in PValues. Q is a column vector.

[FDR, Q, Pi0] = mafdr(PValues) also returns Pi0, the estimated true null hypothesis, , if using the procedure introduced by Storey, 2002.

[FDR, Q, Pi0, R2] = mafdr(PValues) also returns R2, the square of the correlation coefficient, if using the procedure introduced by Storey, 2002, and the polynomial method to calculate the true null hypothesis, , from the tuning parameter, lambda, λ.

... = mafdr(PValues, ...'PropertyName', PropertyValue, ...) calls mafdr with optional properties that use property name/property value pairs. You can specify one or more properties in any order. Each PropertyName must be enclosed in single quotation marks and is case insensitive. These property name/property value pairs are as follows:

... = mafdr(PValues, ...'BHFDR', BHFDRValue, ...) controls the use of the linear step-up (LSU) procedure originally introduced by Benjamini and Hochberg, 1995, to computes an FDR-adjusted p-value for each value in PValues. Choices are true or false (default).

Note If BHFDRValue is set to true, the Lambda and Method properties are ignored.

... = mafdr(PValues, ...'Lambda', LambdaValue, ...) specifies lambda, λ, the tuning parameter used to estimate the true null hypotheses, . LambdaValue can be either:

A single value that is > 0 and < 1.

A series of values. Each value must be > 0 and < 1. There must be at least four values in the series.

Default LambdaValue is the series of values [0.01:0.01:0.95].

Note If LambdaValue is set to a single value, the Method property is ignored.

... = mafdr(PValues, ...'Method', MethodValue, ...) specifies a method to calculate the true null hypothesis, , from the tuning parameter, LambdaValue, when LambdaValue is a series of values. Choices are bootstrap (default) or polynomial.

... = mafdr(PValues, ...'Showplot', ShowplotValue, ...) controls the display of two plots:

Plot of the estimated true null hypotheses, , versus the tuning parameter, lambda, with a cubic polynomial fitting curve
Plot of q-values versus p-values

Choices are true or false (default).

Examples

Load the MAT-file, included with the Bioinformatics Toolbox software, that contains Affymetrix data from a prostate cancer study, specifically probe intensity data from Affymetrix HG-U133A GeneChip arrays. The two variables in the MAT-file, dependentData and independentData, are two matrices of gene expression values from two experimental conditions.
```
load prostatecancerexpdata
```
Use the mattest function to calculate p-values for the gene expression values in the two matrices.
```
pvalues = mattest(dependentData, independentData, 'permute', true);
```
Use the mafdr function to calculate positive FDR values and q-values for the gene expression values in the two matrices and plot the data.
```
[fdr, q] = mafdr(pvalues, 'showplot', true);
```

The prostatecancerexpdata.mat file used in this example contains data from Best et al., 2005.

References

[1] Best, C.J.M., Gillespie, J.W., Yi, Y., Chandramouli, G.V.R., Perlmutter, M.A., Gathright, Y., Erickson, H.S., Georgevich, L., Tangrea, M.A., Duray, P.H., Gonzalez, S., Velasco, A., Linehan, W.M., Matusik, R.J., Price, D.K., Figg, W.D., Emmert-Buck, M.R., and Chuaqui, R.F. (2005). Molecular alterations in primary prostate cancer after androgen ablation therapy. Clinical Cancer Research 11, 6823–6834.

[2] Storey, J.D. (2002). A direct approach to false discovery rates. Journal of the Royal Statistical Society 64(3), 479–498.

[3] Storey, J.D., and Tibshirani, R. (2003). Statistical significance for genomewide studies. Proc Nat Acad Sci 100(16), 9440–9445.

[4] Storey, J.D., Taylor, J.E., 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 66, 187–205.

[5] Benjamini, Y., and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society 57, 289–300.