mafdr - Estimate false discovery rate (FDR) for multiple hypothesis testing

Syntax

Input 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	Controls the use of the linear step-up (LSU) procedure originally introduced by Benjamini and Hochberg, 1995 (instead of the procedure introduced by Storey, 2002). Choices are true or false (default). Note   If you set BHFDRValue to true, then: Lambda and Method properties are ignored. There can be only one output argument, FDR.
LambdaValue	Specifies lambda, λ, the tuning parameter used to estimate the a priori probability that the null hypothesis, , is true. LambdaValue can be either: A single value that is > 0 and < 1. A vector of four or more values. Each value must be > 0 and < 1. 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 you set LambdaValue to a single value, the Method property is ignored. If you set LambdaValue to a vector of values, mafdr chooses the optimal value using the method specified by the Method property.
MethodValue	String that specifies a method to choose lambda, λ, the tuning parameter, from LambdaValue, when it is a vector. Choices are: 'bootstrap' (default) 'polynomial' Note   MethodValue must be 'polynomial' to return the fourth output argument, R2.
ShowplotValue	Property to display two plots: Plot of the estimated a priori probability that the null hypothesis, , is true 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). Note   If you set the BHFDR property to true, only the second plot displays.

Output Arguments

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, which are measures of hypothesis testing error for each observation in PValues.
Pi0	Estimated a priori probability that the null hypothesis, , is true.
R2	Square of the correlation coefficient.

Description

FDR = mafdr(PValues) estimates a positive FDR (pFDR) value for each value in PValues, a column vector or DataMatrix object containing p-values for each feature (for example, gene) in a data set, using the 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, using the procedure introduced by Storey, 2002. Q is a column vector containing measures of hypothesis testing error for each observation in PValues.

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

[FDR, Q, Pi0, R2] = mafdr(PValues) also returns R2, the square of the correlation coefficient, using the procedure introduced by Storey, 2002, and the polynomial method to choose 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:

FDR = mafdr(PValues, ...'BHFDR', BHFDRValue, ...) controls the use of the linear step-up (LSU) procedure originally introduced by Benjamini and Hochberg, 1995 (instead of the procedure introduced by Storey, 2002), to estimate an FDR-adjusted p-value for each value in PValues. Choices are true or false (default).

Note   If you set BHFDRValue to true, then: Lambda and Method properties are ignored. There can be only one output argument, FDR.

... = mafdr(PValues, ...'Lambda', LambdaValue, ...) specifies lambda, λ, the tuning parameter used to estimate the a priori probability that the null hypothesis, , is true. LambdaValue can be either:

• A single value that is > 0 and < 1.

• A vector of four or more values. Each value must be > 0 and < 1.

  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 you set LambdaValue to a single value, the Method property is ignored. If you set LambdaValue to a vector of values, mafdr chooses the optimal value using the method specified by the Method property.

... = mafdr(PValues, ...'Method', MethodValue, ...) specifies a method to choose lambda, λ, the tuning parameter, from LambdaValue, when it is a vector. Choices are bootstrap (default) or polynomial.

Note   MethodValue must be 'polynomial' to return the fourth output argument, R2.

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

• Plot of the estimated a priori probability that the null hypothesis, , is true 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).

Note   If you set the BHFDR property to true, only the second plot displays.

Examples

1. 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

2. Use the mattest function to calculate p-values for the gene expression values in the two matrices.

   pvalues = mattest(dependentData, independentData, 'permute', true);

3. 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.

See Also

affygcrma | affyrma | gcrma | mairplot | maloglog | mapcaplot | mattest | mavolcanoplot | rmasummary

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