Estimate false discovery rate (FDR) for multiple hypothesis testing
FDR
= mafdr(PValues
)
[FDR, Q
] = mafdr(PValues
)
[FDR, Q, Pi0
] = mafdr(PValues
)
[FDR, Q, Pi0, R2
] = mafdr(PValues
)
FDR
= mafdr(PValues
,
...'BHFDR', BHFDRValue
, ...)
...
= mafdr(PValues
,
...'Lambda', LambdaValue
, ...)
...
= mafdr(PValues
,
...'Method', MethodValue
, ...)
...
= mafdr(PValues
,
...'Showplot', ShowplotValue
, ...)
PValues  Either of the following:

BHFDRValue  Controls the use of the linear stepup (LSU) procedure originally
introduced by Benjamini and Hochberg, 1995 (instead of the procedure
introduced by Storey, 2002). Choices are true or false (default). NoteIf you set

LambdaValue  Specifies lambda, λ, the tuning parameter used to estimate
the a priori probability that the null hypothesis, $$\widehat{\pi}0(\lambda )$$, is true. LambdaValue can
be either:
LambdaValue is the
series of values [0.01:0.01:0.95] .NoteIf you set If you set 
MethodValue  Character vector that specifies a method to choose lambda,
λ, the tuning parameter, from LambdaValue ,
when it is a vector. Choices are:
Note

ShowplotValue  Property to display two plots:
Choices are NoteIf you set the 
FDR  One of the following:

Q  Column vector of qvalues, which are measures of hypothesis
testing error for each observation in PValues . 
Pi0  Estimated a priori probability that the null hypothesis, $$\widehat{\pi}0$$, is true. 
R2  Square of the correlation coefficient. 
estimates
a positive FDR (pFDR) value for each value in FDR
= mafdr(PValues
)PValues
,
a column vector or DataMatrix
object containing pvalues 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.
[
also
returns a qvalue for each pvalue in FDR, Q
] = mafdr(PValues
)PValues
,
using the procedure introduced by Storey, 2002. Q
is
a column vector containing measures of hypothesis testing error for
each observation in PValues
.
[
also
returns FDR, Q, Pi0
] = mafdr(PValues
)Pi0
, the estimated a priori probability
that the null hypothesis, $$\widehat{\pi}0$$,
is true, using the procedure introduced by Storey, 2002.
[
also
returns FDR, Q, Pi0, R2
] = mafdr(PValues
)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(
calls PValues
, ...'PropertyName
', PropertyValue
,
...)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:
controls
the use of the linear stepup (LSU) procedure originally introduced
by Benjamini and Hochberg, 1995 (instead of the procedure introduced
by Storey, 2002), to estimate an FDRadjusted pvalue for each value
in FDR
= mafdr(PValues
,
...'BHFDR', BHFDRValue
, ...)PValues
. Choices are true
or false
(default).
If you set BHFDRValue
to true
,
then:
Lambda
and Method
properties
are ignored.
There can be only one output argument, FDR
.
specifies
lambda, λ, the tuning parameter used to estimate the a priori
probability that the null hypothesis, $$\widehat{\pi}0(\lambda )$$, is true. ...
= mafdr(PValues
,
...'Lambda', LambdaValue
, ...)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
.
The series of values can be expressed by a colon operator with
the form [
,
where first
:incr
:last
]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]
.
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.
specifies
a method to choose lambda, λ, the tuning parameter, from ...
= mafdr(PValues
,
...'Method', MethodValue
, ...)LambdaValue
,
when it is a vector. Choices are bootstrap
(default)
or polynomial
.
MethodValue
must be 'polynomial'
to
return the fourth output argument, R2
.
controls
the display of two plots:...
= mafdr(PValues
,
...'Showplot', ShowplotValue
, ...)
Plot of the estimated a priori probability that the null hypothesis, $$\widehat{\pi}0(\lambda )$$, is true versus the tuning parameter, lambda, λ, with a cubic polynomial fitting curve
Plot of qvalues versus pvalues
Choices are true
or false
(default).
If you set the BHFDR
property to true
,
only the second plot displays.
Load the MATfile, included with the Bioinformatics
Toolbox™ software,
that contains Affymetrix^{®} data from a prostate cancer study, specifically
probe intensity data from Affymetrix HGU133A GeneChip^{®} arrays.
The two variables in the MATfile, dependentData
and independentData
,
are two matrices of gene expression values from two experimental conditions.
load prostatecancerexpdata
Use the mattest
function to calculate
pvalues 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 qvalues 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.
[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., EmmertBuck, 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.
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