Statistical functions for multiple testing correction. More...

#include <OpenMS/MATH/STATISTICS/MultipleTesting.h>

Public Types
enum class	Pi0Method { Smoother , Bootstrap }
	Method for estimating proportion of true null hypotheses (pi0) More...

enum class	LfdrTransform { Probit , Logit }
	Transformation for local FDR estimation. More...

Static Public Member Functions
static std::string	pi0MethodToString (Pi0Method m)
	Convert Pi0Method enum to string representation.

static Pi0Method	toPi0Method (const std::string &s)
	Convert string to Pi0Method enum (throws if invalid)

static std::string	lfdrTransformToString (LfdrTransform t)
	Convert LfdrTransform enum to string representation.

static LfdrTransform	toLfdrTransform (const std::string &s)
	Convert string to LfdrTransform enum (throws if invalid)

static std::vector< double >	qValue (const std::vector< double > &p_values, double pi0, bool pfdr=false)
	Calculate q-values (FDR-adjusted p-values) for multiple testing correction.

static Pi0Result	pi0Est (const std::vector< double > &p_values, const std::vector< double > &lambda_=std::vector< double >(), Pi0Method method=Pi0Method::Smoother, int smooth_df=3, bool smooth_log_pi0=false)
	Estimate the proportion of true null hypotheses (pi0).

static std::vector< double >	lfdr (const std::vector< double > &p_values, double pi0, bool trunc=true, bool monotone=true, LfdrTransform transf=LfdrTransform::Probit, double adj=1.5, double eps=1e-8, std::size_t gridsize=512, double cut=3.0)
	Estimate local false discovery rate (local FDR) from p-values.

static std::vector< double >	pNorm (const std::vector< double > &stat, const std::vector< double > &stat0)
	Compute tail probabilities under a fitted normal distribution.

template<class T >
static std::vector< double >	computeModelFDR (const std::vector< T > &data_in)
	Compute model-based FDR estimates from posterior error probabilities.

template<class T >
static std::vector< double >	pEmp (const std::vector< T > &stat, const std::vector< T > &stat0)
	Compute empirical p-values from test statistics and null distribution.

Detailed Description

Statistical functions for multiple testing correction.

Provides FDR estimation, q-value calculation, and local FDR computation based on the Storey-Tibshirani method. This struct contains static methods and enum classes for the various multiple testing correction procedures.

References:

Storey JD and Tibshirani R. (2003) "Statistical significance for genome-wide experiments." PNAS 100: 9440-9445. doi: 10.1073/pnas.1530509100
Storey JD. (2002) "A direct approach to false discovery rates." J. R. Statist. Soc. B. 64(3): 479-498. doi: 10.1111/1467-9868.00346

Member Enumeration Documentation

◆ LfdrTransform

enum class LfdrTransform

strong

Transformation for local FDR estimation.

Enumerator
Probit	Inverse normal (Gaussian) transformation (default)
Logit	Log-odds transformation.

◆ Pi0Method

enum class Pi0Method

strong

Method for estimating proportion of true null hypotheses (pi0)

Enumerator
Smoother	Spline smoothing method (default)
Bootstrap	Bootstrap resampling method.

Member Function Documentation

◆ computeModelFDR()

template<class T >

std::vector< double > computeModelFDR ( const std::vector< T > & data_in )

inlinestatic

Compute model-based FDR estimates from posterior error probabilities.

Parameters

data_in Vector of posterior error probabilities (PEPs)

Returns: Vector of FDR estimates

References RankData::Max, and RankData::Propagate.

Referenced by OpenMS::Math::computeModelFDR().

◆ lfdr()

static std::vector< double > lfdr	(	const std::vector< double > &	p_values,
		double	pi0,
		bool	trunc = `true`,
		bool	monotone = `true`,
		LfdrTransform	transf = `LfdrTransform::Probit`,
		double	adj = `1.5`,
		double	eps = `1e-8`,
		std::size_t	gridsize = `512`,
		double	cut = `3.0`
	)

static

Estimate local false discovery rate (local FDR) from p-values.

Parameters

p_values	Vector of p-values from hypothesis tests
pi0	Estimated proportion of true null hypotheses
trunc	If true, truncate lfdr values to [0,1] range (default true)
monotone	If true, enforce monotonicity constraint (default true)
transf	Transformation to apply: Probit (default) or Logit
adj	Bandwidth adjustment factor (default 1.5)
eps	Small constant to avoid division by zero (default 1e-8)
gridsize	Number of FFT grid points for KDE (default 512)
cut	Grid extension factor in units of bandwidth (default 3.0)

Returns: Vector of local FDR values

◆ lfdrTransformToString()

static std::string lfdrTransformToString ( LfdrTransform t )

static

Convert LfdrTransform enum to string representation.

◆ pEmp()

template<class T >

std::vector< double > pEmp	(	const std::vector< T > &	stat,
		const std::vector< T > &	stat0
	)

inlinestatic

Compute empirical p-values from test statistics and null distribution.

Parameters

stat	Vector of observed test statistics
stat0	Vector of null test statistics

Returns: Vector of empirical p-values

References RankData::Average, and RankData::Propagate.

Referenced by OpenMS::Math::pEmp().

◆ pi0Est()

static Pi0Result pi0Est	(	const std::vector< double > &	p_values,
		const std::vector< double > &	lambda_ = `std::vector< double >()`,
		Pi0Method	method = `Pi0Method::Smoother`,
		int	smooth_df = `3`,
		bool	smooth_log_pi0 = `false`
	)

static

Estimate the proportion of true null hypotheses (pi0).

Parameters

p_values	Vector of p-values from hypothesis tests (range [0,1])
lambda_	Vector of lambda threshold values for estimation. If empty, defaults to seq(0.05, 0.95, 0.05).
method	Method for pi0 estimation: Smoother (default) or Bootstrap
smooth_df	Degrees of freedom for smoothing spline (default: 3)
smooth_log_pi0	If true, perform smoothing in log-space (default: false)

Returns: Pi0Result structure with estimation results

◆ pi0MethodToString()

static std::string pi0MethodToString ( Pi0Method m )

static

Convert Pi0Method enum to string representation.

◆ pNorm()

static std::vector< double > pNorm	(	const std::vector< double > &	stat,
		const std::vector< double > &	stat0
	)

static

Compute tail probabilities under a fitted normal distribution.

Parameters

stat	Vector of test statistics
stat0	Vector of null statistics used to estimate N(mu, sigma^2)

Returns: Vector of upper tail probabilities (p-values)

References OpenMS::Math::computeModelFDR(), and OpenMS::Math::pEmp().

Referenced by OpenMS::Math::pNorm().

◆ qValue()

static std::vector< double > qValue	(	const std::vector< double > &	p_values,
		double	pi0,
		bool	pfdr = `false`
	)

static

Calculate q-values (FDR-adjusted p-values) for multiple testing correction.

Converts p-values to q-values using the Storey-Tibshirani method. A q-value is the minimum FDR at which a test is called significant.

Parameters

p_values	Vector of p-values to be adjusted (must be in range [0,1])
pi0	Proportion of true null hypotheses (typically estimated by pi0Est())
pfdr	If true, compute positive FDR; if false (default), compute regular FDR

Returns: Vector of q-values corresponding to input p-values. NaN values are propagated.

Referenced by OpenMS::Math::qValue().

◆ toLfdrTransform()

static LfdrTransform toLfdrTransform ( const std::string & s )

static

Convert string to LfdrTransform enum (throws if invalid)

◆ toPi0Method()

static Pi0Method toPi0Method ( const std::string & s )

static

Convert string to Pi0Method enum (throws if invalid)

Public Types

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ LfdrTransform

◆ Pi0Method

Member Function Documentation

◆ computeModelFDR()

◆ lfdr()

◆ lfdrTransformToString()

◆ pEmp()

◆ pi0Est()

◆ pi0MethodToString()

◆ pNorm()

◆ qValue()

◆ toLfdrTransform()

◆ toPi0Method()