Binomial.SGoF: Binomial SGoF multiple testing procedure

In sgof: Multiple Hypothesis Testing

Binomial SGoF multiple testing procedure

Description

Performs the Binomial SGoF method (Carvajal Rodríguez et al., 2009) for multiple hypothesis testing.

Usage

Binomial.SGoF(u, alpha = 0.05, gamma = 0.05)

Arguments

u	A (non-empty) numeric vector of p-values.
alpha	Numeric value. The significance level of the metatest.
gamma	Numeric value. The p-value threshold, so Binomial SGoF looks for significance in the amount of p-values below gamma.

Details

Binomial SGoF starts by counting the amount of p-values below gamma. This amount is compared to the expected one under the intersection or complete null hypothesis (all the nulls are true) in a metatest, performed at level alpha. Note that, under the intersection null, the p-values will be uniformly distributed on the (0,1) interval, so one expects gamma times the length of u p-values falling below gamma. If the intersection null is accepted, Binomial SGoF reports no effects. If the intersection null is rejected, the excess of observed significant cases are reported as number of existing effects N (by effects it is meant null hypotheses to be rejected). Finally, the effects are identified by considering the smallest N p-values. The only input you need is the set of p-values. Binomial SGoF procedure weakly controls the family-wise error rate (FWER) and the false discovery rate (FDR) at level alpha. That is, the probability of committing one or more than one type I errors along the multiple tests is bounded by alpha when all the null hypotheses are true. SGoF does not control for FWER nor FDR in the presence of effects. It has been quoted that Binomial SGoF provides a good balance between FDR and power, particularly when the number of tests is large, and the effect level is weak to moderate. It is also known that the number of effects declared by Binomial SGoF is a 100(1-alpha)% lower bound for the true number of existing effects with p-value below the initial threshold gamma so, interestingly, at probability 1-alpha, the number of false discoveries of SGoF does not exceed the number of false non-discoveries (de Uña Álvarez, 2012). Typically, the choice alpha=gamma will be used; this common value will be set as one of the usual significance levels (0.001, 0.01, 0.05, 0.1). Note however that alpha and gamma have different roles. The FDR is estimated by the simple method proposed by: Dalmasso, Broet, Moreau (2005), by taking n=1 in their formula. The adjusted p-value of a given p-value pi is defined as the smallest alpha0 for which the null hypothesis attached to pi is rejected by SGoF with alpha=gamma=alpha0. Actually, Binomial.SGoF function provides these adjusted p-values by restricting alpha0 to the set of original p-values. Castro-Conde and de Uña-Álvarez (2015) proved that this restriction does not change the adjusted p-values, while reducing the computational time.

Value

A list containing the following values:

Rejections	The number of effects declared by Binomial SGoF.
FDR	The estimated false discovery rate.
Adjusted.pvalues	The adjusted p-values.
data	The original p-values.
alpha	The specified significance level for the metatest.
gamma	The specified p-value threshold.
call	The matched call.

Author(s)

Irene Castro Conde and Jacobo de Uña Álvarez

References

Carvajal Rodríguez A, de Uña Álvarez J and Rolán Álvarez E (2009). A new multitest correction (SGoF) that increases its statistical power when increasing the number of tests. BMC Bioinformatics 10:209.

Castro Conde I and de Uña Álvarez J (2015). Adjusted p-values for SGoF multiple test procedure. Biometrical Journal, 57(1): 108-122. DOI: 10.1002/bimj.201300238

Dalmasso C, Broet P and Moreau T (2005) A simple procedure for estimating the false discovery rate. Bioinformatics 21:660–668

de Uña Álvarez J (2011). On the statistical properties of SGoF multitesting method. Statistical Applications in Genetics and Molecular Biology, Vol. 10, Iss. 1, Article 18.

See Also

plot.Binomial.SGoF,summary.Binomial.SGoF

Examples

p<-runif(387)^2  #387 independent p-values, non-uniform intersection null violated

res<-Binomial.SGoF(p)
summary(res)   #number of rejected nulls, estimated FDR
plot(res)   #adjusted p-values

sgof documentation built on Sept. 8, 2023, 5:34 p.m.