Abstract
A method for addressing the multiplicity problem is proposed in the setting where the hypotheses test sites may be arranged in some order based on a notion of proximity, such as SNPs of a chromosome in genetic association studies. It is shown that this method is able to control family-wise error rate in the weak sense and numerical evidence shows that this method controls false discovery rate in the strong sense under sparsity. The method is applied to some genome- wide association studies data with asthma and it is argued that this Power Boosting method may be combined with existing error- rate controlling methods in order to improve true positive rates at controllable and possibly negligible cost to the nominal level of error- rate control.
Highlights
In multiple testing, maintaining a practicable balance between type 1 error rate control and statistical power is a common issue (Aslam & Albassam, 2020; Verhoeven et al, 2005; Yang et al, 2005)
This is because these methods maintain control over their respective type 1 error rates by imposing penalties on the individual significance levels based on the nominal significance level
In exchange for this, the combined test can detect as significant, a group of test sites that may seem obviously interesting to the practitioner, but would have failed detection otherwise because their individual signals are not strong enough to be detected by the α adjusting method
Summary
In multiple testing, maintaining a practicable balance between type 1 error rate control and statistical power is a common issue (Aslam & Albassam, 2020; Verhoeven et al, 2005; Yang et al, 2005). An individual test that is calibrated to have sufficient power for detecting a minimum effect size cannot be relied upon to maintain that same power if the common corrections for multiplicity, such as the Bonferroni correction for family-wise error rate (FWER) or the Benjamini-Hochberg procedure for false discovery rate (FDR) (Benjamini & Hochberg, 1995), are to be applied to the results of several, individually powerful enough tests This is because these methods maintain control over their respective type 1 error rates by imposing penalties on the individual significance levels based on the nominal significance level. If there are N hypotheses and it is desired to maintain level α control over type 1 error, application of the Bonferroni correction would mean that an individual null hypothesis can only be rejected if its corresponJdoiunrgnapl -ovf CaloumepiustalteiosnsatlhInannovαa/tNio.nFaondr AlanraglyetiNcs,, Vitolc.a1n, Nbuemcboemr 1e(pJarnaucatricy)a2ll0y22im, ppp:o1s–s1ib7le to reject any hypothesis despite there being clearly strong evidence for rejection when considering a single hypothesis
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