Control of directional errors in fixed sequence multiple testing

Document Type

Article

Publication Date

1-1-2019

Abstract

In this paper, we consider the problem of simultaneously testing many two-sided hypotheses when rejections of null hypotheses are accompanied by claims of the direction of the alternative. The fundamental goal is to construct methods that control the mixed directional familywise error rate (mdFWER), which is the probability of making any type 1 or type 3 (directional) error. In particular, attention is focused on cases where the hypotheses are ordered as H1, . . ., Hn, so that Hi+1 is tested only if H1, . . ., Hi have all been previously rejected. In this situation, one can control the usual familywise error rate under arbitrary dependence by the basic procedure which tests each hypothesis at level α, and no other multiplicity adjustment is needed. However, we show that this is far too liberal if one also accounts for directional errors. But, by imposing certain dependence assumptions on the test statistics, one can retain the basic procedure. Through a simulation study and a clinical trial example, we numerically illustrate good performance of the proposed procedures compared to the existing mdFWER controlling procedures. The proposed procedures are also implemented in the R-package FixSeqMTP.

Identifier

85072081732 (Scopus)

Publication Title

Statistica Sinica

External Full Text Location

https://doi.org/10.5705/ss.202017.0072

ISSN

10170405

First Page

1047

Last Page

1064

Issue

2

Volume

29

Grant

DMS-1309162

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS