TY - JOUR
T1 - Control of directional errors in fixed sequence multiple testing
AU - Grandhi, Anjana
AU - Guo, Wenge
AU - Romano, Joseph P.
N1 - Funding Information:
The research of Wenge Guo was supported in part by NSF Grant DMS-1309162 and the research of Joseph Romano was supported in part by NSF Grant DMS-0707085. We sincerely thank three referees for giving helpful and insightful comments and Yalin Zhu for implementing the proposed procedures in the R package FixSeqMTP.
Publisher Copyright:
© 2019 Institute of Statistical Science. All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Directional error
KW - Fixed sequence multiple testing
KW - Mixed directional familywise error rate
KW - Monotone likelihood ratio
KW - Positive dependence
KW - Type 1 error
UR - http://www.scopus.com/inward/record.url?scp=85072081732&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85072081732&partnerID=8YFLogxK
U2 - 10.5705/ss.202017.0072
DO - 10.5705/ss.202017.0072
M3 - Article
AN - SCOPUS:85072081732
SN - 1017-0405
VL - 29
SP - 1047
EP - 1064
JO - Statistica Sinica
JF - Statistica Sinica
IS - 2
ER -