For a nonparametric Behrens-Fisher problem, a directional-sum test is proposed based on division-combination strategy. A one-layer wild bootstrap procedure is given to calculate its statistical significance. We conduct simulation studies with data generated from lognormal, t and Laplace distributions to show that the proposed test can control the type I error rates properly and is more powerful than the existing rank-sum and maximum-type tests under most of the considered scenarios. Applications to the dietary intervention trial further show the performance of the proposed test.
NanselTRLaffelLMBHaynieDL, et al.
Improving dietary quality in youth with type 1 diabetes: randomized clinical trial of a family-based behavioral intervention.Int J Behav Nutr Phys Act2015;
12: 58.
2.
ZhangWLiuAYTangLL, et al.
A cluster-adjusted rank-based test for a clinical trial concerning multiple endpoints with application to dietary intervention assessment.Biometrics2019;
75: 821–830.
3.
O’DonnellCJNabelEG.Genomics of cardiovascular disease.New Engl J Med2011;
365: 2098–2109.
4.
LuYPLiuQXuW, et al.
TGFA and IRF6 contribute to the risk of nonsyndromic cleft lip with or without cleft palate in northeast China. PLoS One2013;
8: e70754.
5.
PotthoffRF.Use of the Wilcoxon statistic for a generalized Behrens-Fisher problem. Ann Math Stat1963;
34: 1596–1599.
6.
BrunnerEMunzelUPuriML.The multivariate nonparametric Behrens-Fisher problem. J Stat Plan Inference2002;
108: 37–53.
7.
O’BrienPC.Procedures for comparing samples with multiple endpoints. Biometrics1984;
40: 1079–1087.
8.
HuangPTilleyBCWoolsonRF, et al.
Adjusting O’Brien’s test to control type I error for the generalized nonparametric Behrens-Fisher problem.Biometrics2005;
61: 532–539.
9.
LiuALiQLiuCL, et al.
A Rank-Based test for comparison of multidimensional outcomes.J Am Stat Assoc2010;
105: 578–587.
10.
HuangPTanMT.Multistage nonparametric tests for treatment comparisons in clinical trials with multiple primary endpoints. Stat Interface2016;
9: 343–354.
11.
HotellingH.The generalization of Student’s ratio. Ann Math Stat1931;
2: 360–378.
12.
FisherRA.Statistical methods for research workers. 4th ed.Edinburgh:
Oliver & Boyd, 1934.
13.
WangJJLiJLXiongWJ, et al.
Group analysis of distance matrices.Genet Epidemiol2020;
44: 620–628.
14.
LiuYWXieJ.Cauchy combination test: a powerful test with analytic p-value calculation under arbitrary dependency structures.J Am Stat Assoc2019;
115: 393–402.
15.
LiuYWChenSXLiZL, et al.
ACAT: A fast and powerful p value combination method for rare-variant analysis in sequencing studies.Am J Hum Genet2019;
104: 410–421.
16.
BuDLYangQLMengZ, et al.
Truncated tests for combining evidence of summary statistics.Genet Epidemiol2020;
44: 687–701.
17.
MannHBWhitneyDR.On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat1947;
18: 50–60.
18.
XieTFCaoRYYuP.Rank-based test for partial functional linear regression models. J Syst Sci Complex2020;
33: 1571–1584.
