Statistics and Its Interface

Volume 4 (2011)

Number 4

Optimal two-stage sequential robust design for gene-intervention studies

Pages: 431 – 441



Zhaohai Li (Department of Statistics, The George Washington University, Washington, D.C., U.S.A.)

Aiyi Liu (Biostatistics and Bioinformatics Branch, National Institute of Child Health and Human Development, Rockville, Maryland, U.S.A.)

Lihan K. Yan (Office of Biostatistics and Epidemiology, Center for Biologics Evaluation and Research, U.S. Food and Drug Administration, Rockville, Maryland, U.S.A.)

Gang Zheng (Office of Biostatistics Research, National Heart, Lung and Blood Institute, Bethesda, Maryland, U.S.A.)


Gene-intervention studies investigate the responsiveness to therapies according to individuals’ genetic profiles. We propose a two-stage sequential design for these studies and investigate the cost of the sample size versus the statistical power. In a typical sequential design, a single normally distributed test statistic is used. For a genetic study, the robust test is used because of the uncertainty of the underlying genetic model (e.g. the recessive, additive or dominant models). The robust test statistic that we consider in the twostage sequential design is the maximum of three correlated normally distributed statistics, each which is optimal under the corresponding genetic model. We study various factors that affect minimizing the average sample number (ASN) or maximizing the power of a gene-intervention study under the two-stage sequential design and make recommendations for the optimal solutions under different scenarios.


optimal two-stage design, MAX, group sequential, gene-intervention

2010 Mathematics Subject Classification


Published 17 November 2011