Controlling the False Discovery Rate in Two-Stage Combination Tests for Multiple Endpoints Sanat K. Sarkar, Jingjing Chen and Wenge Guo May 29, 2011 Sanat K. Sarkar is Professor and Senior Research Fellow, Department of Statis- tics, Temple University, Philadelphia, PA 19122 (Email: sanat@temple.edu). Jingjing Chen is PhD candidate, Department of Statistics, Temple University, Philadelphia, PA 19122 (Email: jjchen@temple.edu). Wenge Guo is Assistant Professor, Department of Mathematical Sciences New Jersey Institute of Technology, Newark, NJ 07102 (Email: wenge.guo@gmail.com). The research of Sarkar and Guo were supported by NSF Grants DMS-1006344 and DMS-1006021 respectively. ABSTRACT We consider the problem of simultaneous testing of null hypotheses associated with multiple endpoints in the setting of a two-stage adaptive design where the hypothe- ses are sequentially screened at the first stage as being rejected or accepted based on boundaries on the false discovery rate (FDR) and the remaining null hypotheses are tested at the second stage having combined their p-values from the two stages through some combination function. We propose two procedures to control the false discovery rate (FDR), extending the Benjamini-Hochberg (BH) procedure and its adaptive ver- sion incorporating an estimate of the number of true nulls from single-stage to two-stage setting. These procedures are theoretically proved to control the FDR under the as- sumption that the pairs of first- and second-stage p-values are independent and those corresponding to the null hypotheses are identically distributed as a pair (p 1 ,p 2 ) satisfy- ing the p-clud property of Brannath et al. (2002). We consider two types of combination function, Fisher’s and Simes’, and present explicit formulas involving these functions