title: Statistical inference for extended or shortened phase II studies based on Simon's two-stage designs.
abstract: BACKGROUND
  Simon's two-stage designs are popular choices for conducting phase II clinical trials, especially in the oncology trials to reduce the number of patients placed on ineffective experimental therapies. Recently Koyama and Chen (2008) discussed how to conduct proper inference for such studies because they found that inference procedures used with Simon's designs almost always ignore the actual sampling plan used. In particular, they proposed an inference method for studies when the actual second stage sample sizes differ from planned ones.
  
  
  METHODS
  We consider an alternative inference method based on likelihood ratio. In particular, we order permissible sample paths under Simon's two-stage designs using their corresponding conditional likelihood. In this way, we can calculate p-values using the common definition: the probability of obtaining a test statistic value at least as extreme as that observed under the null hypothesis.
  
  
  RESULTS
  In addition to providing inference for a couple of scenarios where Koyama and Chen's method can be difficult to apply, the resulting estimate based on our method appears to have certain advantage in terms of inference properties in many numerical simulations. It generally led to smaller biases and narrower confidence intervals while maintaining similar coverages. We also illustrated the two methods in a real data setting.
  
  
  CONCLUSIONS
  Inference procedures used with Simon's designs almost always ignore the actual sampling plan. Reported P-values, point estimates and confidence intervals for the response rate are not usually adjusted for the design's adaptiveness. Proper statistical inference procedures should be used.
authors.affiliation: Department of General Dentistry, Shanghai Ninth People's Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, 639 Zhi Zao Ju Road, Shanghai, 200011, P.R. China. 13611967296@163.com.
authors.forename: Junjun
authors.initials: J
authors.lastname: Zhao
authors.affiliation: Department of Biostatistics & Medical Informatics, University of Wisconsin, K6/446 CSC 600 Highland Ave., Madison, Wisconsin, USA. meyu@biostat.wisc.edu.
authors.forename: Menggang
authors.initials: M
authors.lastname: Yu
authors.affiliation: Shanghai Ninth People's Hospital, College of Stomatology, Shanghai Jiao Tong University School of Medicine, Shanghai, 639 Zhi Zao Ju Road200011, P.R. China. fxiping1808@qq.com.
authors.forename: Xi-Ping
authors.initials: XP
authors.lastname: Feng
mesh_terms: D000465:Algorithms; D001699:Biometry / Q000379:methods*; D017322:Clinical Trials, Phase II as Topic / Q000379:methods*; D003198:Computer Simulation; D016001:Confidence Intervals; D006801:Humans; D016013:Likelihood Functions; D009369:Neoplasms / Q000628:therapy*; D011336:Probability; D012107:Research Design; D018401:Sample Size