title: Informative simultaneous confidence intervals in hierarchical testing.
abstract: OBJECTIVE
  In clinical trials involving multiple tests it is often difficult to obtain informative simultaneous confidence intervals (SCIs). In particular in hierarchical testing, no quantification of effects is possible for the first tested (and most important) hypothesis after its rejection. Our goal is a construction of SCIs that are always informative.
  
  
  METHODS
  We present an approach where the level is split after rejection of each hypothesis to obtain an informative confidence bound. The splitting weights are continuous functions of the parameters. Our method is realizable by a simple algorithm and is illustrated by an intuitive graphical representation.
  
  
  RESULTS
  We show theoretically and by an example that the new SCIs always provide information when a hypothesis is rejected. The power to reject the first hypothesis is not smaller than for the classical fixed-sequence procedure. The price for the extra information is a small power loss in the hypotheses proceeding the most important one.
  
  
  CONCLUSIONS
  Given the substantial gain in information, a small loss of power for the non-primary hypotheses seems often acceptable. Especially in the context of non-inferiority trials, this method is a useful alternative. The flexibility in the choice of the weight functions makes the procedure attractive for applications.
authors: Sylvia Schmidt, Kompetenzzentrum für Klinische Studien Bremen, Linzer Str. 4, 28359 Bremen, Germany, E-mail: sylviaschmidt@math.uni-bremen.de.
authors: S
authors: S
authors: Schmidt
authors: W
authors: W
authors: Brannath
mesh_terms: D000465:Algorithms; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D003196:Computer Graphics; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D008432:Mathematical Computing
keywords: Confidence interval; family wise error rate; fixed-sequence test; simultaneous coverage probability