title: Futility interim monitoring with control of type I and II error probabilities using the interim Z-value or confidence limit.
abstract: BACKGROUND
  It is highly desirable to terminate a clinical trial early if the emerging data suggests that the experimental treatment is ineffective, or substantially less effective than the level the study was designed to detect. Many studies have used a conditional power calculation as the basis for termination for futility. However, in order to compute conditional power one must posit an assumption about the distribution of the future data yet to be observed, such as that the original design assumptions will apply, or that the future data will have the same treatment effect as that estimated from the current 'trend' in the data. Each such assumption will yield a different conditional power value.
  
  
  OBJECTIVE
  The assessment of futility is described in terms of the observed quantities alone, specifically the interim Z-value or the interim confidence limit on the magnitude of the treatment effect, such that specified type I and II error probabilities are achieved. No assumption is required regarding the distribution of the future data yet to be observed.
  
  
  METHODS
  Lachin [1] presents a review of futility stopping based on assessment of conditional power and evaluates the statistical properties of a futility stopping rule. These methods are adapted to futility stopping using only the observed data without any assumption about the future data yet to be observed.
  
  
  RESULTS
  The statistical properties of the futility monitoring plan depend specifically on the corresponding boundary value for the interim Z-value. These include the probability of interim stopping under the null or under a specific alternative hypothesis, and the resulting type I and II error probabilities. Thus, the stopping rule can be uniquely specified in terms of a boundary for the interim Z-value. Alternately, the stopping rule can be specified in terms of a boundary on the upper confidence limit for the treatment group effect (favoring treatment). Herein it is shown that this approach is equivalent to a boundary on the test Z-value, from which the operating characteristics of the stopping rule can then be calculated.
  
  
  CONCLUSIONS
  While the statistical properties described herein strictly apply to a pre-specified futility boundary, it is also shown that these methods can be applied in an ad-hoc manner. In the event that a sequence of interim assessments for futility is desired, other sequential methods with an outer effectiveness boundary and inner futility boundary would be preferred.
  
  
  CONCLUSIONS
  These methods allow the design of clinical trials that have specified operating characteristics with a pre-specified futility analysis based only on the interim quantities that have been observed. Examples are presented.
authors.affiliation: The Biostatistics Center, Departments of Epidemiology and Biostatistics, and Statistics, The George Washington University, Rockville 20852, MD, USA. jml@biostat.bsc.gwu.edu
authors.forename: John M
authors.initials: JM
authors.lastname: Lachin
mesh_terms: D002986:Clinical Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data*; D003627:Data Interpretation, Statistical; D003657:Decision Making; D006801:Humans; D011336:Probability; D012107:Research Design / Q000706:statistics & numerical data*