title: Sample size calculations for evaluating treatment policies in multi-stage designs.
abstract: BACKGROUND
  Sequential multiple assignment randomized (SMAR) designs are used to evaluate treatment policies, also known as adaptive treatment strategies (ATS). The determination of SMAR sample sizes is challenging because of the sequential and adaptive nature of ATS, and the multi-stage randomized assignment used to evaluate them.
  
  
  OBJECTIVE
  We derive sample size formulae appropriate for the nested structure of successive SMAR randomizations. This nesting gives rise to ATS that have overlapping data, and hence between-strategy covariance. We focus on the case when covariance is substantial enough to reduce sample size through improved inferential efficiency.
  
  
  METHODS
  Our design calculations draw upon two distinct methodologies for SMAR trials, using the equality of the optimal semi-parametric and Bayesian predictive estimators of standard error. This 'hybrid' approach produces a generalization of the t-test power calculation that is carried out in terms of effect size and regression quantities familiar to the trialist.
  
  
  RESULTS
  Simulation studies support the reasonableness of underlying assumptions as well as the adequacy of the approximation to between-strategy covariance when it is substantial. Investigation of the sensitivity of formulae to misspecification shows that the greatest influence is due to changes in effect size, which is an a priori clinical judgment on the part of the trialist.
  
  
  CONCLUSIONS
  We have restricted simulation investigation to SMAR studies of two and three stages, although the methods are fully general in that they apply to 'K-stage' trials.
  
  
  CONCLUSIONS
  Practical guidance is needed to allow the trialist to size a SMAR design using the derived methods. To this end, we define ATS to be 'distinct' when they differ by at least the (minimal) size of effect deemed to be clinically relevant. Simulation results suggest that the number of subjects needed to distinguish distinct strategies will be significantly reduced by adjustment for covariance only when small effects are of interest.
authors.affiliation: Frontier Science and Technology Research Foundation, Boston, MA 02215, USA. dawson@fstrf.dfci.harvard.edu
authors.forename: Ree
authors.initials: R
authors.lastname: Dawson
authors.forename: Philip W
authors.initials: PW
authors.lastname: Lavori
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D015999:Multivariate Analysis; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D012044:Regression Analysis; D012107:Research Design; D018401:Sample Size; D013223:Statistics as Topic; D016896:Treatment Outcome