title: The transitive fallacy for randomized trials: if A bests B and B bests C in separate trials, is A better than C?
abstract: BACKGROUND
  If intervention A bests B in one randomized trial, and B bests C in another randomized trial, can one conclude that A is better than C? The problem was motivated by the planning of a randomized trial, where A is spiral-CT screening, B is x-ray screening, and C is no screening. On its surface, this would appear to be a straightforward application of the transitive principle of logic.
  
  
  METHODS
  We extended the graphical approach for omitted binary variables that was originally developed to illustrate Simpson's paradox, applying it to hypothetical, but plausible scenarios involving lung cancer screening, treatment for gastric cancer, and antibiotic therapy for clinical pneumonia.
  
  
  RESULTS
  Graphical illustrations of the three examples show different ways the transitive fallacy for randomized trials can arise due to changes in an unobserved or unadjusted binary variable. In the most dramatic scenario, B bests C in the first trial, A bests B in the second trial, but C bests A at the time of the second trial.
  
  
  CONCLUSIONS
  Even with large sample sizes, combining results from a previous randomized trial of B versus C with results from a new randomized trial of A versus B will not guarantee correct inference about A versus C. A three-arm trial of A, B, and C would protect against this problem and should be considered when the sequential trials are performed in the context of changing secular trends in important omitted variables such as therapy in cancer screening trials.
authors.affiliation: Division of Cancer Prevention, National Cancer Institute. sb16i@nih.gov
authors.forename: Stuart G
authors.initials: SG
authors.lastname: Baker
authors.forename: Barnett S
authors.initials: BS
authors.lastname: Kramer
mesh_terms: D000971:Antineoplastic Combined Chemotherapy Protocols / Q000627:therapeutic use; D003627:Data Interpretation, Statistical; D006801:Humans; D008175:Lung Neoplasms / Q000401:mortality / Q000517:prevention & control; D008403:Mass Screening; D011014:Pneumonia / Q000188:drug therapy / Q000401:mortality; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000592:standards*; D013274:Stomach Neoplasms / Q000401:mortality / Q000628:therapy; D016019:Survival Analysis; D015996:Survival Rate