title: Use of re-randomized data in meta-analysis.
abstract: BACKGROUND
  Outcomes collected in randomized clinical trials are observations of random variables that should be independent and identically distributed. However, in some trials, the patients are randomized more than once thus violating both of these assumptions. The probability of an event is not always the same when a patient is re-randomized; there is probably a non-zero covariance coming from observations on the same patient. This is of particular importance to the meta-analysts.
  
  
  METHODS
  We developed a method to estimate the relative error in the risk differences with and without re-randomization of the patients. The relative error can be estimated by an expression depending on the percentage of the patients who were re-randomized, multipliers (how many times more likely it is to repeat an event) for the probability of reoccurrences, and the ratio of the total events reported and the initial number of patients entering the trial.
  
  
  RESULTS
  We illustrate our methods using two randomized trials testing growth factors in febrile neutropenia. We showed that under some circumstances the relative error of taking into account re-randomized patients was sufficiently small to allow using the results in the meta-analysis. Our findings indicate that if the study in question is of similar size to other studies included in the meta-analysis, the error introduced by re-randomization will only minimally affect meta-analytic summary point estimate. We also show that in our model the risk ratio remains constant during the re-randomization, and therefore, if a meta-analyst is concerned about the effect of re-randomization on the meta-analysis, one way to sidestep the issue and still obtain reliable results is to use risk ratio as the measure of interest.
  
  
  CONCLUSIONS
  Our method should be helpful in the understanding of the results of clinical trials and particularly helpful to the meta-analysts to assess if re-randomized patient data can be used in their analyses.
authors.affiliation: Department of Mathematics, Indiana University Northwest, Gary, IN, USA. ihozo@iun.edu
authors.forename: Iztok
authors.initials: I
authors.lastname: Hozo
authors.forename: Benjamin
authors.initials: B
authors.lastname: Djulbegovic
authors.forename: Otavio
authors.initials: O
authors.lastname: Clark
authors.forename: Gary H
authors.initials: GH
authors.lastname: Lyman
mesh_terms: D003115:Colony-Stimulating Factors / Q000627:therapeutic use; D003627:Data Interpretation, Statistical; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D009503:Neutropenia / Q000139:chemically induced / Q000628:therapy; D016017:Odds Ratio; D017063:Outcome Assessment, Health Care / Q000706:statistics & numerical data*; D018579:Patient Selection; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data*; D012008:Recurrence; D003294:Seizures, Febrile / Q000139:chemically induced / Q000628:therapy; D015983:Selection Bias
chemical_list: D003115:Colony-Stimulating Factors