title: Prior event rate ratio adjustment: numerical studies of a statistical method to address unrecognized confounding in observational studies.
abstract: OBJECTIVE
  The purpose of this study was to evaluate a statistical method, prior event rate ratio (PERR) adjustment, and an alternative, PERR-ALT, both of which have the potential to overcome "unmeasured confounding," both analytically and via simulation.
  
  
  METHODS
  Formulae were derived for the target estimates of both PERR methods, which were compared with results from simulations to ensure their validity. In addition to the theoretical insights gained, relative biases of both PERR methods for estimating exposure effects were also investigated via simulation studies and compared empirically with electronic medical record database study results.
  
  
  RESULTS
  Theoretical derivations closely matched simulated results. In simulation studies, both PERR methods significantly reduce bias from unmeasured confounding compared with the standard Cox model. When there is no interaction between unmeasured confounders and time intervals, the estimate from PERR-ALT is unbiased, whereas the estimate from PERR has well-controlled relative bias. When interactions exist, relative biases tend to increase but not greatly, especially when the exposure effect is relatively large in comparison with the interaction effects. When the event rate is low and the sample size is limited, PERR is more computationally stable than PERR-ALT. In empiric study comparisons with randomized controlled trials, both PERR methods show potential to reduce bias from the standard Cox model similarly when unmeasured confounding is present.
  
  
  CONCLUSIONS
  Extensive simulation studies and theoretical derivation show that PERR-based methods may reduce bias from unmeasured confounders when the exposure effect is relatively large in comparison with confounder-exposure interaction. The rare study event situation warrants further investigation.
authors.affiliation: Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA. meyu@biostat.wisc.edu
authors.forename: Menggang
authors.initials: M
authors.lastname: Yu
authors.forename: Dawei
authors.initials: D
authors.lastname: Xie
authors.forename: Xingmei
authors.initials: X
authors.lastname: Wang
authors.forename: Mark G
authors.initials: MG
authors.lastname: Weiner
authors.forename: Richard L
authors.initials: RL
authors.lastname: Tannen
mesh_terms: D015982:Bias; D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D016208:Databases, Factual / Q000706:statistics & numerical data; D004812:Epidemiologic Methods; D015233:Models, Statistical; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000379:methods / Q000706:statistics & numerical data; D012107:Research Design