title: On the role of marginal confounder prevalence - implications for the high-dimensional propensity score algorithm.
abstract: OBJECTIVE
  The high-dimensional propensity score algorithm attempts to improve control of confounding in typical treatment effect studies in pharmacoepidemiology and is increasingly being used for the analysis of large administrative databases. Within this multi-step variable selection algorithm, the marginal prevalence of non-zero covariate values is considered to be an indicator for a count variable's potential confounding impact. We investigate the role of the marginal prevalence of confounder variables on potentially caused bias magnitudes when estimating risk ratios in point exposure studies with binary outcomes.
  
  
  METHODS
  We apply the law of total probability in conjunction with an established bias formula to derive and illustrate relative bias boundaries with respect to marginal confounder prevalence.
  
  
  RESULTS
  We show that maximum possible bias magnitudes can occur at any marginal prevalence level of a binary confounder variable. In particular, we demonstrate that, in case of rare or very common exposures, low and high prevalent confounder variables can still have large confounding impact on estimated risk ratios.
  
  
  CONCLUSIONS
  Covariate pre-selection by prevalence may lead to sub-optimal confounder sampling within the high-dimensional propensity score algorithm. While we believe that the high-dimensional propensity score has important benefits in large-scale pharmacoepidemiologic studies, we recommend omitting the prevalence-based empirical identification of candidate covariates.
authors: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada.|Centre for Clinical Epidemiology, Lady Davis Institute, Jewish General Hospital, Montreal, Quebec, Canada.
authors: Tibor
authors: T
authors: Schuster
authors: Centre for Clinical Epidemiology, Lady Davis Institute, Jewish General Hospital, Montreal, Quebec, Canada.
authors: Menglan
authors: M
authors: Pang
authors: Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Quebec, Canada.|Department of Pediatrics, McGill University, Montreal, Quebec, Canada.
authors: Robert W
authors: RW
authors: Platt
mesh_terms: D000465:Algorithms; D015986:Confounding Factors, Epidemiologic; D016208:Databases, Factual / Q000706:statistics & numerical data; D006801:Humans; D016017:Odds Ratio; D017891:Pharmacoepidemiology / Q000706:statistics & numerical data*; D015995:Prevalence; D057216:Propensity Score
keywords: bias formula; confounder prevalence; high-dimensional propensity score; pharmacoepidemiology; risk ratio