title: Selection bias modeling using observed data augmented with imputed record-level probabilities.
abstract: OBJECTIVE
  Selection bias is a form of systematic error that can be severe in compromised study designs such as case-control studies with inappropriate selection mechanisms or follow-up studies that suffer from extensive attrition. External adjustment for selection bias is commonly undertaken when such bias is suspected, but the methods used can be overly simplistic, if not unrealistic, and fail to allow for simultaneous adjustment of associations of the exposure and covariates with the outcome, when of interest. Internal adjustment for selection bias via inverse probability weighting allows bias parameters to vary with the levels of covariates but has only been formalized for longitudinal studies with covariate data on patients up until loss to follow-up.
  
  
  METHODS
  We demonstrate the use of inverse probability weighting and externally obtained bias parameters to perform internal adjustment of selection bias in studies lacking covariate data on unobserved participants.
  
  
  RESULTS
  The "true" or selection-adjusted odds ratio for the association between exposure and outcome was successfully obtained by analyzing only data on those in the selected stratum (i.e., responders) weighted by the inverse probability of their being selected as function of their observed covariate data.
  
  
  CONCLUSIONS
  This internal adjustment technique using user-supplied bias parameters and inverse probability weighting for selection bias can be applied to any type of observational study.
authors.affiliation: Palo Alto Medical Foundation Research Institute, Palo Alto, CA; Department of Epidemiology, UCLA Fielding School of Public Health, Los Angeles, CA. Electronic address: cathompson@ucla.edu.
authors.forename: Caroline A
authors.initials: CA
authors.lastname: Thompson
authors.affiliation: Department of Epidemiology, UCLA Fielding School of Public Health, Los Angeles, CA; UCLA Center for Health Policy Research, Los Angeles, CA; California Center for Population Studies, UCLA, Los Angeles; Department of Public Health, Academic Medical Center, University of Amsterdam, Amsterdam, The Netherlands.
authors.forename: Onyebuchi A
authors.initials: OA
authors.lastname: Arah
mesh_terms: D016010:Binomial Distribution; D015986:Confounding Factors, Epidemiologic; D015340:Epidemiologic Research Design; D006801:Humans; D016015:Logistic Models; D008137:Longitudinal Studies; D011336:Probability; D015983:Selection Bias
keywords: Casual inference; Epidemiologic methods; Selection bias