title: The ACCE method: an approach for obtaining quantitative or qualitative estimates of residual confounding that includes unmeasured confounding.
abstract: BACKGROUND
  Nonrandomized studies typically cannot account for confounding from unmeasured factors.
  
  
  METHODS
  A method is presented that exploits the recently-identified phenomenon of  "confounding amplification" to produce, in principle, a quantitative estimate of total residual confounding resulting from both measured and unmeasured factors.  Two nested propensity score models are constructed that differ only in the deliberate introduction of an additional variable(s) that substantially predicts treatment exposure.  Residual confounding is then estimated by dividing the change in treatment effect estimate between models by the degree of confounding amplification estimated to occur, adjusting for any association between the additional variable(s) and outcome.
  
  
  RESULTS
  Several hypothetical examples are provided to illustrate how the method produces a quantitative estimate of residual confounding if the method's requirements and assumptions are met.  Previously published data is used to illustrate that, whether or not the method routinely provides precise quantitative estimates of residual confounding, the method appears to produce a valuable qualitative estimate of the likely direction and general size of residual confounding.
  
  
  CONCLUSIONS
  Uncertainties exist, including identifying the best approaches for: 1) predicting the amount of confounding amplification, 2) minimizing changes between the nested models unrelated to confounding amplification, 3) adjusting for the association of the introduced variable(s) with outcome, and 4) deriving confidence intervals for the method's estimates (although bootstrapping is one plausible approach).
  
  
  CONCLUSIONS
  To this author's knowledge, it has not been previously suggested that the phenomenon of confounding amplification, if such amplification is as predictable as suggested by a recent simulation, provides a logical basis for estimating total residual confounding. The method's basic approach is straightforward.  The method's routine usefulness, however, has not yet been established, nor has the method been fully validated. Rapid further investigation of this novel method is clearly indicated, given the potential value of its quantitative or qualitative output.
authors.affiliation: Psychiatrist, The Center for Organizational and Implementation Research (CHOIR) and the Mental Health Service Line of the Department of Veterans Affairs, Edith Nourse Rogers Memorial Medical Center, Bedford, MA 01730, USA ; Departments of Psychiatry and Quantitative Health Sciences, University of Massachusetts Medical School, Worcester, MA 01655, USA.
authors.forename: Eric G
authors.initials: EG
authors.lastname: Smith
keywords: bias amplification; confounding amplification; intervention research; nonrandomized study; observational study; propensity scores; residual confounding; unmeasured confounding