title: Comparing simulation and threshold approaches when analysing data with probabilities of categories.
abstract: OBJECTIVE
  Constructing categories based on probabilities is not unusual in defining the outcome or the exposure. We compare the threshold approach and the simulation approach in making inferences.
  
  
  METHODS
  We used a simple structured example as well as published data to illustrate the difference between the simulation and the threshold approaches.
  
  
  RESULTS
  We demonstrated that simulation results were different from the threshold approach in estimating the effect of a high-deductible health plan. For repeat visits, we estimated a statistically significant ratio of incident rate ratio (IRR) 0.78 (95% CI: 0.64, 0.93) for non-preventable emergency department visits using the simulation approach while the high-severity category showed no statistical significance with the ratio of IRR 0.98 (95% CI: 0.64, 1.49) using a threshold of 75%. We also demonstrated that none of the threshold values could achieve the results of the simulation approach.
  
  
  CONCLUSIONS
  The simulation approach is preferred over the threshold one when analysing data with probability-based outcome, exposure and/or other covariates if the size of the data permits.
authors.affiliation: Department of Ambulatory Care and Prevention, Harvard Medical School and Harvard Pilgrim Health Care, Boston, MA 02215, USA. fang_zhang@hphc.org
authors.forename: Fang
authors.initials: F
authors.lastname: Zhang
authors.forename: J Frank
authors.initials: JF
authors.lastname: Wharam
authors.forename: Dennis
authors.initials: D
authors.lastname: Ross-Degnan
mesh_terms: D004636:Emergency Service, Hospital / Q000706:statistics & numerical data*; D006801:Humans; D008962:Models, Theoretical; D012720:Severity of Illness Index