title: Propensity score interval matching: using bootstrap confidence intervals for accommodating estimation errors of propensity scores.
abstract: BACKGROUND
  Propensity score methods have become a popular tool for reducing selection bias in making causal inference from observational studies in medical research. Propensity score matching, a key component of propensity score methods, normally matches units based on the distance between point estimates of the propensity scores. The problem with this technique is that it is difficult to establish a sensible criterion to evaluate the closeness of matched units without knowing estimation errors of the propensity scores.
  
  
  METHODS
  The present study introduces interval matching using bootstrap confidence intervals for accommodating estimation errors of propensity scores. In interval matching, if the confidence interval of a unit in the treatment group overlaps with that of one or more units in the comparison group, they are considered as matched units.
  
  
  RESULTS
  The procedure of interval matching is illustrated in an empirical example using a real-life dataset from the Nursing Home Compare, a national survey conducted by the Centers for Medicare and Medicaid Services. The empirical example provided promising evidence that interval matching reduced more selection bias than did commonly used matching methods including the rival method, caliper matching. Interval matching's approach methodologically sounds more meaningful than its competing matching methods because interval matching develop a more "scientific" criterion for matching units using confidence intervals.
  
  
  CONCLUSIONS
  Interval matching is a promisingly better alternative tool for reducing selection bias in making causal inference from observational studies, especially useful in secondary data analysis on national databases such as the Centers for Medicare and Medicaid Services data.
authors.affiliation: School of Nursing, Duke University, DUMC 3322, 307 Trent Drive, Durham, NC, 27710, USA. wei.pan@duke.edu.
authors.forename: Wei
authors.initials: W
authors.lastname: Pan
authors.affiliation: Department of Educational and Human Sciences, University of Central Florida, PO Box 161250, Orlando, FL, 32816, USA. haiyan.bai@ucf.edu.
authors.forename: Haiyan
authors.initials: H
authors.lastname: Bai
mesh_terms: D000465:Algorithms; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006297:Health Services Accessibility; D006801:Humans; D009735:Nursing Homes / Q000592:standards; D057216:Propensity Score; D011785:Quality Assurance, Health Care / Q000379:methods*; D012044:Regression Analysis; D012424:Rural Population; D015983:Selection Bias; D014481:United States; D014505:Urban Population