title: Handling over-dispersion of performance indicators.
abstract: OBJECTIVE
  A problem can arise when a performance indicator shows substantially more variability than would be expected by chance alone, since ignoring such "over-dispersion" could lead to a large number of institutions being inappropriately classified as "abnormal". A number of options for handling this phenomenon are investigated, ranging from improved risk stratification to fitting a statistical model that robustly estimates the degree of over-dispersion.
  
  
  METHODS
  Retrospective analysis of publicly available data on survival following coronary artery bypass grafts, emergency readmission rates, and teenage pregnancies.
  
  
  METHODS
  NHS trusts in England.
  
  
  RESULTS
  Funnel plots clearly show the influence of the method chosen for dealing with over-dispersion on the "banding" a trust receives. Both multiplicative and additive approaches are feasible and give intuitively reasonable results, but the additive random effects formulation appears to have a stronger conceptual foundation.
  
  
  CONCLUSIONS
  A random effects model may offer a reasonable solution. This method has now been adopted by the UK Healthcare Commission in their derivation of star ratings.
authors.affiliation: MRC Biostatistics Unit, Institute of Public Health, Cambridge CB2 2SR, UK. david.spiegelhalter@mrc-bsu.cam.ac.uk
authors.forename: D J
authors.initials: DJ
authors.lastname: Spiegelhalter
mesh_terms: D000293:Adolescent; D019985:Benchmarking; D016000:Cluster Analysis; D016001:Confidence Intervals; D001026:Coronary Artery Bypass / Q000401:mortality* / Q000706:statistics & numerical data*; D004630:Emergencies; D005240:Feasibility Studies; D005260:Female; D006801:Humans; D008297:Male; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care; D010359:Patient Readmission / Q000706:statistics & numerical data*; D011247:Pregnancy; D011253:Pregnancy in Adolescence / Q000706:statistics & numerical data*; D011785:Quality Assurance, Health Care; D012189:Retrospective Studies; D018570:Risk Assessment; D006113:United Kingdom