title: Intraclass correlation coefficient and outcome prevalence are associated in clustered binary data.
abstract: OBJECTIVE
  To describe the association between values for a proportion and the intraclass correlation coefficient (ICC).
  
  
  METHODS
  Analysis of data obtained from the General Practice Research Database (GPRD) for variation between United Kingdom general practices and results from a Health Technology Assessment (HTA) review for a range of outcomes in community and health services settings.
  
  
  RESULTS
  There were 188 ICCs from the GPRD, the median prevalence was 13.1% (interquartile range IQR 3.5 to 28.4%) and median ICC 0.051 (IQR 0.011 to 0.094). There were 136 ICCs from the HTA review, with median prevalence 6.5% (IQR 0.4 to 20.7%) and median ICC 0.006 (IQR 0.0003 to 0.036). There was a linear association of log ICC with log prevalence in both datasets (GPRD, regression coefficient 0.61, 95% confidence interval 0.53 to 0.69, P < 0.001; HTA, 0.91, 0.81 to 1.01, P < 0.001). When the prevalence was 1% the predicted ICC was 0.008 from the GPRD or 0.002 from the HTA, but when the prevalence was 40% the predicted ICC was 0.075 (GPRD) or 0.046 (HTA).
  
  
  CONCLUSIONS
  The prevalence of an outcome may be used to make an informed assumption about the magnitude of the intraclass correlation coefficient.
authors.affiliation: Department of Public Health Sciences, King's College London, Capital House, 42 Weston St, London SE1 3QD, UK. martin.gulliford@kcl.ac.uk
authors.forename: M C
authors.initials: MC
authors.lastname: Gulliford
authors.forename: G
authors.initials: G
authors.lastname: Adams
authors.forename: O C
authors.initials: OC
authors.lastname: Ukoumunne
authors.forename: R
authors.initials: R
authors.lastname: Latinovic
authors.forename: S
authors.initials: S
authors.lastname: Chinn
authors.forename: M J
authors.initials: MJ
authors.lastname: Campbell
mesh_terms: D003627:Data Interpretation, Statistical; D016208:Databases, Factual; D005194:Family Practice; D006302:Health Services Research / Q000379:methods*; D006801:Humans; D015995:Prevalence; D011320:Primary Health Care; D016032:Randomized Controlled Trials as Topic / Q000379:methods*; D012107:Research Design; D013673:Technology Assessment, Biomedical / Q000379:methods; D006113:United Kingdom