title: Cox regression was used to compare the measurement error of two tests vs. a gold standard.
abstract: OBJECTIVE
  The use of survival analysis has been proposed to compare the diagnostic performance of two tests. We expanded it to compare two tests with a gold standard simultaneously.
  
  
  METHODS
  In this diagnostic study, the spherical equivalent component of refraction was measured with the PowerRefractor and the Canon R-50 autorefractor. The reference test was Canon R-50 autorefraction with cycloplegic blockage of accommodation. The error of the two index tests was compared with Cox regression analysis with robust standard error estimation to take into account repeated measures on the same subject. We evaluated 1,559 children aged 5-6 from 25 schools in three urban locations in Ecuador.
  
  
  RESULTS
  The main strength of survival analysis was that it does not assume a specific distribution of measurement errors, which were not normally distributed in this study. The proportional hazards assumption, a requirement of Cox regression, was met only after removal of the bias of each test. When this was done, noncycloplegic autorefraction was better than the PowerRefractor regardless of the magnitude and direction of the error.
  
  
  CONCLUSIONS
  The potential of Cox regression can be applied to diagnostic studies that compare more tests with a gold standard.
authors.affiliation: Department of Oto-Neuro-Ophthalmological Surgical Sciences, University of Florence, Viale Morgagni 85, Florence 50134, Italy. gianni.virgili@unifi.it
authors.forename: Gianni
authors.initials: G
authors.lastname: Virgili
authors.forename: Mario
authors.initials: M
authors.lastname: Angi
authors.forename: Andrea
authors.initials: A
authors.lastname: Molinari
authors.forename: Veronica
authors.initials: V
authors.lastname: Casotto
mesh_terms: D000065:Accommodation, Ocular / Q000187:drug effects; D000293:Adolescent; D015982:Bias; D002648:Child; D002675:Child, Preschool; D003951:Diagnostic Errors; D006801:Humans; D009184:Mydriatics / Q000494:pharmacology; D016016:Proportional Hazards Models; D012029:Refraction, Ocular / Q000502:physiology; D012030:Refractive Errors / Q000175:diagnosis*; D012044:Regression Analysis; D015203:Reproducibility of Results; D016019:Survival Analysis; D014787:Vision Tests / Q000379:methods
chemical_list: D009184:Mydriatics