title: Accounting for standard errors of vision-specific latent trait in regression models.
abstract: OBJECTIVE
  To demonstrate the effectiveness of Hierarchical Bayesian (HB) approach in a modeling framework for association effects that accounts for SEs of vision-specific latent traits assessed using Rasch analysis.
  
  
  METHODS
  A systematic literature review was conducted in four major ophthalmic journals to evaluate Rasch analysis performed on vision-specific instruments. The HB approach was used to synthesize the Rasch model and multiple linear regression model for the assessment of the association effects related to vision-specific latent traits. The effectiveness of this novel HB one-stage "joint-analysis" approach allows all model parameters to be estimated simultaneously and was compared with the frequently used two-stage "separate-analysis" approach in our simulation study (Rasch analysis followed by traditional statistical analyses without adjustment for SE of latent trait).
  
  
  RESULTS
  Sixty-six reviewed articles performed evaluation and validation of vision-specific instruments using Rasch analysis, and 86.4% (n = 57) performed further statistical analyses on the Rasch-scaled data using traditional statistical methods; none took into consideration SEs of the estimated Rasch-scaled scores. The two models on real data differed for effect size estimations and the identification of "independent risk factors." Simulation results showed that our proposed HB one-stage "joint-analysis" approach produces greater accuracy (average of 5-fold decrease in bias) with comparable power and precision in estimation of associations when compared with the frequently used two-stage "separate-analysis" procedure despite accounting for greater uncertainty due to the latent trait.
  
  
  CONCLUSIONS
  Patient-reported data, using Rasch analysis techniques, do not take into account the SE of latent trait in association analyses. The HB one-stage "joint-analysis" is a better approach, producing accurate effect size estimations and information about the independent association of exposure variables with vision-specific latent traits.
authors.affiliation: Singapore Eye Research Institute, Singapore National Eye Centre, Singapore Department of Ophthalmology, Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore.
authors.forename: Wan Ling
authors.initials: WL
authors.lastname: Wong
authors.affiliation: Singapore Eye Research Institute, Singapore National Eye Centre, Singapore Department of Statistics and Applied Probability, National University of Singapore, Singapore Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, New York, United States.
authors.forename: Xiang
authors.initials: X
authors.lastname: Li
authors.affiliation: Department of Statistics and Applied Probability, National University of Singapore, Singapore.
authors.forename: Jialiang
authors.initials: J
authors.lastname: Li
authors.affiliation: Singapore Eye Research Institute, Singapore National Eye Centre, Singapore Department of Ophthalmology, Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore Office of Clinical Sciences, Duke-NUS Graduate Medical School, Singapore.
authors.forename: Tien Yin
authors.initials: TY
authors.lastname: Wong
authors.affiliation: Singapore Eye Research Institute, Singapore National Eye Centre, Singapore Department of Ophthalmology, Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, New York, United States Office of Clinical Sciences, Duke-NUS Graduate Medical School, Singapore.
authors.forename: Ching-Yu
authors.initials: CY
authors.lastname: Cheng
authors.affiliation: Singapore Eye Research Institute, Singapore National Eye Centre, Singapore Office of Clinical Sciences, Duke-NUS Graduate Medical School, Singapore.
authors.forename: Ecosse L
authors.initials: EL
authors.lastname: Lamoureux
mesh_terms: D001499:Bayes Theorem; D006801:Humans; D015233:Models, Statistical; D017063:Outcome Assessment, Health Care / Q000379:methods / Q000706:statistics & numerical data*; D012044:Regression Analysis; D014786:Vision Disorders / Q000175:diagnosis*
keywords: Rasch analysis; latent trait; measurement error