title: Comparison of regression models for serial visual field analysis.
abstract: OBJECTIVE
  Our aim was to compare fit and predictive performance effectiveness of four pointwise regression models in measuring the visual field (VF) decay rate of progression in patients with open-angle glaucoma.
  
  
  METHODS
  We selected Humphrey VF data of patients with open-angle glaucoma with a minimum follow-up time of 6 years. For each eye (n = 798 from 588 patients), we regressed threshold sensitivity (y) at each VF test location for the entire VF series against follow-up time (x), with four candidate first-order regression models: (1) ordinary least-squares linear regression model (y = β 0 + β 1 x); (2) nondecay exponential regression model (y = β 0 + β 1e (x) ); (3) decay exponential regression model ([Formula: see text]); (4) Tobit-censored, maximum-likelihood linear regression model (y* = [Formula: see text], ε ~ N(0, σ(2))), where x is follow-up time and y is threshold sensitivity.
  
  
  RESULTS
  The average [± standard deviation (SD)] baseline VF mean deviation (MD) was -8.2 (±5.5) dB, the mean follow-up was 8.7 (±1.9) years, and the number of follow-up VFs was 14.7 (±4.4). The decay exponential model was the best-fitting (42.7 % of locations) and best-forecasting (65.5 % of locations) model. The decay exponential model was the best prediction model in all categories of severity.
  
  
  CONCLUSIONS
  It is not clear that the ordinary least-squares linear regression model is always the favored model for fitting and forecasting VF data in patients with glaucoma. The pointwise decay exponential regression (PER) model was the best-fitting and best-predicting model across a wide range of glaucoma severity and can be readily understood by clinicians.
authors.affiliation: Glaucoma Division, Siloam Eye Hospital, Seoul, South Korea, eyejune.lee@gmail.com.
authors.forename: Jun Mo
authors.initials: JM
authors.lastname: Lee
authors.forename: Kouros
authors.initials: K
authors.lastname: Nouri-Mahdavi
authors.forename: Esteban
authors.initials: E
authors.lastname: Morales
authors.forename: Abdelmonem
authors.initials: A
authors.lastname: Afifi
authors.forename: Fei
authors.initials: F
authors.lastname: Yu
authors.forename: Joseph
authors.initials: J
authors.lastname: Caprioli
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D018450:Disease Progression; D005188:False Negative Reactions; D005260:Female; D005500:Follow-Up Studies; D005902:Glaucoma, Open-Angle / Q000175:diagnosis / Q000503:physiopathology*; D006801:Humans; D007429:Intraocular Pressure; D016014:Linear Models; D008297:Male; D015233:Models, Statistical; D009901:Optic Nerve Diseases / Q000175:diagnosis / Q000503:physiopathology*; D011237:Predictive Value of Tests; D011336:Probability; D014794:Visual Fields / Q000502:physiology*