Combining structural and functional measurements to improve detection of glaucoma progression using Bayesian hierarchical models.

PURPOSE To present and evaluate a new methodology for combining longitudinal information from structural and functional tests to improve detection of glaucoma progression and estimation of rates of change. METHODS This observational cohort study included 434 eyes of 257 participants observed for an average of 4.2 ± 1.1 years and recruited from the Diagnostic Innovations in Glaucoma Study (DIGS). The subjects were examined annually with standard automated perimetry, optic disc stereophotographs, and scanning laser polarimetry with enhanced corneal compensation. Rates of change over time were measured using the visual field index (VFI) and average retinal nerve fiber layer thickness (TSNIT average). A bayesian hierarchical model was built to integrate information from the longitudinal measures and classify individual eyes as progressing or not. Estimates of sensitivity and specificity of the bayesian method were compared with those obtained by the conventional approach of ordinary least-squares (OLS) regression. RESULTS The bayesian method identified a significantly higher proportion of the 405 glaucomatous and suspect eyes as having progressed when compared with the OLS method (22.7% vs. 12.8%; P < 0.001), while having the same specificity of 100% in 29 healthy eyes. In addition, the bayesian method identified a significantly higher proportion of eyes with progression by optic disc stereophotographs compared with the OLS method (74% vs. 37%; P = 0.001). CONCLUSIONS A bayesian hierarchical modeling approach for combining functional and structural tests performed significantly better than the OLS method for detection of glaucoma progression. (ClinicalTrials.gov number, NCT00221897.).

[1]  Pranab K Sen,et al.  Estimating correlation by using a general linear mixed model: evaluation of the relationship between the concentration of HIV‐1 RNA in blood and semen , 2003, Statistics in medicine.

[2]  D. Zucker,et al.  Inference for the association between coefficients in a multivariate growth curve model. , 1995, Biometrics.

[3]  Geert Verbeke,et al.  Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles , 2006, Biometrics.

[4]  M. Nicolela,et al.  Rates of neuroretinal rim and peripapillary atrophy area change: a comparative study of glaucoma patients and normal controls. , 2009, Ophthalmology.

[5]  F. Fitzke,et al.  Scaling the hill of vision: the physiological relationship between light sensitivity and ganglion cell numbers. , 2000, Investigative ophthalmology & visual science.

[6]  F. Medeiros,et al.  The Relationship between intraocular pressure and progressive retinal nerve fiber layer loss in glaucoma. , 2009, Ophthalmology.

[7]  P. Khaw,et al.  Primary open-angle glaucoma , 2004, The Lancet.

[8]  Jost B Jonas,et al.  Optic disc progression in glaucoma: comparison of confocal scanning laser tomography to optic disc photographs in a prospective study. , 2009, Investigative ophthalmology & visual science.

[9]  F. Medeiros,et al.  Improved Prediction of Rates of Visual Field Loss in Glaucoma Using Empirical Bayes Estimates of Slopes of Change , 2012, Journal of glaucoma.

[10]  David P Crabb,et al.  Structure and function in glaucoma: The relationship between a functional visual field map and an anatomic retinal map. , 2006, Investigative ophthalmology & visual science.

[11]  G. Verbeke,et al.  The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data , 1997 .

[12]  R. Weinreb,et al.  Individualized compensation of anterior segment birefringence during scanning laser polarimetry. , 2002, Investigative ophthalmology & visual science.

[13]  G. Holder,et al.  Relationship between electrophysiological, psychophysical, and anatomical measurements in glaucoma. , 2002, Investigative ophthalmology & visual science.

[14]  Shu Liu,et al.  Evaluation of retinal nerve fiber layer progression in glaucoma: a study on optical coherence tomography guided progression analysis. , 2010, Investigative ophthalmology & visual science.

[15]  Yangxin Huang,et al.  Skew‐normal Bayesian nonlinear mixed‐effects models with application to AIDS studies , 2010, Statistics in medicine.

[16]  Donald C. Hood,et al.  A framework for comparing structural and functional measures of glaucomatous damage , 2007, Progress in Retinal and Eye Research.

[17]  D. Grewal,et al.  Comparing rates of retinal nerve fibre layer loss with GDxECC using different methods of visual-field progression , 2010, British Journal of Ophthalmology.

[18]  E. E. Hartmann,et al.  The Ocular Hypertension Treatment Study: a randomized trial determines that topical ocular hypotensive medication delays or prevents the onset of primary open-angle glaucoma. , 2002, Archives of ophthalmology.

[19]  D. Garway-Heath,et al.  The spatial pattern of neuroretinal rim loss in ocular hypertension. , 2009, Investigative ophthalmology & visual science.

[20]  F. Medeiros,et al.  Detection of glaucoma progression with stratus OCT retinal nerve fiber layer, optic nerve head, and macular thickness measurements. , 2009, Investigative ophthalmology & visual science.

[21]  Robert N Weinreb,et al.  Impact of atypical retardation patterns on detection of glaucoma progression using the GDx with variable corneal compensation. , 2009, American journal of ophthalmology.

[22]  M. D. Branco,et al.  Bivariate random effect model using skew‐normal distribution with application to HIV‐RNA , 2007, Statistics in medicine.

[23]  Valter Torri,et al.  Results of the European Glaucoma Prevention Study. , 2005, Ophthalmology.

[24]  A. Gelman Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) , 2004 .

[25]  H. Jampel,et al.  Natural history of normal-tension glaucoma. , 2001, Ophthalmology.

[26]  Chris A Johnson,et al.  Glaucomatous progression in series of stereoscopic photographs and Heidelberg retina tomograph images. , 2010, Archives of ophthalmology.

[27]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[28]  B. Chauhan,et al.  Longitudinal changes in the visual field and optic disc in glaucoma , 2005, Progress in Retinal and Eye Research.

[29]  M. C. Leske,et al.  Natural history of open-angle glaucoma. , 2009, Ophthalmology.

[30]  J. M. Miller,et al.  Correlation of structure and function in glaucoma. Quantitative measurements of disc and field. , 1988, Ophthalmology.

[31]  D. Grewal,et al.  Detecting glaucomatous progression using GDx with variable and enhanced corneal compensation using Guided Progression Analysis , 2010, British Journal of Ophthalmology.

[32]  B C Chauhan,et al.  Optic disc and visual field changes in a prospective longitudinal study of patients with glaucoma: comparison of scanning laser tomography with conventional perimetry and optic disc photography. , 2001, Archives of ophthalmology.

[33]  Dipankar Bandyopadhyay,et al.  Linear mixed models for skew-normal/independent bivariate responses with an application to periodontal disease. , 2010, Statistics in medicine.

[34]  Cong Ye,et al.  Evaluation of retinal nerve fiber layer progression in glaucoma: a comparison between the fast and the regular retinal nerve fiber layer scans. , 2011, Ophthalmology.

[35]  M. Steel,et al.  On Bayesian Modelling of Fat Tails and Skewness , 1998 .

[36]  Simon G Thompson,et al.  Flexible parametric models for random‐effects distributions , 2008, Statistics in medicine.

[37]  L A Beckett,et al.  Multivariate longitudinal models for complex change processes , 2004, Statistics in medicine.

[38]  Robert N Weinreb,et al.  Detection of progressive retinal nerve fiber layer loss in glaucoma using scanning laser polarimetry with variable corneal compensation. , 2009, Investigative ophthalmology & visual science.

[39]  Chris A. Johnson,et al.  Comparison of different methods for detecting glaucomatous visual field progression. , 2003, Investigative ophthalmology & visual science.

[40]  H. Lemij,et al.  Enhanced imaging algorithm for scanning laser polarimetry with variable corneal compensation. , 2006, Investigative ophthalmology & visual science.

[41]  Ernesto San Martín,et al.  Linear mixed models with skew-elliptical distributions: A Bayesian approach , 2008, Comput. Stat. Data Anal..

[42]  N. Scott,et al.  Perimetric Progression in Open Angle Glaucoma and the Visual Field Index (VFI) , 2011, Journal of glaucoma.

[43]  F. Medeiros,et al.  Prediction of functional loss in glaucoma from progressive optic disc damage. , 2009, Archives of ophthalmology.

[44]  F. Medeiros,et al.  Rates of progressive retinal nerve fiber layer loss in glaucoma measured by scanning laser polarimetry. , 2010, American journal of ophthalmology.

[45]  G. Verbeke,et al.  A Linear Mixed-Effects Model with Heterogeneity in the Random-Effects Population , 1996 .

[46]  G. Wollstein,et al.  Optical coherence tomography longitudinal evaluation of retinal nerve fiber layer thickness in glaucoma. , 2005, Archives of ophthalmology.

[47]  Yangxin Huang,et al.  A bayesian approach to joint mixed-effects models with a skew-normal distribution and measurement errors in covariates. , 2011, Biometrics.

[48]  F. Medeiros,et al.  Agreement for detecting glaucoma progression with the GDx guided progression analysis, automated perimetry, and optic disc photography. , 2010, Ophthalmology.

[49]  H. Lemij,et al.  Relationships between standard automated perimetry, HRT confocal scanning laser ophthalmoscopy, and GDx VCC scanning laser polarimetry. , 2005, Investigative ophthalmology & visual science.

[50]  Earl L. Smith,et al.  Neural losses correlated with visual losses in clinical perimetry. , 2004, Investigative ophthalmology & visual science.

[51]  Robert N Weinreb,et al.  Use of progressive glaucomatous optic disk change as the reference standard for evaluation of diagnostic tests in glaucoma. , 2005, American journal of ophthalmology.

[52]  Hans G Lemij,et al.  Structure-function relationship is stronger with enhanced corneal compensation than with variable corneal compensation in scanning laser polarimetry. , 2007, Investigative ophthalmology & visual science.

[53]  G Molenberghs,et al.  Random-effects models for multivariate repeated measures , 2007, Statistical methods in medical research.

[54]  D. Garway-Heath,et al.  Factors affecting the test-retest variability of Heidelberg retina tomograph and Heidelberg retina tomograph II measurements , 2005, British Journal of Ophthalmology.

[55]  R. Weinreb,et al.  Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness. , 1990, Archives of ophthalmology.

[56]  Robert N Weinreb,et al.  The African Descent and Glaucoma Evaluation Study (ADAGES): design and baseline data. , 2009, Archives of ophthalmology.

[57]  D. Garway-Heath,et al.  Relationship between visual field sensitivity and retinal nerve fiber layer thickness as measured by scanning laser polarimetry. , 2004, Investigative ophthalmology & visual science.

[58]  Nicholas G Strouthidis,et al.  Optic disc and visual field progression in ocular hypertensive subjects: detection rates, specificity, and agreement. , 2006, Investigative ophthalmology & visual science.

[59]  Inchi Hu,et al.  Flexible modelling of random effects in linear mixed models - A Bayesian approach , 2008, Comput. Stat. Data Anal..

[60]  L. Zangwill,et al.  Scanning laser polarimetry to measure the nerve fiber layer of normal and glaucomatous eyes. , 1995, American journal of ophthalmology.

[61]  Balint Kovacs,et al.  Relationship between visual field sensitivity and retinal nerve fiber layer thickness as measured by optical coherence tomography. , 2007, Investigative ophthalmology & visual science.

[62]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[63]  B. Bengtsson,et al.  A visual field index for calculation of glaucoma rate of progression. , 2008, American journal of ophthalmology.

[64]  V. Greenstein,et al.  A comparison of functional and structural measures for identifying progression of glaucoma. , 2011, Investigative ophthalmology & visual science.