title: Log-gamma linear-mixed effects models for multiple outcomes with application to a longitudinal glaucoma study.
abstract: Glaucoma is a progressive disease due to damage in the optic nerve with associated functional losses. Although the relationship between structural and functional progression in glaucoma is well established, there is disagreement on how this association evolves over time. In addressing this issue, we propose a new class of non-Gaussian linear-mixed models to estimate the correlations among subject-specific effects in multivariate longitudinal studies with a skewed distribution of random effects, to be used in a study of glaucoma. This class provides an efficient estimation of subject-specific effects by modeling the skewed random effects through the log-gamma distribution. It also provides more reliable estimates of the correlations between the random effects. To validate the log-gamma assumption against the usual normality assumption of the random effects, we propose a lack-of-fit test using the profile likelihood function of the shape parameter. We apply this method to data from a prospective observation study, the Diagnostic Innovations in Glaucoma Study, to present a statistically significant association between structural and functional change rates that leads to a better understanding of the progression of glaucoma over time.
authors.affiliation: Department of Mathematics, Zhejiang University, 86 Zheda Road, Hangzhou, Zhejiang, 310012, China.
authors.forename: Peng
authors.initials: P
authors.lastname: Zhang
authors.affiliation: Bank of Montreal, Toronto M5X 1A1, Canada.
authors.forename: Dandan
authors.initials: D
authors.lastname: Luo
authors.affiliation: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
authors.forename: Pengfei
authors.initials: P
authors.lastname: Li
authors.affiliation: Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, La Jolla, CA, 92093, USA.
authors.forename: Lucie
authors.initials: L
authors.lastname: Sharpsten
authors.affiliation: Hamilton Glaucoma Center, Department of Ophthalmology, University of California, San Diego, La Jolla, CA, 92093, USA.
authors.forename: Felipe A
authors.initials: FA
authors.lastname: Medeiros
mesh_terms: D001699:Biometry / Q000379:methods*; D005260:Female; D005901:Glaucoma / Q000175:diagnosis* / Q000453:epidemiology* / Q000473:pathology / Q000503:physiopathology; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D008137:Longitudinal Studies; D008297:Male; D008875:Middle Aged; D011379:Prognosis
keywords: Functional progression; Glaucoma; Log-gamma distribution; Markov chain Monte Carlo; Multivariate longitudinal data; Profile likelihood; Structural progression