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Yukai Zhao, Pan Zhang, Fang Hou, Luis A Lesmes, Zhong-Lin Lu; Comparing contrast sensitivity at individual spatial frequencies on qCSF data . Invest. Ophthalmol. Vis. Sci. 2020;61(7):4616.
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© ARVO (1962-2015); The Authors (2016-present)
The qCSF method provides an accurate, precise and efficient assessment of the contrast sensitivity function (CSF;Lesmes, et al, 2010;Hou, et al, 2015) with a four-parameter model and a Bayesian adaptive framework. However, hypothesis testing on contrast sensitivity (CS) at individual spatial frequencies (SFs) on the data obtained from the qCSF method is challenging because the CSs covary. In this study, we quantified the covariance among the CSs across different SFs from a published qCSF dataset with 112 subjects tested at three luminance conditions (Hou et al., 2016) with a hierarchical Bayesian model, and conducted hypothesis tests on CS at individual spatial frequencies.
The CSF was modeled as a linear interpolation of CS at six SFs(1, 1.5, 3, 6, 12 and 18 cpd). There were two hierarchies, one for the three luminance conditions and the other for each individual subject, with 18 CS hyperparameters (6 for each luminance level) and their covariance matrix. Parameters of individual subjects were drawn from their corresponding hyperparameter distributions. The distributions of all the hyperparameters and parameters and their covariance were constrained by the maximum likelihood. With luminance as the main factor, one-way ANOVA and post-hoc multiple comparison (PHMS) tests (Tukey-Kramer) were conducted on the distributions of the hyperparameters and parameters of individual subjects after considering the covariance.
The correlation between the 18 SF hyperparameters ranged from -0.078 to 0.762. The main effect (luminance) were significant (all p = 0) for CS of all 6 SFs for all 112 individual subjects as well as the aggregate of all the subjects. PHMS showed significant CS difference (α= 0.01) between all pairs of luminance conditions at all 6 SFs at the group level, and between conditions L1 and L3 for all subjects at the individual level. Between conditions L1 and L3, and between L2 and L3, CS were significantly different for at least 94.6% and 90.2% subjects, respectively, at all six SFs.
The covariance among the CSs at different SFs was obtained from the hierarchical Bayesian model, and then accounted for in hypothesis tests on CS at individual SFs at both the individual subject and group levels. The method developed in this study would allow us to obtain more detailed assessments of CSF changes in different experimental conditions or disease states.
This is a 2020 ARVO Annual Meeting abstract.
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