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Zhong-Lin Lu, Yukai Zhao, Pan Zhang, Fang Hou, Luis A Lesmes; Comparing parameters of the contrast sensitivity functions obtained from the qCSF Method. Invest. Ophthalmol. Vis. Sci. 2020;61(7):4615.
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Using a four-parameter function to model the contrast sensitivity function (CSF), the qCSF method uses a Bayesian adaptive framework to provide an accurate, precise and efficient assessment of vision (Lesmes, et al, 2010). However, hypothesis testing on individual parameters of the CSF has been challenged by potential covariance between them. In this study, we developed a hierarchical Bayesian model to explicitly quantify the covariance among the CSF parameters and analyzed a published qCSF dataset with 112 subjects each tested in three luminance conditions (Hou et al., 2016).
The CSF was modeled with a truncated log parabola with peak gain (PG), peak spatial frequency (PF), bandwidth at half height (BH), and low frequency truncation level (LT). There were two hierarchies, one for the luminance conditions and the other for individual subjects, with eight hyperparameters and their covariance: 3 PG and 3 PF for the three luminance conditions, and 1 BH and 1 LT across all conditions. Parameters of individual subjects were drawn from the corresponding hyperparameter distributions. The maximum likelihood was used to compute the distributions of all the hyperparameters and parameters and the covariance. We conducted one-way ANOVA and post-hoc multiple comparison (PHMS) tests (Tukey-Kramer) on the distributions of the hyperparameters and the parameters of individual subjects after accounting for the covariance.
The correlation between the 8 hyperparameters ranged from -0.293 to 0.566. The main effect (luminance) was significant for both PG and PF for each of the 112 individual subjects (all p = 0) as well as their aggregate (p = 0). PHMS showed significant PG and PF differences (alpha =0.01) between all pairs of luminance conditions at the group level, and between conditions L1 and L2, and between conditions L1 and L3 for every individual subject. Between conditions L2 and L3, PG and PF were significantly different for 94% and 97% subjects, respectively.
The hierarchical Bayesian model enabled us to explicitly quantify the covariance among the parameters of the CSF from the qCSF method and conduct hypothesis testing on individual parameters after removing the covariance at both the individual subject and group levels. In addition, the distributions of the hyperparameters and their covariance can be used as informative priors to further improve the efficiency of the qCSF method.
This is a 2020 ARVO Annual Meeting abstract.
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