The data from each child's most recent visit were first fit by a simple exponential model describing the visual acuity deficit as a function of the NOFF.
19 Subsequently, a second component was added in order to account for the visual deprivation, thus establishing a two-component model. The first term corresponds to the child's nystagmus characteristics at the time of the last visit (as quantified by the NOFF), and the second term describes the child's history of pendular nystagmus:
where NOFF is in logit units;
D =
D(onset, transition) is a deprivation parameter determined by the age at onset of pendular nystagmus and the age at transition to waveforms with extended foveation; and
a,
b, and
c are the model parameters. For each child, the deprivation parameter
D corresponded to the individual proportion of the sensitive period during which the child experienced pendular nystagmus (
Fig. 1). The shape of the sensitivity profile was described mathematically by the difference of two exponentials for ease of computing. This function is a simplified version of the one proposed by Banks et al.,
29 which has been used for modeling the sensitive period for binocular vision.
29,30 The parameters of the profile were set such that it had an onset at age 1.5 months, peaked at age 12 months, and diminished to zero after age 8 years (95% of the area under the curve prior to age 8 years). Published data on the actual human sensitivity profile for spatial vision (form vision deprivation) are all derived from monocular deprivation studies, but it seems reasonable to assume an initial “latent period” of less than 3 months (possibly none), a peak between 12 and 24 months of age, and a gradual decline to zero between ages 7 and 10 years.
31–34 This also corresponds roughly to the sensitive period for spatial vision in rhesus monkeys.
35 All data analyses and model fitting were performed in the R Environment for Statistical Computing.
36