Samuel Berchuck is a Postdoctoral Associate in Duke University’s Department of Statistical Science and Forge-Duke’s Center for Actionable Health Data Science.
Joshua L. Warren is an Assistant Professor of Biostatistics at Yale University.
Introduction
Glaucoma is a leading cause of blindness worldwide, with a prevalence of 4% in the population aged 40-80. The disease is characterized by retinal ganglion cell death and corresponding damage to the optic nerve head. Since visual impairment caused by glaucoma is irreversible and efficient treatments exist, early detection of the disease is essential. Determining if the disease is progressing remains one of the most challenging aspects of glaucoma management, since it is difficult to distinguish true progression from variability due to natural degradation or noise. In practice, clinicians monitor progression using a multifactorial approach that relies on various measurements of the disease. In this series of blog posts, we focus on the use of visual fields. Visual field examinations obtain levels of a patient’s actual vision, and the practice is thus referred to as a functional measurement. As such, visual fields are a proxy for a patient’s quality of life, and therefore are typically prioritized in practice.
Visual Field Data
Visual fields are complex spatiotemporal data generated from an intricate anatomical system, which is important to understand for modeling purposes. To illustrate visual field data, we load an example data set from the womblR package on CRAN. The package womblR was developed specifically for analyzing visual field data, and uses a Bayesian hierarchical model that accounts for the complex nature of the data (more details will be provided in Part II). The specific data set comes from the Vein Pulsation Study Trial in Glaucoma and the Lions Eye Institute trial registry, Perth, Western Australia. We begin by loading the package.
library(womblR)
The data set of interest is loaded lazily and can be accessed as follows; we also view the first six rows for illustration.
data(VFSeries)
head(VFSeries)
## Visit DLS Time Location
## 1 1 25 0 1
## 2 2 23 126 1
## 3 3 23 238 1
## 4 4 23 406 1
## 5 5 24 504 1
## 6 6 21 588 1
The data object VFSeries contains a longitudinal series of visual fields for a glaucoma patient that we will use throughout the three blog posts to exemplify the study of visual fields. This patient has been determined to be progressing, based on the expertise of two clinicians. VFSeries has four variables: Visit, DLS, Time, and Location. The variable Visit represents the visual field test visit number, DLS the observed measure, Time the time of the visual field test (in days from baseline visit), and Location the spatial location on the visual field where the observation occurred. There are 9 visual field exams contained in this data set, and on average 117.25 days between visits.
To help visualize the dataframe, we can use the PlotVFTimeSeries function. PlotVFTimeSeries is a function that plots a patient’s observed visual acuity over time at each location on the visual field.
PlotVfTimeSeries(Y = VFSeries$DLS,
Location = VFSeries$Location,
Time = VFSeries$Time,
main = &quot;Visual field sensitivity time series \n at each location&quot;,
xlab = &quot;Days from baseline visit&quot;,
ylab = &quot;Differential light sensitivity (dB)&quot;,
line.reg = FALSE)
The above figure demonstrates the visual field from a Humphrey Field Analyzer-II (HFA-II) testing machine, which generates 54 spatial locations (only 52 informative locations; note the 2 blanks spots corresponding to the blind spot). The visual field map is constructed by assessing a patient’s response to varying levels of light. Patients are instructed to focus on a central fixation point as light is introduced randomly in a preceding manner over a grid on the visual field. As light is observed, the patient presses a button and the current light intensity is recorded. The process is repeated until the entire visual field is tested. The light intensity is measured in differential light sensitivity (DLS), which quantifies the difference in the HFA-II background and observed light intensity. Smaller values indicate worsening vision.
Spatial Anatomy on the Visual Field
The spatial surface of the visual field is observed on a lattice (i.e., uniform areal data); however, it is a complex projection of the underlying optic nerve head and exhibits anatomically induced spatial dependencies. In particular, localized damage to the optic disc can result in clinically deterministic deterioration across the visual field. Incorporating this non-standard spatial dependence structure into our methodology is a priority for properly analyzing these data, although it is commonly ignored. Translating this into math lingo, this means that a naive modeling of the spatial surface of the visual field would be inappropriate (i.e., neighbors defined through adjacent locations). Instead, the definition of a neighbor when considering vision loss on the visual field must depend on the underlying anatomical proximities.
To illustrate this concept, we begin by displaying the visual field neighborhood structure. The adjacency matrix for the HFA-II is available in the womblR package. In this analysis, we use a queen specification, meaning that an adjacency is defined as any location that shares an edge or corner on the lattice. We now load this adjacency matrix and remove the two locations that correspond to the blind spot.
blind_spot