A glaucoma specialist at Bascom Palmer Eye Institute of the University of Miami Miller School of Medicine has developed novel statistical models for disease progression using the advanced computing resources of the Institute for Data Science and Computing (IDSC).
“Glaucoma is a painless blinding disease that progresses at varied rates in different people,” said Swarup S. Swaminathan, M.D., assistant professor of clinical ophthalmology. “While most patients progress at a slow rate, a small percentage of patients progress at a fast rate and can rapidly develop visual disability. It is vital to understand a patient’s rate of progression, so treatment can be appropriately initiated or augmented.”
Dr. Swaminathan was the lead author of a new collaborative study, “Rates of Glaucoma Progression Derived from Linear Mixed Models Using Varied Random Effect Distributions,” published in February in the journal Translational Vision Science and Technology.
J. Sunil Rao, Ph.D., professor and director of the Division of Biostatistics at the Miller School, was a co-author (pictured below, left). Dr. Swaminathan received a Mentoring for the Advancement of Physician Scientists (MAPS) grant from the American Glaucoma Society for this study, which was also supported by grants from the National Eye Institute and the National Institutes of Health.
Screening for Glaucoma
As there are no dramatic symptoms of glaucoma, clinicians typically screen for the disease using eye pressure and ancillary measures such as visual field testing. A decrease in peripheral vision or elevated eye pressure can be suggestive of glaucoma.
“Because we can’t directly measure the rate of change in an individual’s eye, we use metrics from visual field tests as proxies,” said Dr. Swaminathan. However, in clinical practice, patients are often tested only on an annual or semiannual basis, resulting in only a handful of data points over an extended period. This timeframe makes it difficult to accurately determine the rate of disease progression until several years have passed.
“Conventional modeling relies on ordinary least square (OLS) regression to calculate rates of progression, but these rates are highly inaccurate when using fewer than 5 or 6 data points. Prior research has looked at utilizing linear mixed models (LMM). These models consider the overall population’s mean when estimating an individual patient’s rate (i.e., the random effect component of the LMM). However, such models assume that these rates are normally distributed, which is not the case with glaucoma progression. Rather, most patients have rates around 0 (i.e., minimal progression) while approximately 5 to 10 percent of individuals exhibit rapid rates of visual field loss, thereby producing a left-skewed distribution,” said Dr. Swaminathan.
Building Alternate Models
In the new study, Dr. Swaminathan and his colleagues used a different approach, employing the log-gamma (LG) distribution to model the LMM random effects to see if the estimation of rates of change could be improved. As the LG distribution is a left-skewed distribution, the study team hypothesized that its use would better describe a glaucoma population.
“We used IDSC resources and the UM Triton supercomputer to build different models,” he said. “We then presented 1,500 simulated eyes to the models with various rates of change and asked the models to estimate the rate of change. We found that the LG model was more flexible and provided the greatest accuracy, especially amongst faster progressors.”
The study was a collaborative effort with investigators from the Duke Eye Center and used data from the Duke Glaucoma Registry. A total of 52,900 visual field tests from 6,558 eyes of 3,981 subjects were included. “We used about 80 percent of the data to train the models and the remaining 20 percent to test the models,” said Dr. Swaminathan. “Even with Triton, it took a week to run the models, and an additional two weeks to test the models on the large set of simulated eyes. Triton’s computational power is a tremendous benefit to us investigators at UM.”
While further studies are necessary, Dr. Swaminathan said linear mixed models using the LG distribution may provide valuable tools for clinicians and their patients in the future. The model might be able to predict the rate of change more quickly by using fewer data points. He added, “This work is an important step forward in our quest to identify high-risk glaucoma patients at an early stage and to act decisively to prevent vision loss.”
Swarup S. Swaminathan, Samuel I. Berchuck, Alessandro A. Jammal, J. Sunil Rao, Felipe A. Medeiros; Rates of Glaucoma Progression Derived from Linear Mixed Models Using Varied Random Effect Distributions. Trans. Vis. Sci. Tech. 2022;11(2):16. doi: https://doi.org/10.1167/tvst.11.2.16.
Story by Richard Westlund
Bascom Palmer Eye Institute on YouTube | Dr. Swaminathan discusses Glaucoma Research . . .