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Glaucoma 20-year incidence may be estimated by mathematical model


Using a mathematical model, investigators have estimated that people with ocular hypertension have a nearly 30% risk of developing glaucoma over 20 years, adjusting for the competing risk of mortality. Among ocular hypertensive patients aged more than 70 years, however, a 90% risk of mortality exists over that 20-year period, suggesting that preventive treatment would have little benefit.

Key Points

St. Louis-One of the most problematic issues ophthalmologists may have to address is determining which patients with ocular hypertension should be treated to prevent glaucoma and which should be monitored instead, and how the patient's age should be factored into the decision. A mathematical model may help answer this question.

Using a decision analytic approach, scientists at Washington University in St. Louis (WUSTL) learned that the 20-year incidence of glaucoma among those with ocular hypertension was lower among individuals aged more than 70 years because of their shorter life expectancy, suggesting that preventive treatment is unlikely to have much benefit. Treatment for those with ocular hypertension who are aged fewer than 70 years, however, could result in a significant lowering of the 20-year incidence of primary open-angle glaucoma (POAG), said Steven M. Kymes, PhD, research assistant professor, Department of Ophthalmology and Visual Sciences, and research instructor, Division of Biostatistics, at WUSTL.

The investigators decided to examine the 20-year incidence of glaucoma among individuals with ocular hypertension, because 20 years is the average life expectancy of individuals in whom ocular hypertension is diagnosed.

He added that it would be difficult to determine the long-term risk of developing glaucoma in this group with a population-based study, because following the participants for 20 years would be expensive and complicated. Thus, he and his colleagues adopted an alternative approach, using a model that incorporated data from various studies and extrapolating to estimate what would happen if the trends persisted over 20 years. They adapted a model that had been developed for the Ocular Hypertension Treatment Study (OHTS) to examine the cost-effectiveness of treatment of ocular hypertension to prevent glaucoma, removing the cost data and concentrating on the incidence data.

"The key issue when we consider the risk of developing glaucoma over 20 years is that some people are going to die, so we need to consider mortality in our estimates," Dr. Kymes said.

Markov model

The Markov model of disease process is a mathematical method of describing complex mathematical process over time. The model for this study was built on information such as the known distribution of ocular hypertension by age (from the Baltimore Eye Study), incidence data from OHTS, and additional data from the OHTS risk model showing that the incidence of POAG increases with age. U.S. Census life tables also were used, and the model was stratified for age (40 to 50, 51 to 60, 61 to 70, and 70+ years). The simulated cohort included 25,000 individuals with ocular hypertension.

Results of the simulation indicated that individuals with hypertension who were aged 50 to 70 years had approximately a 29% to 31% risk of developing glaucoma over a 20-year period if they had no medical treatment. Individuals aged more than 70 years had a slightly smaller risk of developing glaucoma, 26.2%, due to the higher probability of death before the development of glaucoma. The expected 20-year incidence of POAG for all age groups combined was 29.3%.

If only individuals with a 5% annual risk of developing POAG were treated, the model predicted that the 20-year incidence would range from 25.3% to 27.7% in patients aged 50 to 70 years and 21.6% in those aged more than 70 years. The total risk for all groups was 24.8%. Limiting treatment to those patients with a 2% annual risk of developing the disease, the expected 20-year incidence was about 20% in the three younger age groups and 16.5% in the over-70 group. If all patients were treated, the estimated 20-year incidence range from 14.1% to 16.7% in the three under-70 groups and was 14.7% in those aged more than 70 years. The total was 15.7%.

The expected mortality rates over the 20-year period among those with ocular hypertension were 15.1% (age 50); 29.2% (51 to 60 years); 59.3% (61 to 70 years); and 89.0% (70+ years).

"The message from this is that if we're considering who we're going to treat to prevent glaucoma among patients with ocular hypertension, people over the age of 70 may not be good candidates for treatment because they're more likely to die during that period of time than they are to develop glaucoma," Dr. Kymes said. "For those who are under the age of 70, we find that if we treat them that we're likely to reduce the 20-year incidence by more than 30%."

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