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Editors Selection IGR 11-4

Progression: A linear model

Felipe Medeiros

Comment by Felipe Medeiros on:

24975 Prediction of glaucomatous visual field loss by extrapolation of linear trends, Bengtsson B; Patella VM; Heijl A, Archives of Ophthalmology, 2009; 127: 1610-1615

See also comment(s) by Ananth Viswanathan


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The main purpose of calculating rates of visual field loss in glaucoma is to predict future outcomes for an individual patient. That is, it is assumed that current rates of disease progression will remain relatively unchanged unless further interventions take place and, therefore, are good predictors of future observations. Bengtsson and colleagues (1721) evaluated whether linear regression of the initial Visual Field Index (VFI) values on a series of visual fields was a reliable estimator of future values for this index. They evaluated a group of 100 patients with a median number of visual fields of 11 (range: 10 to 16) and calculated the initial linear rate of change from the first five visual fields. The linear rate of change was used to predict the final VFI value in the full series of visual fields and compared to the observed value. In 70% of the subjects, the predicted VFI on the basis of the initial five tests was within 10% of the final VFI. The authors concluded that linear extrapolation of the fist five visual fields was a reliable estimator of future observations. Although these results may be encouraging for the use of VFI for estimating rates of change, they need to be seen with caution.

A large number of patients (30%) had a difference between predicted and observed VFI values greater than 10%, which can be considered quite substantial. Glaucoma is a slowly progressing disease and only a minority of patients actually progress fast enough to be at risk of significant disability from the disease. These could be exactly the ones that the linear extrapolation failed in predicting future observations. It should also be noted that Bengtsson et al. did not compare linear regression with other non-linear methods of fitting visual field data over time, therefore, their work cannot be considered as evidence that rates of visual field deterioration are linear over the time course of the disease.

More evidence is needed to conclude that rates of visual field deterioration are linear over the time course of the disease

It is possible that non-linear methods would actually perform better for prediction of future observations. Bengtsson et al. looked at a small interval of time. It is likely that a linear fit will be a good approximation if one looks at relatively short periods of time, as when you approximate a curve with several contiguous short lines. As glaucoma is very slowly progressing, this relatively short period of time could actually mean several years, perhaps five or more. However, when looking at the full course of the disease from early damage to blindness, the interval would be much longer ‐ 30, 40 years ‐ and most likely the rate of change would not be linear.

One should exercise caution when trying to predict future visual field loss from linear regression estimates of initial visual field data

In fact, as VFI is derived from measures of functional loss expressed on a logarithmic scale, it would actually be surprising that rates of VFI loss were shown to be linear over the entire time course of the disease. In conclusion, one should exercise caution when trying to predict future visual field loss from linear regression estimates of initial visual field data. Further studies are necessary to evaluate and compare linear and non-linear methods for evaluation of rates of progressive functional loss in glaucoma. Is visual field loss progression linear?

Biography: Felipe A. Medeiros, MD, Ph.D. is Associate Professor at the University of California San Diego and Medical Director of the Hamilton Glaucoma Center. He is member of the Glaucoma Research Society, Associate Advisory Board of The WGA and Research Committee of the American Glaucoma Society.



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