Estimating the true distribution of visual field progression rates in glaucoma

Bayesian methods allow the distribution of glaucomatous visual field progression rates in the population to constrain individual progression rate estimates. As the true population distribution is never known, it must itself be estimated from a finite number of noisy individual estimates of rate. We used simulations to investigate the relationship between the true distribution of progression rates and that estimated from noisy empirical data.

We generated series of visual fields (3-10 per patient) using different variabilities (SD of 0.5-2.0 dB) for the summary index mean deviation (MD) to determine the relationship between the distribution of empirical estimates of progression rates determined by linear regression and the true underlying distribution of progression rates.

Estimating the underlying distribution from empirical data produced biases that broadened the distribution and made it more symmetrical, particularly for a short series of variable visual field estimates. Decreasing cohort size increased the variability in distribution parameter estimates, but produced no bias. Variability in distribution tails produced a 3.5-fold variation in the proportion of rapid progressors for the smallest cohort (200), falling to 1.8- and 1.3-fold for cohort sizes of 800 and 3200, respectively.

The underlying distribution of glaucomatous visual field progression rates for the population is likely to be narrower, and less symmetric, than that predicted from empirical data. Therefore, care should be exercised when inferring the benefits of Bayesian estimators, particularly where prior information is itself derived from a small sample of noisy empirical estimates.