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Application of empirical Bayes methods to predict the rate of decline in ERG at the individual level among patients with retinitis pigmentosa
Author(s) -
Qiu Weiliang,
Sandberg Michael A.,
Rosner Bernard
Publication year - 2018
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7662
Subject(s) - retinitis pigmentosa , bayes' theorem , erg , demography , amplitude , ophthalmology , statistics , medicine , macular degeneration , population , correlation , mathematics , bayesian probability , retinal , physics , geometry , sociology , quantum mechanics
Retinitis pigmentosa is one of the most common forms of inherited retinal degeneration. The electroretinogram (ERG) can be used to determine the severity of retinitis pigmentosa—the lower the ERG amplitude, the more severe the disease is. In practice for career, lifestyle, and treatment counseling, it is of interest to predict the ERG amplitude of a patient at a future time. One approach is prediction based on the average rate of decline for individual patients. However, there is considerable variation both in initial amplitude and in rate of decline. In this article, we propose an empirical Bayes (EB) approach to incorporate the variations in initial amplitude and rate of decline for the prediction of ERG amplitude at the individual level. We applied the EB method to a collection of ERGs from 898 patients with 3 or more visits over 5 or more years of follow‐up tested in the Berman‐Gund Laboratory and observed that the predicted values at the last ( k th) visit obtained by using the proposed method based on data for the first k −1 visits are highly correlated with the observed values at the k th visit (Spearman correlation =0.93) and have a higher correlation with the observed values than those obtained based on either the population average decline rate or those obtained based on the individual decline rate. The mean square errors for predicted values obtained by the EB method are also smaller than those predicted by the other methods.