Retinitis pigmentosa (RP) is a category of inherited retinal dystrophies that is best prognosticated using electroretinography (ERG). In this retrospective cohort study of 25 patients with RP, we evaluated the correlation between 30 Hz flicker ERG and structural parameters in the retina. Internationally standardized 30 Hz flicker ERG recordings, short-wavelength autofluorescence (SW-AF), and spectral domain–optical coherence tomography (SD-OCT) were acquired at two visits at least one year apart. Vertical and horizontal hyperautofluorescent ring diameter measurements with SW-AF, as well as ellipsoid zone (EZ) line width measurements with SD-OCT, were used as structural parameters of disease progression. The 30 Hz flicker ERG amplitude decreased by 2.2 ± 0.8 µV/year (p = 0.011), while implicit times remained unchanged. For SD-OCT, the EZ line decreased by 204.1 ± 34.7 µm/year (p < 0.001). Horizontal and vertical hyperautofluorescent ring diameters decreased by 161.9 ± 25.6 µm/year and 146.9 ± 34.6 µm/year, respectively (p = 0.001), with SW-AF. A correlation was found between the progression rates of the 30 Hz flicker amplitude recorded with Burian–Allen electrodes and both the horizontal ring diameter (p = 0.020) and EZ line (p = 0.044). SW-AF and SD-OCT, two readily available imaging techniques, may be used to prognosticate disease progression because of the reliability of their measurements and correlation with functional outcome.

This paper proposes a linear regression model for scalar-valued responses and two-way functional (bivariate) predictors. Our motivation stems from the quality evaluation of products based on optical emission spectroscopy data from virtual metrology of semiconductor manufacturing. We focus on multivariate cases where the smoothness and shapes of the data vary significantly across variables. We propose a two-step solution to this problem, consisting of decomposition and prediction. First, we decompose the two-way functional data into pairs of component functions using functional singular value decomposition. Next, we build functional linear models for the decomposed functional variables and obtain the final predictor by averaging the models. Results from numerical studies, including simulation studies and real data analysis, demonstrate the promising empirical properties of the proposed approach, especially when the number of predictors is large.