Statistical analysis

We used a fully ARIA method to acquire and analyze retinal images in our study. ARIA was applied and validated in different disease cohorts, including stroke, diabetes and chronic kidney disease.22–24 The fully ARIA was developed using R and Matlab computer software.25^,26 The detailed ARIA method have been reported (US Patent 8787638 B2; http://www.google.com/patents/US8787638). The methods include the use of fractal analysis, high order spectra analysis and statistical texture analysis incorporating a machine learning approach. These approaches were used to estimate the probability of ARWMC score ≥ 2. For the overall validation of the risk of ARWMC, we use a completely separate set of subjects with MRI not previously used in the model building process. A box-plot for the probability of ARWMC score ≥ 2 for the testing samples between ARWMC < 2 (i.e. low-risk group) and ARWMC ≥ 2 (i.e. high-risk group) is shown.

For the localization analysis of brain WMH, we applied transfer learning with the pre-trained deep convolutional neural networks ResNet50 to extract features from retinal images.27 We then incorporated the extracted image features with the retinal characteristics and estimated the probability of ARWMC scores corresponding to each brain region. The following are a description of the detailed analysis using Matlab. The methodology is shown in the flow chart (Fig. 1). We applied a DL approach such as transfer net of ResNet50 convolutional neural network—input retinal images (RGB and size 224×224×3). Labels are WMH present/absent on each of six regions. The purpose is to generate features based on pixels associated with WMH. Next, we extracted the texture/fractal/spectrum-related features such as high order spectrum and fractal dimensions from our previous ARIA automatic algorithm model. Input retinal images (RGB and size 576×720×3). The purpose is to generate features based on the above three descriptors associated with WMH for each of six regions, respectively. After we extracted the pixel-based features from the above ResNet50 net at the layer of ‘fc1000_softmax’, we combined them with the above extracted features. All of these features will be refined by using the glmnet approach to select important potential features based on penalized maximum likelihood. These refined features were highly associated with WMH for each of the six regions. We then used the above features to estimate retinal characteristics that are meaningful and interpretable for our study (Random forest in Matlab was used). Then we applied a conventional statistical approach such as logistic regression to find the statistically significant risk factors (which is highly associated with WMH for each of six regions).

Flowchart for the development of classification model.

Finally, we applied the classification and regression tree method to investigate the overall patterns of localization for the presence of WMH for all six brain regions.28 The classification and regression tree split the data according to WMH on a specific location of the brain region as a node and applied the splitting criterion to decide the brain region's choice at that particular level. The splitting criterion is the maximum difference in probability estimate for the presence or absence of WMH in that node. The results of the classification and regression tree model were validated using a 10-folder cross-validation method.