## 3 Results  
The overall prevalence of glaucoma estimated from the dataset was about 16%. Among the different race groups, the incidence of glaucoma was higher in African Americans (23.2%), Asians (16.8%), and East Indians (16.2%) compared to other races (i.e., Hispanics (11.0%). When comparing gender, a higher prevalence of glaucoma (16.6%) was observed among the female population than the male population (15.7%) in this dataset. The four machine learning models' power of prediction is shown in Table 2. The sensitivity for different classifiers of the data showed the highest with MLP (81%), XGBoost (81%), and random forest (81%), followed by logistic regression (73%). We further computed the precision of different models. The MLP has the highest precision (82%), followed by the random forest (83%) and XGBoost (83%). The recall (glaucoma cases) was highest for logistic regression (82%), and XGBoost (83%). Similarly, the actual positive prediction rate is also higher with MLP, Random Forest, and XGBoost than with other models' performances. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Learning Model** & **Loss Function** & **Parameter** & **Complexity** \\  & & **Estimation** & **Reduction** \\ \hline Logistic Regression & Log loss & Gradient descent & L2 regularization \\ XGBoost classifier & Squared error & Booster parameters & Regression \\ Random Forest & Square loss: & & Move down tree based on x predict \\  & (Y-Y) 2 & CART & value at the leaf \\ MLP Classifier & Activation: relu & Solver: adam & Learning rate init = 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used in different machine learning methods. The accuracy of model prediction was plotted on the AUC plot, which showed a similar trend. We also performed the ROC of all these models built by different ML algorithms (Figure 2), and the performance of these models was evaluated by examining the true value (the actual glaucoma label) versus the predicted value (the predicted glaucoma label). The plot of TPF (sensitivity) versus FPF (1-specificity) across varying cut-offs generates a curve in the unit square, which shows the tradeoff between the true positive fraction (TPF) and a false-positive fraction (FFF). The ROC curve lying on the diagonal line (black dots) reflects a diagnostic test performance that is no better than the chance level. The ROC curve slope is equal to the ratio of the two density functions describing the separator variable's distribution at a given point in glaucoma versus the non-glaucoma likelihood ratio. The ROC curve also shows the models' discriminatory ability and displays how useful the classification model is at distinguishing between glaucoma and non-glaucoma. Further, the error rate (unpredicting the actual label by these models) may be due to the EHR data's inherent ambiguity or the fact that the heterogeneity of all variability is not saturated in the present dataset. Further, the type 1 error rate is high in LR, and the type II error rate is high in the RF model compared to all other models (Table 3). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Prediction** & **Precision** & **Recall** & **F1** & **Accuracy** \\ \hline \multirow{2}{*}{LR} & 0 & 0.7830 & 0.6341 & 0.7007 & \multirow{2}{*}{0.7281} \\  & 1 & 0.6904 & 0.8228 & 0.7508 & \\ \hline \multirow{2}{*}{RF} & 0 & 0.7911 & 0.8427 & 0.8161 & \multirow{2}{*}{0.8105} \\  & 1 & 0.8308 & 0.7763 & 0.8024 & \\ \hline \multirow{2}{*}{XGB} & 0 & 0.8033 & 0.8386 & 0.8026 & \multirow{2}{*}{0.8161} \\  & 1 & 0.8302 & 0.7936 & 0.8115 & \\ \hline \multirow{2}{*}{MLP} & 0 & 0.8086 & 0.8259 & 0.8171 & \multirow{2}{*}{0.8146} \\  & 1 & 0.8210 & 0.8033 & 0.8121 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy metric for evaluating classification models. The highest accuracies (in bold) are from XGBoost and MLP. Figure 2: Area under the curve (AUC) for five machine learning methods. AUC measures the entire two-dimensional area underneath the entire ROC curve.