I$$m a beginner in survival analysis, working with a Cox model using a deep neural network $($DNN$).$ I want to predict and visualize low$-$risk and high$-$risk groups based on the model's predictions. Here are my specific questions:

Calculations for Model Prediction:

How can I calculate risk scores for each sample using a Cox model with DNN$?$What are the formulas and steps for calculating the cumulative baseline hazard, particularly with the Breslow method? Could you break down each part in detail?Could you provide example code in Python for calculating both the risk scores and cumulative baseline hazard?

Visualization of Predicted Risk Groups:

Once I have risk scores and the cumulative baseline hazard, how can I create a plot that visualizes the model's predicted low$-$risk and high$-$risk groups?Could you provide sample code specifically for plotting these model$-$predicted risk groups?

Log$-$Rank Test for Predicted Risk Groups:

How do I use the log$-$rank test to compare the survival curves between the predicted high$-$risk and low$-$risk groups?Could you include code for performing the log$-$rank test in Python to calculate the p$-$value for these predicted risk groups?