Table 4.
Model, basic architecture, and hyperparameters tuned | Range explored during tuning | Final selected value after tuning |
---|---|---|
XGBoost | ||
Tree based booster with GPU_hist; gradient based subsampling; RMSE evaluation metric | 1-6 | 6 |
Maximum tree depth: | ||
Learning rate (eta) | 0.0001-0.1 | 0.073 |
Subsampling proportion | 0.1-0.5 | 0.1 |
No of boosting rounds | 1-500 | 251 |
Alpha (regularisation) | 0-20 | 18 |
Gamma (regularisation) | 0-20 | 0 |
Lambda (regularisation) | 0-20 | 3 |
Column sampling by tree | 0.1-0.8 | 0.501 |
Column sampling by level | 0.1-0.8 | 0.518 |
Neural network | ||
Feed forward ANN with fully connected layers; 26 input nodes (No of predictors); ReLU activation functions in hidden layers; Adam optimiser; single output node with linear activation; RMSE loss function; batch size 1024: | ||
No of hidden layers | 1-5 | 2 |
No of nodes in each hidden layer | 26-50 | 30 |
No of epochs | 1-50 | 32 |
Initial learning rate | 0.001-0.1 | 0.032 |
ANN=artificial neural network; ReLU=rectified linear unit; RMSE=root mean squared error.
The continuous outcome variables for both models were the jack-knife pseudovalues for the cumulative incidence function for breast cancer related mortality at 10 years. The final neural network model had a total of 1771 parameters (all trainable).