I used a regularized (LASSO) Cox regression to estimate relapse times of patients and used Frank Harrell's bootstrapping method to obtain an optimism-corrected performance estimate of my model.
Question: Could I use the same method to correct the regression coefficients of my best model (based on minimum lambda)?
optimism-corrected b = b of best model - optimism estimated by Harrell's method for prediction accuracy
Would be such an optimism-corrected b be a better predictor for unseen cases?
This goes against what Harrell seems to mean when he writes about bootstrap validation.
Harrell's argument basically goes like this.
Splitting the data wastes data that could have been used for training, so train on the entire dataset.
However, then we risk overfitting. We always risk overfitting, but when we have holdout data, we can catch that we have just played connect-the-dots.
Therefore, bootstrap your data, fit the model to the bootstrap sample, evaluate that model on the full data set, and see how that performance compares to the performance of the model that was trained on the entire data set. Because we do these many times with bootstrap samples, we can get a good estimate of overfitting when we trained on the entire data set.
If we are happy with how little overfitting there is, then we should use the model that was trained on the entire data set, which we now consider validated.
At no point do we adjust the coefficients.
