Thank you very much, Dr. @FurlanLeo and Dr. @f2harrell.

I have moved the post here, and if anything I do is inappropriate, please let me know.

First, I want to confirm whether my understanding in the aforementioned post is **totally correct**, except for the part about the **Test** sample.

Next, I want to briefly describe my understanding of the Efron-Gong Optimism Bootstrap. (I have the rms book, but for me, I still find many contents difficult to understand, so I would like to get your confirmation to ensure I am not doing anything wrong)

Assuming that there is a model `y ∼ k * x,`

where `x`

is a predictor and `k`

is the coefficient of `x`

, and `y`

is the outcome.

- Calculate the performance measures (e.g., R
^{2}) in the original data, which corresponds to the performance measures in the`Original Sample`

column in`rms.validate`

. - Calculate the performance measures in a bootstrap sample, and there is a new coefficient
`k1`

(model:`y ∼ k1 * x`

) in this bootstrap sample. - Use the coefficient
`k1`

(model:`y ∼ k1 * x`

) to get new performance measures in the original data. - Calculate the optimism by (performance measures in step 2) - (performance measures in step 3).
- Repeat steps 2 to 4 for
`n`

times to get`n`

performance measures in both bootstrap samples and original samples. - Calculate the average value of the performance measures in step 5, which correspond to the performance measures in the
`Training Sample`

(average in step 2) and`Test Sample`

(average in step 3) columns respectively in`rms.validate`

. - Calculate the average value of the optimisms in step 6, which corresponds to the performance measures in the “Optimism” column in
`rms.validate`

.

`ie. Training Sample - Test Sample = Optimism`

Thank you for your patience, and I really appreciate it if anyone could point out any misunderstandings I have. It would be very helpful for me.