Why do we need to create a model when creating a ROC curve?

Question

I do not have strong background in statistics but I believe I know the basics to understand what a ROC curve means.

I have a table, first column with probabilities (from 0 to 1) from a predictive test and second with true outcomes with 1 and 0 (1 when the prediction was correct and 0 when failed). I consider the predicted test fails when the sample is pathogenic and shows <0.5. If prediction is >0.5 and sample is pathogenic the test is correct. With this criteria I have created the following table. below.

Samples    predicted_test    experimentally_validated  Comments
1          0.6               1                         Pathogenic, test correct.
2          0.8               0                         Benign,     test incorrect
3          0.2               1                         Benign,     test correct
4          0.3               0                         Pathogenic  test incorrect    

From this data I can to compute sensitivity, specificity, accuracy, PPV and NVP. Finally I want to create a ROC curve.

Looking at tutorials on the internet, they always develop a model (e.g. Logistic Regression ) with train and. My question is why.

Answer 1

YOU DO NOT

All you need are values to compare. How you create the values will influence how you interpret the ROC curve or the AUC, but the calculation does not know or care about their origin. For instance...

library(pROC)
set.seed(2023)
N <- 1000
p_true <- rbeta(N, 1/4, 1/4)
y_true <- rbinom(N, 1, p_true)
y_pred <- ecdf(p_true)(p_true)
r <- pROC::roc(y_true, y_pred)
plot(r, main = paste("AUC =", round(r$auc, 2)))

The reason so many tutorials first create a model is because most people care about these curves for model evaluation, so it makes sense to do some kind of model evaluation in the tutorial. Note, however, that a model does not have to be a machine learning or statistical model. A model could be showing an x-ray to a physician and asking for a probability that the patient is sick, which seems to be along the lines of what your "predictive test" is.