Identifying threshold from Youden Index - Using ROC curve to calculate minimally important change (MIC)

Question

I am trying to determine the minimally important change (MIC) of a frailty instrument using an anchor-based approach outlined below.

Step 1. Fit a logistic regression model between change_in_fi (a change in the frailty measure) and srh_decline (1/0 referring to a decline in self-reported health), which is my anchor.

Step 2. Use the predicted probabilities of the above model to fit an ROC curve.

Step 3. Identify the Youden Index, i.e. point on ROC curve which maximises the sensitivity and specificity.

Step 4. I am stuck on here - how do I find out the threshold value of change_in_fi that the above Youden Index refers to? This value is my MIC.

Please find a mock dataset and code below:

library(pROC)

dat = structure(list(change_in_fi = structure(c(-0.05825, -0.0375, 
0.04575, 0.202, 0.01675, -0.1, -0.0125, -0.04775, 0.00624999999999999, 
-0.00625000000000001, -0.01875, 0.052, -0.01025, -0.025, 0.04375, 
0.00825, -0.048, 0.09575, 0.073, 0), label = "FI score", class = c("labelled", 
"numeric")), srh_decline = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
1, 1, 0, 0, 0, 0, 0, 0, 1)), row.names = c(NA, 20L), class = "data.frame")

# Step 1
mod = glm(srh_decline ~ change_in_fi, family=binomial, data=dat)

# Step 2
rocobj= roc(mod$y, mod$fitted.values)

# Step 3
coords(rocobj, "best")
```

Answer 1

If you are interested in the value of your change measure, then you should build the ROC curve directly on this data, without building a model.

rocobj <- roc(dat$srh_decline, dat$change_in_fi)
coords(rocobj, "best")
#   threshold specificity sensitivity
# 1 -0.011375         0.5           1

You will notice that the ROC curve is exactly identical, as you model was only applying a linear transformation.