ROC-Sensitivity & Specificity for a given variable value

[Michelle S]

Dear All,

Would appreciate any help with this question please: Is there a way to get the sensitivity, specificity or even LR+ LR- for a specific variable cutoff of interest?

I know the command "roctab outcome variable, detail " gives you the sensitivity & specificity for different variable cutoffs, but the cutoff may not be the exact one I need.

Is it possible to specify the cutoff, and do it the other way round?

Thank you very much.
Michelle

[Leonardo Guizzetti]

There are at least two ways you can do this.

1) Assuming that you have already fit a logistic regression model, -logit y x1 x2-, you can use the postestimation command -estat class, cut(<threshold value>)- where the default threshold value is 0.5.

Example output looks like:

              -------- True --------
Classified |         D            ~D  |      Total
-----------+--------------------------+-----------
     +     |       338           171  |        509
     -     |       150           341  |        491
-----------+--------------------------+-----------
   Total   |       488           512  |       1000

Classified + if predicted Pr(D) >= .5
True D defined as y1 != 0
--------------------------------------------------
Sensitivity                     Pr( +| D)   69.26%
Specificity                     Pr( -|~D)   66.60%
Positive predictive value       Pr( D| +)   66.40%
Negative predictive value       Pr(~D| -)   69.45%
--------------------------------------------------
False + rate for true ~D        Pr( +|~D)   33.40%
False - rate for true D         Pr( -| D)   30.74%
False + rate for classified +   Pr(~D| +)   33.60%
False - rate for classified -   Pr( D| -)   30.55%
--------------------------------------------------
Correctly classified                        67.90%
--------------------------------------------------

2) If you were to manually compute the number of true and false positives and true and false negatives for a given threshold, then you can achieve a similar output table using a user-contributed command -classtabi- where you must specify -classtabi #TN #FP #FN #TP- such as -classtabi 1231 397 50 324-

[Michelle S]

Dear Leonardo,

Thanks for your reply.

I have used the estat classification command as you mentioned before,
However, the cutoff is NOT the actual value of the variable (eg blood pressure of 140mmHg). Stata only allows a cutoff value between 0 to 1. The cutoff is what you define as a positive outcome, and the default is 0.5.

Best wishes
Michelle

[Leonardo Guizzetti]

My apologies, your original question was ambiguous. Perhaps you can describe exactly what you are trying to do.

[Clyde Schechter]

Try this:

gen byte bp_dichotomy = (blood_pressure < 140) if !missing(blood_presure)
tab outcome bp_dichotomy, col

The column percentages will show you the sensitivity and specificity of outcome at that value of the blood pressure cutoff.

[Michelle S]

Thanks Mr Schechter - a very effective and simple solution!

BW
Michellle