SAS : Calculating the optimal predicted probability cutoff

There are three ways to calculate optimal probability cut-off :
  1. Youden's J Index
  2. Minimize Euclidean distance of sensitivity and specificity from the point (1,1)
  3. Profit Maximization / Cost Minimization

Youden's J index is used to select the optimal predicted probability cut-off. It is the maximum vertical distance between ROC curve and diagonal line. The idea is to maximize the difference between True Positive and False Positive.

Youden Index Formula
J = Sensitivity - (1 - Specificity )
Optimal probability cutoff is at where J is maximum.

Euclidean Distance Formula
D = Sqrt ((1-Sensitivity)^2 + (1-Specificity)^2)
Optimal probability cutoff is at where D is minimum.

SAS Code

proc logistic data = test descending;
model y = x1 x2 / outroc=rocstats;
run;

data check;
set rocstats;
_SPECIF_ = (1 - _1MSPEC_);
J = _SENSIT_ + _SPECIF_ - 1;
D= Sqrt((1-_SENSIT_)**2 + (1-_SPECIF_)**2);
run;

proc sql noprint;
create table cutoff as
select _PROB_ , J
from check
having J = max(J);
run;

proc sql noprint;
create table cutoff1 as
select _PROB_ , D
from check
having D = min(D);
run;
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About Author:

Deepanshu founded ListenData with a simple objective - Make analytics easy to understand and follow. He has over 10 years of experience in data science. During his tenure, he has worked with global clients in various domains like Banking, Insurance, Private Equity, Telecom and Human Resource.

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