Predicted probabilities and actual values

[Humphrey Mulenga]

I want to calculate the sensitivity and specificity of a diagnostic test for TB. The index test is a numerical variable TBscore with values ranging from 0.86 to 100. However, I also want to adjust for age, sex, cough and BMI, and I have decided to use logistic regression as below

logistic TBDisease TBscore age sex cough bmi
predict p if e(sample), p
roctab TBDisease p, detail


I then get the output below

Detailed report of Sensitivity and Specificity
------------------------------------------------------------------------------
Correctly
Cutpoint Sensitivity Specificity Classified LR+ LR-
------------------------------------------------------------------------------
( >= 1.46e-10 ) 100.00% 0.00% 2.53% 1.0000
( >= 6.42e-08 ) 100.00% 0.04% 2.57% 1.0004 0.0000
( >= .0001824 ) 100.00% 0.07% 2.60% 1.0007 0.0000
( >= .0003155 ) 100.00% 0.11% 2.63% 1.0011 0.0000
( >= .0003179 ) 100.00% 0.14% 2.67% 1.0014 0.0000
( >= .0003397 ) 100.00% 0.18% 2.70% 1.0018 0.0000
( >= .000353 ) 100.00% 0.21% 2.74% 1.0021 0.0000
( >= .0003924 ) 100.00% 0.25% 2.77% 1.0025 0.0000
( >= .0004425 ) 100.00% 0.28% 2.81% 1.0028 0.0000
( >= .0004429 ) 100.00% 0.32% 2.84% 1.0032 0.0000
( >= .0004773 ) 100.00% 0.35% 2.87% 1.0035 0.0000
( >= .0004885 ) 100.00% 0.39% 2.91% 1.0039 0.0000
( >= .0005115 ) 100.00% 0.42% 2.94% 1.0042 0.0000
( >= .0005456 ) 100.00% 0.46% 2.98% 1.0046 0.0000
( >= .0005482 ) 100.00% 0.49% 3.01% 1.0049 0.0000
( >= .0005705 ) 100.00% 0.53% 3.04% 1.0053 0.0000
( >= .0005847 ) 100.00% 0.56% 3.08% 1.0056 0.0000
( >= .0005957 ) 100.00% 0.60% 3.11% 1.0060 0.0000
( >= .0006096 ) 100.00% 0.63% 3.15% 1.0064 0.0000
( >= .0006124 ) 100.00% 0.67% 3.18% 1.0067 0.0000

Question: How do I get the actual scores in the adjusted model (cut-point)? I want to know what value of the actual TB score each of these predicted values correspond to. I can get the values in the unadjusted model by simply using "roctab TBDisease TBScore, detail" but this wont give me the same AUC as well as sensitivity and specificity given by the adjusted model.Is there a way of back transforming the predicted values to the actual score. When I select the cut-off using the predicted values, I want to know what TB score values correspond to it.

Thanks
Humphrey

[Clyde Schechter]

Is there a way of back transforming the predicted values to the actual score.

No, there isn't. Because your model contains predictors other than just the TBscore itself, the same predicted probability can correspond to different values of TBScore, depending on the person's age, sex, and cough.

[Humphrey Mulenga]

Thanks a lot Clyde