# multiple roc predicted probability to find cut off value of combining variables

##### New Member
Find cut off value of combining variables when combining roc curves

I have 2 continuous variables for which I have roc curves for an outcome. Now I used binary logistic and predicted probability to get a combined roc with higher area under curve. But the cut off value in terms of the initial 2 variables?. Predicted probability more than 0.032 doesn't mean anything practically . I need to say that if variable a is more than x and variable b is more than y then together it has 90 per cent sensitivity in predicting outcome. How do I get this value of the 2 variables from the new cut off predicted probability I got from binary logistic regression in spss? Kindly help

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##### New Member
Can I use regression equation for this. If so, how in spss

#### hlsmith

##### Omega Contributor
What is the purpose of the model, to have the highest accuracy or sensitivity or specificity or other? And you want to dichotomize both continuous variables?

##### New Member
I want to say with the max sensitivity and specificity possible on the roc curve that variable a over a certain value and variable b over a certain measure predicts outcome to happen in the dependant variable. I got the predicted probability value for this max sensitivity and specificity from the combined roc but from that I am not able to get the individual variable values at that particular point on the roc curve. Pls help, can a regression equation get these values from the predicted probability and coefficients

#### hlsmith

##### Omega Contributor
What program are you using? Did the program dichotomize the continuous variables or not? Typically most programs don't do that in logistic regression automatically. Did it kick out an ROC curve? If so, it shouldn't look like a curve anymore, it should consist of three line segments where the curve normally is.

##### New Member
Spss 20 was used.Binary logistic regression was done taking both variables as continuous. I did not enter them in the categorical box. The resulting Pred probability which came in the spss 20 data sheet was used to run an roc curve using analyse and roc

#### hlsmith

##### Omega Contributor
And the curves are curves, yes? Well your predictions are likely for one unit increases in the continuous variables. Are the two continuous variables independent of each other?

##### New Member
Yes, they are independent of each other.

#### hlsmith

##### Omega Contributor
Well you need to determine the optimal cut-offs for both of your continuous variables. If they are truly independent and you want to optimize SEN and SPEC at the same time you may be able to determine the Youden Index for both of them independently then use both cut-offs in the same logistic model.

I would also try to fit a spline or loess regression to examine the linear relationship between the predictors and the dependent variable, which could influence your decision. you could probably also run Random Forests to see how that procedure likes to split the continuous variables and in which order. Though Random Forests typically use Gini Index not Youden index, so keep that in mind.

Not sure how approachable the latter procedures may be in SPSS.

Random forest