Dear Colleagues;
I want to know how can I combine multiple predictors in one ROC curve.
I want to know whether AUC increased if I used two predictors instead of using each one separately.
I.e Alfapheto protein, carcinoembryonic antigen, and both in the diagnosis of GIT malignancy.
suppose AUC for the first biomarker is 0.7, for the second is 0.75 what is the AUC if I used both?
Dear Ghzay
I had the same problem. When you want to determine a cut off value for a variable it is OK to use ROC analysis. For two or more variables I used logistic regression to predict the outcome. You can report odds ratio for each variable when putting themtogether to predict the outcome instead of reporting AUCs.
For further information please refer to https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/the-logistic-regression-analysis-in-spss/
Farid Javandoust Gharehbagh
Dear Farid can you check the ROC curve in this Manuscript
(Comparison of the performances of cardiac troponins,
including sensitive assays, and copeptin in the
diagnostic of acute myocardial infarction and long-term
prognosis between women and men)
Dear Ghazy
I read the manuscript. Yes you are right. They created multivariate ROC curves and reported new AUCs using combination of variables. I searched to find the process that how we can perform multivariate ROC and I found this.
Look at the following process
(1) Analyse 2) Regression 3) Binary logistic, put in the state variable as the dependent variable, subsequently enter the variables you wish to combine into the covariates, then click on "save" and check the box "probabilities". This process will compute a new variable in your SPSS database, termed "PRE_1". 4) Run the ROC curve using "PRE_1" as test variable. 5) Obtain the result.))
See the following link
https://stats.stackexchange.com/questions/169920/how-can-i-calculate-the-auc-of-combined-variables-using-spss
@Farid
Thank you very much. I will try this wasy.
I have another solution.
First determine the cutoff point for prdictor1 and2. Then create new variable 3 which has two categories1(if above the cutoff point of prdictor 1 and2), categorie 2(all the other probabilities). Despite being categorical variable u can determine are under the curve, however, i think this may increase sensitivity and ignore specificity.
You are welcome dear@Ramy
Thanks for sharing this useful question.
Good luck
Dear Ghazy,
apologies for delay - one standard approach would be to combine the 2 predictors by logistic regression and then find the ROC curve of the weighted sum You might need to look at test / training data sets or crossvalidation or bootstrapping to adjust for over fitting
Ramy Ghazy Can’t explain in detail but let’s first understand AUC or Area Under Curve. AUC is an output of several or single variables. When we classify we get sensitivity and specificity which go against each other. If you go on adding significant variables in a model the output will be better. Try recalling linear regression and R square. If you check AUC you may get it better than combined or may not depending upon the data. Try seeing the coefficient of each variable with Y to see the answer.
@anuraj thank you for you response, kindly, can I ask you about your opinion regarding the previous answers?
I'm interested in how we use logistic regression predictions with ROC curves to predict a condition eg GIT malignancy. We can combine the predictors to get predictions (called PRE_1 in SPSS) and then use those predictions in a ROC curve and obtain sensitivity and specificity (perhaps using the Youden criteria ie picking the cutoff of PRE_1 that maximises sensitivity + specificity).
But what are the pros and cons of getting an optimal cutoff via ROC in this way as opposed to not using ROC at all and just using the 50% value of PRE_1 as the cutoff ? After all values of PRE_1 above 50% mean, by definition, that the individual is more than 50% "likely" to have the condition and
I also wonder what it would mean if we find (by Youden or whatever ) a cutoff for PRE_1 (the prediction eg from logistic regression) with good sensitivity and specificity but that is not close to 50%. Say a cutoff of 70% has good discrimination ie good sensitivity and specificity then what do we do with an individual with a cutoff of 67% ? Do we diagnose the person as not having the condition as their prediction is less than the 70% cutoff with good discriminatory ability or do we diagnose the person as actually having the condition on the grounds that a prediction of 67% means they are twice as likely to have the condition as not ?
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