Suppose that I have the normal and diseased populations as functions of a variable (x), how can I use them to draw a receiver operator curve (ROC)? Assuming the two functions are normal distribution functions and I know the means and the standard deviations of them, how to calculate the ROC at each value of x?
The ROC can have true positive fraction on Y axis and false positive fraction on X axis.
For binary classification (normal versus diseased), you can sweep through your parameter(s) and generate the ROC.
for example, let us say u use a mean estimate M (from the sample) as your parameter, then for a test point whose value V>M, you say 'diseased', otherwise 'normal'
then, you can sweep over M (vary M values from -N:N where N is say, 100), and calculate the number of true positives (Y) and false positives (X) you get for each M value (assuming you have the ground truth labels for each test point which says whether the test point is a truly normal or diseased person)
this gives you a set of (x,y) numbers, plot them to get ROC
I know the principle and I even know the math equation of calculating it using the error function. But I need an application (for example online app) to calculate for me the ROC given the means and SDs of the normal and the diseases population. For example, suppose I read about a study with a large sample size done on the disease and the control groups and the study states the average and SDs of the two groups. My questions, can I draw ROC from those 4 values even without knowing which case is normal and which case is diseased at each value of x?
A thought (which others may wish to say is wrong): If there are, say, n subjects in the diseased cohort with known mean and sd, then randomly generate n values on a normal curve with this mean and sd. Do the same for the m subjects in the non-diseased cohort. You'll then me able to generate an ROC and AUC.
I'd do the process say ~500 times to get a mean AUC with the 5th and 95th percentiles giving the 95% confidence interval.
A word of caution - I often see means and sd's which obviously don't relate to a normal distribution (eg when the sd is a large proportion of the mean).
All the best.
@john W Pickering, but this would be time consuming and lacking the precision as well. The reason is that for any value of x on the horizontal axis, there would be still limited values of normal (n) and diseased (m) cases to the right of x (if the disease has a large x than normal) and to the left of x (if the disease has a lower value than normal). But my idea is to calculate the error function to the right or the to the left of x which represents the area under the two curves. Therefore, I am looking for app that can do this quickly once I feed it with the average(s) and the SD(s) of the two groups and which can calculate the false positive and the true positive rates at every value of x. If not, I will do it on Excel.
If you know the formula, it is not hard to implement it on excel or similar. Do you need to draw ROC curve? or sensitivity specificity pairs? FPR and TPR?
By the way, your very question has no clues that you are looking for an app. Rather it is understood that you are looking for the formula or the method. You said "ROC at each point" which did not remind me anything.
ROC is a true positive (TP) as a function of false positive (FP) by definition and both TP and FP are functions of x. Consequently, ROC is a function or rather a functional of x.
Those two x's are not denoting the same thing (you should be referring to densities as l assumed so). There is no concept of "ROC" as you define.
What two x(s)? there is only one.
I made a fictional example in Excel to show my idea. In the sheet, x denoted the continuous variable where we wish to set up a cut-off value. Assuming both the normal and the diseases groups are following normal distribution functions with the normal and disease groups have means of 5 and 10 and SDs of 1.5 and 2, respectively, Excel creates two distribution functions as functions of x (shown as the first graph from the top). The TP (true positive) is the area under the curve representing the disease at any value of x and mathematically is equal to 1-CDF (1-cumulative distribution function). Similarly, FP(false positive)=1-CDF (of the normal curve). It is now easy to draw ROC from this data as ROC is just TP as a function of FP (third graph). In addition, I used Youden`s index (TP-FP) to set up a cut-off value which in this case is 7.4 (second graph).
That was a bit time consuming and my primary question in this thread, what online application can we use to get ROC and Youden`s index knowing only the means and SDs of the two groups and assuming they follow normal distribution functions?
I am not aware of such an online application. You can write an R script for such a purpose and construct your shiny application easily. Go search for R and shiny. R has many packages for ROC like pROC and ROCR including many others.
Now it is clear that by ROC you mean "ROC curve", by the way.
- Badges
- Science topic
- Similar topics
- Phytochemistry
- Extracts