How to solve this classification problem: multi-class or multi-label?

Question

In a supervised cancer classification task which is given the data containing metrics we want to classify whether the patient has cancer or is at high risk (label 1) or low risk (0). However, there is another attribute which is screening status which I want to include in the prediction. But I don't know how -- should it be a label or an input feature? The information on patients screened have the screening year as the value. Those who were not screened have the value for the year empty. Let the label for is screened be 3 and not screened be 4. So, the idea is:

-- a patient is at high risk and was screened : [1,3]
-- patient is at high risk but not screened: [1,4]
-- patient is at low risk and was screened: [0,3]
-- patient is at low risk but not screened: [0,4]

Basically, I want to assess the importance of early screening in predicting benign/malignant. The patients who have been screened early may not have cancer. On the other hand, it may happen that those who were screened developed cancer in later stages. This implies that the patients who did not pass the screening tests were diagnosed with cancer. So, what are the factors that influence the patient to pass or reject the screening test and whether the screening test itself can help in predicting/classification of malignant/benign. This is the research problem.

Confusion 1: How can I include this screening status? Will the information on screening be included as a label ?

Confusion 2: Will it be multi-label or multi-class classification?

Is my approach correct? Please let me know if I am in the correct direction an please correct me otherwise. Links to papers with similar problem will also be helpful.

Answer 1

So, in regards to your two questions:

1. In terms of including the screening status as a label: this really depends on what exactly you want your model to do and the applications of this model. If you want this model to help clinicians understand which patients should be screened and which shouldn’t, then of course include this feature as an additional predictor.

2. In terms of screening status prediction task being multi-label or multi-class: in this case the classes appear to be mutually exclusive. Therefore, this would be a multi-class classification problem. A multi labelling problem is for example predicting which combination of symptoms would appear if a patient experienced a certain disease.

Answer 2

An alternative approach can be the pre-processing step to determine which the independent variables are checked for correlation with the dependent variable. In R the function is cor(). Example: I used the mtcars dataset to show the correlation between multiple variables.

> data(mtcars)
> cor(mtcars)
            mpg        cyl       disp         hp
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684
cyl  -0.8521620  1.0000000  0.9020329  0.8324475
disp -0.8475514  0.9020329  1.0000000  0.7909486
hp   -0.7761684  0.8324475  0.7909486  1.0000000
drat  0.6811719 -0.6999381 -0.7102139 -0.4487591

Answer to confusion 1

Now, suppose in the above example you find independent variable gross horsepower (hp) is highly correlated with the outcome or the dependent variable miles per gallon(mpg) and is not correlated with the other independent variables then you should almost certainly include it, as it increases the power to detect the effect of other other independent variables.

Answer to confusion 2

Once you have identified the relevant features as stated above, then you ca decide on how to do the modelling. By the way, I think multi-label and multi-class are the same.