# Classification of binary outcomes

I have to differentiate two diseases based on the genetic features. These two diseases are labelled as class '0' and class '1' in the database. Interestingly, all the patients with the class 0 will get the class 1. On other words, if a patient has disease of class 0, surely have diseases class 1. The research question is : How many patients with class 1 will get class 0?

Do you think binary classifications and performance measurement such as AUC can help in this problem?

In fact, the notation you mentioned is confusing. People use $0$ and $1$ to represent if a person HAS disease or NOT, not different diseases.

A better notation can be, two diseases, $A$ and $B$, and $A=1$ means a person has disease $A$. And, the we know the conditional probability of

$$P(B=1|A=1)=1$$

We can start from here, to try to get the joint distribution of $P(A,B)$ as a model of your data, which is a $2 \times 2$ table.

If we are interested to get

$$P(A=1|B=1)$$

We can view this as a binary classification problem, and we can directly model it or derive it from the joint distribution.

• Can we use classification models such as bagged trees or KNN? Can you please explain more about joint distribution? – user27379 Aug 21 '17 at 14:35
• @user27379 technically you can use what ever model you want. But, the data you have is relatively simple. If you check the other answer, you can use "counts" to get the answer. – Haitao Du Aug 21 '17 at 14:37
• The aim is constructing a predictive model for disease one (Class 0)!? I have to find the most informative features and based on these features constructing a predictor! – user27379 Aug 21 '17 at 14:41

More like a comment, but I don't have enough rep. I'm just expanding on hxd1011's answer. From Bayes' theorem,

$$P(A=1|B=1) = \frac{P(B=1|A=1)P(A=1)}{P(B=1)}$$

Since we know $P(B=1|A=1)=1$, then

$$P(A=1|B=1) = \frac{P(A=1)}{P(B=1)}$$