# depth/complexity of decision trees

I have used the same methods/parameters to create two decision trees. The trees classify the presence or absence of a medical condition using the presence or absence of various symptoms. There is a tree for Medical Condition #1 and another tree for Medical Condition #2. Both trees are based on the same set of symptoms, rated by patients. If Medical Condition #1 resulted in a much simpler tree than Medical Condition #2, can that suggest Medical Condition #2 is a more complex disease? If so, can anyone point me to a reference that states the complexity/depth of a tree can be representative of a complex condition?

The goal of my analysis is separate from this question. I am trying to figure out all the conclusions I can draw or suggest from my analysis. Yes, I am interested in saying something about the complexity of condition A to B. When is a condition complex ? When there are many symptoms as the disease is diagnosed by the symptoms. If it's hard to diagnose ? YES if the symptoms are severe ? NO can s.o. have both conditions ? NO

## 1 Answer

No, you can't infer that. I assume you have the same training set with the same predictors (symptoms). The only difference in the training set is the binary class label for each patient.

The smaller tree just means: - with the given symptoms, it might be easier to distinguish between the people who have the condition 1 and the ones not having it. (since you have the same certainty with fewer information) This distinction seems harder with medical condition 2, that's way you have to consider more symptoms to be pretty sure about your classification. So if condition 2 is a very mild condition where it is hard to diagnose even for an expert if someone has it then it would result in a deep tree.

• Thank you . I understand the first paragraph an dthe second paragraph, but to me, they are saying the opposite things. You say I can't infer that in the first sentence but that I can in the last. Can you explain? Thank you!
– DMD
Commented Feb 20, 2015 at 23:00
• what exactly is the goal of your analysis ? Are you interested in saying something about the 'complexity' of condition a in comparison to condition b ? When is a condition complex ? If it's hard to diagnose ? if the symptoms are severe ? can s.o. have both conditions ? Commented Feb 21, 2015 at 6:48