# How to approach a classification problem when the sample size is only about 50

I was given a data consists of 53 people and I was asked to come up with a general classification rule based on biomarkers that can be used to classify each person under one of the three possible causes for their illness.

My questions are:

1. I was thinking of making a use of classification tree via random forest, but I realized that the size of my data is only about 50, and that this can cause overfitting on the data in hand. What are the classification methods that can be taken on the data that is consisted only of ~50 observations?

2. Instead of trying to do the classification, would something like multinomial regression (in this case, response will be nominal, 1 = 1st type of cause for illness, 2= 2nd type of cause for illness, 3= 3rd type of cause for illness) make more sense for this sample size?

3. Should I still be dividing my original data into a test and a training set? Like I mentioned, I think the sample size is too small for this.

Thank you,

Think of 96 as the minimum number of subjects needed to estimate just the intercept in a binary logistic model. And that only achieves a margin of error (with 0.95 confidence) of $$\pm 0.1$$ in the predicted risk of outcome/disease. To nail down the outcome probability to within a margin of error of $$\pm 0.05$$ requires $$4\times$$ that many subjects.
As a rough guess, the total sample size needed for a 3-class unordered problem such that the smallest outcome category has at least $$15 \times$$ the number of candidate features.