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Say that we have a set of treatment plans (the options) available to a patient. Treatment plans can be invasive-surgery, no-surgery, less-invasive surgery ext...

We have a dataset where a treatment plan was chosen for a patient and and we also have their outcome (Survived/Did-not-survive).

What is the best way to go about grading/ranking/choosing an optimal treatment plan so that we retain optimal survival rates.

To me this sounds like a recommendation algorithm but the way it seems most recommendation algorithm work is by modelling best recommendation/option based off of whether that option was selected. Here the outcome is not whether a particular treatment/recommendation was selected (non-selected treatment may have been better) but instead whether a patient survived after the selected treatment. Given the fact that we don't have outcomes for the options that were not selected and only have outcomes for the treatment that was selected - How can I best create a model that produces a rank/grade of optimal treatment plan that increases likelihood of survival? Example dataset below

Example Dataset

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The first step is calculating descriptive statistics. Starting with survival rate by group which can be ordered from highest rate to lowest rate.

The logical follow-up question is - Are the group differences due to chance? Null hypothesis significance testing (NHST) is one way to answer that question. The null hypothesis is that there are no differences between the groups. The chi-squared test is one possible statistical test to assess the evidence if that null hypothesis can be rejected.

Recommendation algorithms are too complex of a tool for this problem.

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