The problem I'm trying to solve here is very simple but the available data is very limited. That makes it a hard problem to solve.

The available data are as follows:

1. I have 100 patients and I need to rank order them in terms of how healthy they are.
2. I only have 5 measurements for each patient. Each of the five readings is coded as a numeric value, and the rule is that the bigger the reading the healthier is the patient.

Should I have some sort of doctor's "expert judgement based ranking" I could use that as the target variable and fit some sort of an ordinal logistic regression model trying to predict doctor's assessment. However, I don't have that. The only thing I have is (1) and (2).

How would you come up with a simple "scoring" algorithm which would combine those five measurements into a single score which would be good enough (not perfect) in rank ordering patients?
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I would just simply sum them up, weighting each factor if necessary.
How about generating a synthetic binary target variable first and then running a logistic regression model?

The synthetic variable should be something like... "If the observation is in the top decile on all of the input variable distributions flag it as 1 else 0"

Having generated the binary target variable... Run logistic regression to come up with probabilistic metric 0 to 1 assesing how far/close in the tails of multiple distributions observation is?