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I am looking for (any) pointers on how to approach the following abstract problem. Not: my statistics background is very limited, so I might very well be missing something obvious.

We have subjects each being subjected to a sequence of procedures. Different subjects might undergo different treatments, in a different order, but all the treatments come from a common catalogue (which can contain hundreds of different treatments). Furthermore, a treatment can be parametrised by one or more continuous parameters (e.g. intensity and duration). We have measurements for subjects state before and after the treatments — these are vectors of continuous values. We can furthermore assume that variables are normally distributed.

The question is: how can one find the sequences (and parameterisation) of treatments that show the strongest effect in maximising/minimizing a selected subset of state. E.g.: "in order to improve score X, one should do treatment A(a=0.5, b=0.7) followed by C(a=1.3) followed by A(a=0.2, b=1)"

My initial idea was to reformulate all this as a linear regression model, but we end up with hundreds of variables, some of them having interactions, so I am not sure that its the way to go...

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