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pierucci / heemod

:chart_with_upwards_trend:Markov Models for Health Economic Evaluations
https://pierucci.org/heemod/
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Microsimulation models #10

Closed pierucci closed 7 years ago

pierucci commented 8 years ago

I want to believe.

pierucci commented 8 years ago

The user interface part is extremely easy: there should be a state_cycle parameter, similar to markov_cycle.

state_cycle would increment depending on the time a person spends in a state.

Now for the implementation...

pierucci commented 8 years ago

I see 3 ways of implementing it:

  1. A classical simulation model. To do that we should program a totally different way of computing the model under the hood, the model would be run probabilistically.
  2. Model all the possible paths between states as a tree and then compute the probabilities of each path. This would be a deterministic way of computing models with state-time dependency. The matrix evaluation part would need to be extensively re-written.
  3. Implicitly transform states with state_cycle into tunnel states. This would allow us to keep the existing implementation.
pierucci commented 8 years ago

Advantages and drawbacks of the different approaches:

1 2 3
Code rewriting Extensive. Like, an entire new package. Limited to matrix eval, but very complex Limited to matrix definition (and maybe use different linear algebra functions to optimize matrix eval)
Complexity Easy (solved problem) Extremely complex (CS PhD level!) Probably easy, but we should check the consequences in details
Computational complexity Average _O(n_sim)_ Terrible. Impossible. _O(n_state^n_cycle)_ Probably easy (product of sparse matrices of size n_state + n_time_varying_state * n_cycle)
Result Imprecise probabilistic result Exact result Exact result

I think solution 3 is worth looking into.

pierucci commented 8 years ago

Solution 3 is mostly implemented & working with 66976b5cc984784021ac9ce6da0b25e645435139. But the TM and states are expanded anew for each model evaluation, this will significantly slow down PSA & co. The expansion part should be included in run_models().

This update just made most microsimulation models obsolete I think?

pierucci commented 8 years ago

state_cycle should work in define_parameters(). To achieve that the expressions in TM and states should be fully expanded (but not evaluated) with parameters references before running the state_cycle detection.