# Special vs. Markov models for analyzing within-patient variability

**URL:** <https://discourse.datamethods.org/t/special-vs-markov-models-for-analyzing-within-patient-variability/4546>\
**Category:** modeling strategy\
**Tags:** longitudinal, markov\
**Created:** [June 19, 2021, 1:53pm UTC](https://discourse.datamethods.org/t/special-vs-markov-models-for-analyzing-within-patient-variability/4546 "2021-06-19T13:53:54Z")\
**Posts on this page:** 1\
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**Author:** ![davidcnorrismd](https://discourse.datamethods.org/user_avatar/discourse.datamethods.org/davidcnorrismd/32/3502_2.png) [@davidcnorrismd](https://discourse.datamethods.org/u/davidcnorrismd)\
**Post date:** [June 20, 2021, 11:03am UTC](https://discourse.datamethods.org/t/special-vs-markov-models-for-analyzing-within-patient-variability/4546/3 "2021-06-20T11:03:22Z")

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I’m inclined to place problems like this in the general frame of state-space modeling [1,2], and then attempt to describe the various other approaches as special cases. For example, do the _stochastic volatility models_ mentioned in [2] subsume the other approaches being discussed here?

The way computational efficiency has motivated WiSER is interesting. I would tend to appeal to [Gustafson’s Law](https://en.wikipedia.org/wiki/Gustafson%27s_law) in approaching these massive patient registries with their distinct, non-interacting individuals. I would estimate n independent state-space models to obtain patient-level parameter vector estimates which could then be subject to a further stages of analysis such as visualization and regression. The problem of “interpretability” ideally is solved by bespoke model construction _ex ante_, rather than by grafting an ‘interpretation’ onto a generic model _post hoc_. Under such a philosophy, one would confront the zero-activity periods ‘head-on’ with a latent state variable having associated Markov transition probabilities (interpretation: _sedentariness_), which has the effect of bringing a crucial scientific question into clear view rather than sweeping it under the rug of a generic modeling approach.

1. Künsch HR. Particle filters. Bernoulli. 2013;19(4):1391-1403. doi:[10.3150/12-BEJSP07](http://projecteuclid.org/euclid.bj/1377612857)

2. Kantas N, Doucet A, Singh SS, Maciejowski J, Chopin N. On Particle Methods for Parameter Estimation in State-Space Models. _Statist Sci._ 2015;30(3):328-351. doi:[10.1214/14-STS511](http://projecteuclid.org/euclid.ss/1439220716)

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