# Continuous Time Markov Model Data Structure

From: Bauer, Robert <Robert.Bauer>
Date: Wed, 11 Aug 2021 16:52:55 +0000

The following is on behalf of Martin Bergstrand, as there is some difficult=
y in posting on to nmusers:

Dear Ya-Feng,

The first data example seems correct but probably requires another record a=
t TIME= 0, to account for what happens before the first observation (e.g.=
TIME=0 & EVID=2). If you have a dose record etc. at TIME=0 this is n=
ot needed. Also notice that with the current code you assume that TOXGR=0=
at TIME= 0 [ IF(NEWIND.NE.2) PDV=0 => A_0(3)=1 ]. This is often a =
reasonable assumption but it is important to be aware of.

Now for some explanation: With a continuous time Markov Model the most rece=
nt preceding state is by default impacting the probability of the next stat=
e (higher order markov effects are possible but most often not needed). The=
"amount" in each compartment in the markov chain represents the probabilit=
y for observing the corresponding state. Right after observing that the TOX=
GR (toxicity score) was = 1 you re-initialize each compartment so that at=
that point the probability is 1 for TOXGR=1 (CMT=4) and 0 for the othe=
r states i.e. TOXGR=0|2 (CMT=3|5). In the time that passes between the =
system being reset and the next observation some probability will distribut=
e from CMT=4 to CMT=3 and CMT = 5 (and some will remain in CMT= 4).=
The rate of distribution of probability between the 3 compartments are giv=
en by the rate constants K34,K43,K45 and K54 (that are not present in your =
example code). Rather than estimating the rate constraints (that can be har=
d to interpret), Schindler et al showed how you can estimate mean equilibri=
um times and steady state probabilities (and from them derive the rate cons=
tants).

Kind regards,

Martin Bergstrand, Ph.D.
Principal Consultant
Pharmetheus AB

+46(0)709 994 396
martin.bergstrand
www.pharmetheus.com<http://www.pharmetheus.com/>

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Received on Wed Aug 11 2021 - 12:52:55 EDT

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