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).

I hope this was helpful?

Kind regards,

Martin Bergstrand, Ph.D.

Principal Consultant

Pharmetheus AB

+46(0)709 994 396

martin.bergstrand

www.pharmetheus.com<http://www.pharmetheus.com/>

+46(0)18 513 328

U-A Science Park, Dag Hammarskjölds v. 36b

752 37 Uppsala, Sweden <br /><br /> ICON plc made the following annotat=

ions. -------------------------------------------------------------------=

----------- This e-mail transmission may contain confidential or legally =

privileged information that is intended only for the individual or entity n=

amed in the e-mail address. If you are not the intended recipient, you ar=

e hereby notified that any disclosure, copying, distribution, or reliance u=

pon the contents of this e-mail is strictly prohibited. If you have recei=

ved this e-mail transmission in error, please reply to the sender, so that =

ICON plc can arrange for proper delivery, and then please delete the messag=

e. Thank You, ICON plc South County Business Park Leopardstow=

n Dublin 18 Ireland Registered number: 145835

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

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).

I hope this was helpful?

Kind regards,

Martin Bergstrand, Ph.D.

Principal Consultant

Pharmetheus AB

+46(0)709 994 396

martin.bergstrand

www.pharmetheus.com<http://www.pharmetheus.com/>

+46(0)18 513 328

U-A Science Park, Dag Hammarskjölds v. 36b

752 37 Uppsala, Sweden <br /><br /> ICON plc made the following annotat=

ions. -------------------------------------------------------------------=

----------- This e-mail transmission may contain confidential or legally =

privileged information that is intended only for the individual or entity n=

amed in the e-mail address. If you are not the intended recipient, you ar=

e hereby notified that any disclosure, copying, distribution, or reliance u=

pon the contents of this e-mail is strictly prohibited. If you have recei=

ved this e-mail transmission in error, please reply to the sender, so that =

ICON plc can arrange for proper delivery, and then please delete the messag=

e. Thank You, ICON plc South County Business Park Leopardstow=

n Dublin 18 Ireland Registered number: 145835

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