# PharmPK Discussion - Probability distribution of Tlag in MC simulation

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• On 1 Apr 2003 at 16:43:32, "Prapoch Watanalumlerd (Keng)" (watanalp.-at-.onid.orst.edu) sent the message
`The following message was posted to: PharmPKDear all,Does anyone have information about the appropriate probabilitydistribution oflag time of absorption (Tlag) for Monte Carlo simulations? Since Tlagobtainedfrom biostudies is a discrete ordinal variable, I have difficultiesincludingits variability in the simulation. Thank you.Best Regards,Prapoch Watanalumlerd (Keng)Pharmaceutic graduate studentCollege of Pharmacy, Oregon State UniversityPhone: 541-737-5789`
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• On 2 Apr 2003 at 08:54:25, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message
`The following message was posted to: PharmPKDear Keng,You wrote:> Does anyone have information about the appropriate probability> distribution of lag time of absorption (Tlag) for Monte Carlo> simulations?> Since Tlag  obtained from biostudies is a discrete ordinal variable,> I have difficulties including its variability in the simulation.For most, if not all, a log-normal distribution of PK parameters is thelogical choice (as was discussed recently in this group). I do no see aspecific reason why this would not hold for the lag time of absorption(Tlag). IMHO, this is the logical choice in case you are using a PKmodelincluding a lag time. If you estimate Tlag from a series ofmeasurements,the obtained value is not a discrete variable, but an estimate of the'true'Tlag.Possibly you are referring to a noncompartmental approach where Tlag isdefined as the last measured time point where the concentration is zero(ormore precisely, below the LOD, or LOQ, or whatever criterion isdefined). Inthis case Tlag is indeed a discrete ordinal variable. Since the 'true'Tlagmay still be described by a log-normal distribution, the followingapproachcould be used. Given a geometric mean and standard deviation for Tlag,theprobability that Tlag is between 0 and t1 (time of first measurement)can becalculated, and this is the probability that the observed Tlag is 0,i.e.the probability that at t1 at least some drug has been absorbed.Similarly,the probability that Tlag is between t1 and t2 (time of firstmeasurement)equals the probability that the observed Tlag is t1 (i.e. at least somedrugabsorbed at t2), et cetera.Any suggestions about this approach are welcomed.Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.-at-.farm.rug.nl`
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