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- [NMusers] allometric scaling

for any comments Frederike From Nick Holford n holford auckland ac nz Subject RE NMusers allometric scaling Date Mon October 18 2004 4 47 am Frederike YES I would consider allometric scaling of clearance and volume to be the correct model a priori to account for differences between the infants due to size I would then look for developmental changes in renal function related to post gestational age and changes

Original URL path: http://nonmem.org/nonmem/nm/99oct182004.html (2016-04-25)

Open archived version from archive - [NMusers] Update for NONMEM bug list October 13, 2004

the second or subsequent subproblems the TABLE record will be treated as though the FORWARD option appears on the record Work around Probably the user would actually prefer that the TABLE record be treated as though the FORWARD option appears on it see the discussion point below But this is not what is suppose to happen and if indeed it is desired that the NOFORWARD option be recognized then after the last TABLE record insert an additional TABLE record using a FILE option with a different file name This file name can be that of the system junk file so that no table is really seen by the user Discussion The following helpful fact is undocumented There is an exception as to when the NOFORWARD option is the default option With a series of contiguous TABLE records in a given problem specification each having a FILE option that uses the same file name the second and subsequent TABLE records in the series are always treated as though the FORWARD option appears on these records because otherwise the presence of these records makes no sense It also really makes no sense to use the NOFORWARD option with any TABLE record regardless of the file name used by the FILE option in a problem specification with an NSUBS value of 2 or more So with NONMEM Version VI this will constitute another exception as to when the NOFORWARD option is the default option VI When each of two different problems within the scope of a superproblem use the same file as either a NONMEM data file Model Specification Input file or Model Specification Output file or table file an abnormal operating system termination may arise If these circumstances do not lead to such a termination the user should not be concerned Fix Before each of the two instances of the statement I2 0 in routine SUPER insert the statement IF I2 EQ 1 CLOSE UN 2 Before each of the two instances of the statement I3 0 in routine SUPER insert the statement IF I3 EQ 1 CLOSE UN 3 Before each of the two instances of the statement I4 0 in routine SUPER insert the statement IF I4 EQ 1 CLOSE UN 4 Work around Avoid such circumstances An example of where these circumstances arise may be found in the Help Guide Superproblem Example 1 For this example the file simulation is used as a table file in problem 2 and as a NONMEM data file in problem 3 This can be avoided by taking the data set of problem 3 to be the internal data set created with problem 2 remove both the TABLE record of problem 2 and the DATA record of problem 3 VII When a mixture model is used estimates of etas available to the PRED routine during problem finalization i e when ICALL 3 are always those for the first submodel With each individual they should be those for the submodel to which the individual is

Original URL path: http://nonmem.org/nonmem/nm/99oct142004.html (2016-04-25)

Open archived version from archive - [NMusers] Error message

guide available immediately I have looked the archives and found one posting to fix buffer 6 problem http www cognigencorp com nonmem nm 96aug162001 html Is there any fix available on the similar lines I am running NONMEM V on Windows 2000 operating system Thanks Pravin Pravin Jadhav Graduate Student Department of Pharmaceutics MCV Virginia Commonwealth University DPE1 CDER OCPB Food and Drug Administration Phone 301 594 2623 Fax 301 480 3212 From Chan Phylinda Phylinda Chan pfizer com Subject RE NMusers Error message Date Tue October 12 2004 2 35 pm Hi Pravin The size of the NONMEM buffers are set by their associated LIM constant i e LIM1 for buffer 1 You can fix your problem in a similar way as fixing buffer 6 problem in the posting you found but instead of altering LIM6 you need to increase LIM1 then recompile NONMEM and rebuild the library According to the installation guide LIM1 is associated with the data records stored in memory at any one time the default value is 400 The magnitude of increase depends on the largest number of data records in any individual in your dataset Hope this help Phylinda Phylinda L S Chan Postdoctoral

Original URL path: http://nonmem.org/nonmem/nm/99oct122004.html (2016-04-25)

Open archived version from archive - [NMusers] Avoiding ABORT in NONMEM Initialization

reason for asking this question I would like to learn if there is a way to either 1 make NONMEM behave consistently during the initialization and subsequent iterations with respect to the NOABORT option or 2 detect the initialization phase so that the condition triggering the EXIT can be avoided The control stream and error message are shown below Thanks in advance for your suggestions Nick PROB INPUT ID AMT TIME DV MDV DATA data SUBROUTINES ADVAN2 TRANS2 SIM 20041008 NEW SUBPROB 1 ESTIM MAXEVAL 9990 SIGDIG 3 NOABORT METHOD CONDITIONAL INTERACTION THETA 0 01 0 693 POPCL 0 01 1 POPV 0 01 1 5 POPKA OMEGA BLOCK 1 0 09 PPVCL OMEGA 0 09 PPVV 0 09 PPVKA SIGMA 0 01 RUVCV PK CL POPCL EXP PPVCL V POPV EXP PPVV KA POPKA EXP PPVKA IF ICALL NE 4 AND KA LE CL V EXIT 1 100 IF ICALL EQ 4 THEN NETA 0 DOWHILE KA LE CL V AND NETA LT 100000 safety net in case of getting stuck in loop CALL SIMETA ETA CL POPCL EXP PPVCL V POPV EXP PPVV KA POPKA EXP PPVKA NETA NETA 1 ENDDO ENDIF SC V ERROR Y F 1

Original URL path: http://nonmem.org/nonmem/nm/99oct072004.html (2016-04-25)

Open archived version from archive - [NMusers] saturable first-pass metabolism

Subject RE NMusers saturable first pass metabolism Date Tue October 5 2004 2 40 am Andy Try the following It empirically models an increase of F1 with dose using an exponential function It also describes the random between subject variability in F1 You can play around with the empirical model to see if you can do better than the exponential If you have more than one dosing occasion in each

Original URL path: http://nonmem.org/nonmem/nm/99oct042004.html (2016-04-25)

Open archived version from archive - [NMusers] Urinary excretion

might be cheaper than manufacturing overhead 2 Incorporate a bioavailability factor which in this case would be greater than one Then get creative about explaining why it is From Michael J Fossler gsk com Subject RE NMusers Urinary excretion Date Tue September 28 2004 9 00 am Our colleagues at Wyeth know a little about getting horses to manufacture drugs in this way Mike Michael J Fossler Pharm D Ph

Original URL path: http://nonmem.org/nonmem/nm/99sep282004.html (2016-04-25)

Open archived version from archive - [NMusers] Modelling individual data using a data file on several subjects

I am not sure how and whether it can be performed using NONMEM alone I have provided the batch file which calls awk codes below for extracting one id data and fit the data for that individual Though this is not the final code the idea is the same It requires some more fine programming like adding loops so that the whole process is automated Sentences starting with REM are comments REM Output data for id 20 from the main datafile to id20 csv gawk 1 ID print 0 datafile csv id20 csv gawk 1 20 print 0 datafile csv id20 csv REM print the name of the datafile in DATA of the ctl file here let us say it is id20 ctl general ctl is a common ctl stream where only the datafile needs to be changed If initial estimates needs to be changed for each that can also be performed by using additional codes gawk f ex5 awk general ctl id20 ctl REM ex5 awk is an awk file called to perform the above mentioned action The code in ex5 awk REM is given below which prints id20 csv after DATA REM 1 DATA 2 id20 csv REM

Original URL path: http://nonmem.org/nonmem/nm/99sep212004.html (2016-04-25)

Open archived version from archive - [NMusers] BOV

occasion effect within a subject ai N 0 BSV i 1 t t 4 in this example bij N 0 BOV j 1 r r 4 in this example N r t assume a balanced design here to simplify the problem Occasion is nested within subject and simply serves as replicates replicates are supposed to come from the same distribution In this case the so called between occasion variability is nothing but residual variability at least you can think of it this way Even though we can think of this as two factor subject and occasion ANOVA it is in fact one factor ANOVA with the second factor being confounded with the true residual error Without replicates the last level of factor is always confounded with the true residual error In this kind of situation I simply think of the last factor as replicates In this simple model we have two variances the between subject variance BSV and the winthin subject variance a combination of true between occasion variance and the true residual variance but we just simply lump them together and call it BOV here In typical ANOVA analysis the esimate for BOV is sum i t sum j r CLij CLavgi 2 N t Let s call this estimate BOVhat Following Nick s calculation say SD2avg sum i t CLavgi CLavgall 2 t 1 Then the estimate for BSV BSVhat is SD2avg BOVhat r This is proved in any stat book for ANOVA with a random effect So even in this simple scenario SD2avg overestimates BSV unless r is quite large or BOV is very small 2 Complex scenario When we assume BOV is different for all occasions this leads to a quite unusual assumption in the ANOVA setting as demonstrated by the following derivation CLij CL ai bij CL is the true CL for the whole population ai is the random subject effect bij is the random occasion effect within a subject ai N 0 BSV i 1 t bij N 0 BOVj j 1 r Note BOV has a subscript now In this case the replicates occasions come from different distributions I went through some math stat derivation and found the following conclusions The individual BOVj is not estimable But the mean of BOVj BOVavg can be estimated by sum i t sum j r CLij CLavgi 2 N t Let s call this estimate BOVavghat Then BSV can be estimated by SD2avg BOVavghat r A conclusion similar to those for a typical ANOVA In order to estimate individual BOVj replicates are needed as Ken pointed out earlier A very important concept clarification should be noted here When we assume BOV is different for all occasions implicitely we already add another level of randomness to the problem I don t want to call it within occasion variance because that does not fit the purpose of BOV when it was first proposed I think of it as a second level of between occasion variance For example the original occasion in our example is different regions New York Huston Rockville Gainesville The second level of occasion is differnt hospitals in those regions There is a reason to assume different BOV in this case because the conditions in the hospitals in one region may be better than those in another region In fact the occassion in BOV is refering to different things in the two scenarios discussed above In the simple scenario the occassion refered in BOV is the region or the hospital in different region In the complex scenario the occassion refered in BOV is the hospital in the same region Yaning Wang PhD Pharmacometrician OCPB CDER FDA From Michael J Fossler gsk com Subject RE NMusers BOV Date Wed September 22 2004 1 19 pm Can we clarify what is meant by occasion In Yaning s example occasion as I understand it a point in time when some measurement is made is confounded by site in other words hospital Given Yaning s proposed experimental design I don t think any model would be satisfactory since there is no way to tease out the effect of site hospital from the effect of occasion A better design would be i subject 1 4 j site 1 4 Sub1 Sub2 Sub3 Sub4 Occ1 CL11 CL22 CL33 CL44 Occ2 CL14 CL21 CL32 CL43 Occ3 CL13 CL24 CL31 CL42 Occ4 CL12 CL23 CL34 CL41 Mean CLavg1 CLavg2 CLavg3 CLavg4 Here site and occasion are no longer confounded and a true BOV controlled for site could be estimated Mike Michael J Fossler Pharm D Ph D F C P Principal Clinical Pharmacokineticist Clinical Pharmacokinetics Modeling Simulation GlaxoSmithKline 610 270 4797 FAX 610 270 5598 Cell 443 350 1194 Michael J Fossler gsk com From Kowalski Ken Subject RE NMusers BOV Date Wed September 22 2004 1 50 pm Yaning Thanks for working out the math stat that I was going to do you saved me the trouble The key point to make here then is that even if the true underlying model is that each occasion has a different BOV we can still obtain an unbiased estimate of BSV we just can t do it the way Nick has suggested unless the number of occasions is large large r in your notation below Moreover even though we can get an unbiased estimate of BSV estimating the BOVj are unestimable unless we have replication of occasions That being said I have a point of clarification and a philosophical issue I d like to raise I believe in Nick s ANOVA analogy it is appropriate to think of the study as a two factor ANOVA in that we would have within subject and within occasion replication e g SS plasma concentrations at multiple time points within an occasion This within occasion replication is our measurement error and would be estimated by the MSE in an ANOVA in addition to the BSV and BOV variance components The philosophical issue I would like to raise regarding this analogy is do we assume occasions are nested or crossed with subjects In your message below you assumed that occasions are nested within subjects I think it may depend on how we interpet the effects of time on biological PK variability If we interpret time effects as transient specific to a moment in time e g what the subject ate over the past few hours then I think it may be reasonable to interpet occasions as nested within subjects since occasion 1 and occasion 2 may not represent the exact same date and times for any two subjects However if time effects are due to duration of time in the study and particularly if the occasions are taken many weeks or months apart e g occasion 1 is at 3 mos and occasion 2 is at 6 mos then it might be reasonable to assume that occasions and subjects are crossed In this setting we could then also estimate a variance component for the subject by occasion interaction This just represents a different partitioning interpretation of the total variability To expand on Nick s ANOVA analogy and to incorporate your comments regarding your region hospital analogy suppose we have 4 occasions where the first two occasions are a week apart say weeks 1 and 2 and the last two occasions are a week apart but 6 mos later say weeks 26 and 27 In this setting it may be reasonable to assume that the BOV is different between these two periods weeks 1 2 vs weeks 26 27 Although we can t estimate different BOV for all four occasions we may be willing to assume the BOV is the same for weeks 1 and 2 call it BOV1 for the BOV in period 1 but different from the BOV for weeks 26 and 27 call it BOV2 for the BOV in period 2 We now have replication of occasions within a given period that would allow us to estimate different BOVs for the two periods I note that Nick is not easily swayed by statistical arguments so I m going to propose a simple simulation estimation exercise as an empirical way to confirm that the model is over parameterized if we try to estimate different BOVj s Hopefully Nick or someone else would be willing to conduct this simulation and report back the findings to NMusers Suppose we have 100 subjects with 3 steady state plasma concentrations following an IV infusion at each of two occasions From these plasma concentrations we can estimate CLijk for the ith subject at the jth occasion at the kth sample time For simplicity let s assume that the CLijk are normally distributed with additive random effects for subjects occasions with different BOVj j 1 2 and measurement error A simple mean model would be CL THETA 1 ETA 1 OCC1 ETA 2 OCC2 ETA 3 Y CL EPS 1 where the omega for ETA1 is the BSV and omegas for ETA2 and ETA3 are different corresponding to the BOVj Let s now consider four different analysis models Model 1 the same model as used to simulate the data CL THETA 1 ETA 1 OCC1 ETA 2 OCC2 ETA 3 Y CL EPS 1 Model 2 the same model as used to simulate the data with the BLOCK SAME option CL THETA 1 ETA 1 OCC1 ETA 2 OCC2 ETA 3 Y CL EPS 1 where omegas for ETA2 and ETA3 are constrained to be the same i e a common BOV Model 3 CL THETA 1 OCC1 ETA 1 OCC2 ETA 2 Y CL EPS 1 where omegas for ETA1 and ETA2 correspond to PPV1 and PPV2 respectively Model 4 CL THETA 1 ETA 1 OCC2 ETA 2 Y CL EPS 1 where the omega for ETA1 corresponds to PPV1 and the sum of the omegas for ETA1 and ETA2 correspond to PPV2 respectively I believe Models 2 4 will essentially give the same fit but with different partitionings of the total variability in CL Note that we may get some bias in the parameters theta and omegas because these models are different from the simulation model but they probably won t be over parameterized On the other hand for Model 1 even though we are fitting the same model that we used to simulate the data I claim this model will be over parameterized This over parameterization will manifest itself as an ill conditioned model fit wherein the COV step will fail I know that Nick places no diagnostic value in the COV step so I ll make one further prediction As long as we are fitting a linear model as described for Model 1 I believe NONMEM will estimate a zero gradient and thus will not iterate on at least one or more of the variance components Anyone interested in doing this little simulation and reporting back the results Ken From Wang Yaning WangYA cder fda gov Subject RE NMusers BOV Date Wed September 22 2004 2 08 pm Micheal Occasion could be either location or time period The hospital region example is used to simply the problem and explain a concept In fact anything in sequence is confounded with time Let s use time period as the occasion e g in a crossover experiment Suppose the whole experiment is conducted in one hospital and there are 4 periods Analogous to my previous example in the simple scenario same BOV in all occasions BOV is just the within subject variance across periods In the complex scenario different BOV in all occasions the interpretation will be different Basically we assume different variance at each period say BOV1 BOV2 BOV3 BOV4 What is the between occasion here It is not between period 1 period 2 period 3 and period 4 It is between period1 in this current experiment and period1 if we can repeat the whole crossover experiment for BOV1 This second level of between occasion in this case is nothing but the true measurement error replicates within a subject for the same period Here period 1 in the current experiment is analogous to the hospital in New York Period 1 in the current experiment and period1 in a repeated experiment are two hospitals in New York Yaning Wang PhD Pharmacometrician From Liang Zhao zhao 80 osu edu Subject RE NMusers BOV Date Wed September 22 2004 2 11 pm I have the same doubt as Mike for Yaning s simplified scenario with BOV is the same for all occasions Based on my understanding the design for both the simplified scenario and complex scenario is the same as Mike suggested In this case the BSV and BOV are not comfounded and they are all estimable Think about the equation system CLij CL ai bij There are 8 unknowns a1 a4 and b 1 b 4 in this case and 8 equations in the system surely all of them are estimable I agree that BOV in the complex scenario is unestimable Liang Zhao PhD Division of Pharmaceutics The Ohio State Univ From Liang Zhao zhao 80 osu edu Subject RE NMusers BOV Date Wed September 22 2004 2 19 pm With a little correction to the equation system CLij CL ai bij There are 9 unknowns CLavg a1 a4 and b 1 b 4 in this case and 9 equations with sum ai bij over i j 0 in the system surely all of them are estimable I agree that BOV in the complex scenario is unestimable Liang Zhao PhD Division of Pharmaceutics The Ohio State Univ From Michael J Fossler gsk com Subject RE NMusers BOV Date Wed September 22 2004 2 53 pm Hi Yaning My comments Occasion could be either location or time period I don t buy it Time is Time and location is location with the right design you should be able to estimate the contribution of both to your variance Also there are clinically meaningful ways in which site could affect your results e g they could be excessively sloppy skilled at sampling and recording times they could mis treat the samples resulting in some degradation of drug etc The point is the two effects are distinct The hospital region example is used to simply the problem and explain a concept In fact anything in sequence is confounded with time Sure that s why you randomize to sequence I still contend in your example that you are unable to measure the true effect of occasion because it is perfectly confounded with site i e you can substitute either variable in the analysis and get the same answer Let s use time period as the occasion e g in a crossover experiment Suppose the whole experiment is conducted in one hospital and there are 4 periods Analogous to my previous example in the simple scenario same BOV in all occasions BOV is just the within subject variance across periods I agree with this with the caveat that the design allows you to model occasion distinctly from some other effect If you stick with your example where site 1 2 3 4 is perfectly correlated with occasion 1 2 3 4 then I disagree with your interpretation With your example I still maintain that you can t assign that bit of variance as either contribution due to occasion or by site since they are perfectly correlated In the complex scenario different BOV in all occasions the interpretation will be different Basically we assume different variance at each period say BOV1 BOV2 BOV3 BOV4 What is the between occasion here It is not between period 1 period 2 period 3 and period 4 It is between period1 in this current experiment and period1 if we can repeat the whole crossover experiment for BOV1 This second level of between occasion in this case is nothing but the true measurement error replicates within a subject for the same period Here period 1 in the current experiment is analogous to the hospital in New York Period 1 in the current experiment and period1 in a repeated experiment are two hospitals in New York In your design I didn t see any replicates within a subject for the same occasion It also seem to me that you are adding additional occasions and sites here or am I just a dumb pill counter Anyway I eagerly await another one of Ken s lucid explainations of this topic Mike Michael J Fossler Pharm D Ph D F C P Principal Clinical Pharmacokineticist Clinical Pharmacokinetics Modeling Simulation GlaxoSmithKline 610 270 4797 FAX 610 270 5598 Cell 443 350 1194 Michael J Fossler gsk com From Liang Zhao zhao 80 osu edu Subject RE NMusers BOV Date Wed September 22 2004 2 59 pm Date To Wang Yaning more Cc Wang Yaning Priority Normal Options View Full Header View Printable Version I have the same doubt as Mike for Yaning s simplified scenario with BOV is the same for all occasions Based on my understanding the design for both the simplified scenario and complex scenario is the same as Mike suggested In this case the BSV and BOV are not comfounded and they are all estimable Think about the equation system CL11 CL a1 b11 CLij CL ai bij There are totally i j 4 4 16 equations in this case where i is number of subjects and j is the number of occasions By adding constraint equations a1 a4 0 b11 b1j 0 bi1 bij 0 in total we have i j 1 j 21 in this case equations We know here CL a1 ai b11 bij are all unknowns and there are 21 of them Solve the equation system we can get all of the values of unknowns Since ai N 0 BSV i 1 t t 4 in this example bij N 0 BOV j 1 r r 4 in this example BSV and BOV can be further estimated by looking at ai s and bij s one step further since estimation of BSV and BOV does not require the full information of ai s and bij s there is big chance that the clinical design can be further reduced and you still get information about BSV and BOV Even the algorithm to calculate BSV and BOV in NONMEM is carried out different degree of freedoms that can be used for parameter estimations will not change and I do think more effort should be put in this field of study for potential fractional clinical designs If my derivation and reasoning is not making sense please point out It is a very stimulating discussion Liang Zhao PhD Division of Pharmaceutics The Ohio State Univ From Mats Karlsson mats karlsson farmbio uu se Subject RE NMusers BOV Date Wed September 22 2004 3 03 pm Hi Ken I m not going to run your example but why complicate things unnecessarily It is a lot easier and conceptually just as valid to assume that you can get a precise estimate of CL at each occasion Thus you can do you example with just two levels of random effects My prediction in this or the original example is that the full model will be supported without having to go to a large number of occasions The analysis model suggested by Fabrice Model 3 below does not really make sense It predicts either i that overall variability is lower on the first occasion than on the other or ii that there is a correlation between the BSV eta and every BOV eta for multiple occasions The latter is problematic for a number of reasons Best regards Mats Mats Karlsson PhD Professor of Pharmacometrics Div of Pharmacokinetics and Drug Therapy Dept of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE 751 24 Uppsala Sweden phone 46 18 471 4105 fax 46 18 471 4003 mats karlsson farmbio uu se From Mats Karlsson mats karlsson farmbio uu se Subject RE NMusers BOV Date Wed September 22 2004 3 20 pm Hi again A quick run of the example I outlined code below show that indeed one can estimate different variabilites at different occasions Whether it is useful is another matter Model PROBLEM INPUT ID DV OCC DATA data1 IGNORE PRED IF OCC EQ 1 Y THETA 1 ETA 1 EPS 1 IF OCC EQ 2 Y THETA 1 ETA 1 EPS 2 IF OCC EQ 3 Y THETA 1 ETA 1 EPS 3 THETA 10 OMEGA 1 SIGMA 1 1 1 SIM 9897667 EST MAXEVAL 9999 COV PRINT E DATA FILE ID DV OCC 1 0 1 1 0 2 1 0 3 2 0 1 2 0 2 100 0 3 OUTPUT FINAL PARAMETER ESTIMATE THETA VECTOR OF FIXED EFFECTS PARAMETERS TH 1 1 01E 01 OMEGA COV MATRIX FOR RANDOM EFFECTS ETAS ETA1 ETA1 8 71E 01 SIGMA COV MATRIX FOR RANDOM EFFECTS EPSILONS EPS1 EPS2 EPS3 EPS1 1 25E 01 EPS2 0 00E 00 8 92E 02 EPS3 0 00E 00 0 00E 00 1 30E 01 1 STANDARD ERROR OF ESTIMATE THETA VECTOR OF FIXED EFFECTS PARAMETERS TH 1 9 60E 02 OMEGA COV MATRIX FOR RANDOM EFFECTS ETAS ETA1 ETA1 1 27E 01 SIGMA COV MATRIX FOR RANDOM EFFECTS EPSILONS EPS1 EPS2 EPS3 EPS1 2 10E 02 EPS2 2 15E 02 EPS3 2 85E 02 1 COVARIANCE MATRIX OF ESTIMATE TH 1 OM11 SG11 SG12 SG13 SG22 SG23 SG33 TH 1 9 21E 03 OM11 5 33E 04 1 63E 02 SG11 2 45E 04 1 39E 04 4 42E 04 SG12 SG13 SG22 1 04E 04 3 06E 04 8 20E 05 4 62E 04 SG23 SG33 4 64E 04 3 18E 04 1 80E 04 4 47E 05 8 15E 04 1 CORRELATION MATRIX OF ESTIMATE TH 1 OM11 SG11 SG12 SG13 SG22 SG23 SG33 TH 1 1 00E 00 OM11 4 35E 02 1 00E 00 SG11 1 22E 01 5 20E 02 1 00E 00 SG12 SG13 SG22 5 04E 02 1 12E 01 1 81E 01 1 00E 00 SG23 SG33 1 69E 01 8 74E 02 2 99E 01 7 28E 02 1 00E 00 1 INVERSE COVARIANCE MATRIX OF ESTIMATE TH 1 OM11 SG11 SG12 SG13 SG22 SG23 SG33 TH 1 1 13E 02 OM11 2 59E 00 6 30E 01 SG11 4 77E 01 2 59E 01 2 63E 03 SG12 SG13 SG22 2 72E 01 3 40E 01 5 17E 02 2 30E 03 SG23 SG33 5 13E 01 2 70E 01 5 92E 02 2 12E 02 1 41E 03 1 EIGENVALUES OF COR MATRIX OF ESTIMATE 1 2 3 4 5 6 10E 01 8 51E 01 9 12E 01 1 21E 00 1 41E 00 Mats Karlsson PhD Professor of Pharmacometrics Div of Pharmacokinetics and Drug Therapy Dept of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE 751 24 Uppsala Sweden phone 46 18 471 4105 fax 46 18 471 4003 mats karlsson farmbio uu se From Liu Qi qi liu merck com Subject RE NMusers BOV Date Wed September 22 2004 3 30 pm Hi Liang Since ai and bij are RANDOM effects here I doubt you can make the assumption of a1 a4 0 b11 b1j 0 bi1 bij 0 Correct me if I am wrong Thanks Qi Qi Liu Department of Drug Metabolism Merck Co Inc WP75 100 Sumneytown Pike West Point PA 19486 Tel 215 652 4096 Fax 215 993 3533 From Kowalski Ken Ken Kowalski pfizer com Subject RE NMusers BOV Date Wed September 22 2004 4 24 pm Hi Mats Hmmm I stand corrected I modified your run to add in the complexity of the third level of random effects and much to my surprize I was able to estimate the different BOVs for each occasion as well as the BSV See below for my code and output I apologize for taking us down this path with numerous emails I should have done this simple simulation first to support or refute my own apparently faulty intuition So now I find myself in unchartered waters where I feel compelled to say to Nick that he was right and I was wrong my apologies Nick Ken Model File PROBLEM INPUT ID OCC TIME DV DATA example dat IGNORE PRED Y THETA 1 ETA 1 1 OCC ETA 2 OCC ETA 3 EPS 1 THETA 10 OMEGA 1 2 2 SIGMA 1 SIM 9897667 EST MAXEVAL 9999 COV PRINT E Data File ID OCC TIME DV 1 0 1 0 1 0 2 0 1 0 3 0 1 1 1 0 1 1 2 0 1 1 3 0 100 1 3 0 Output File FINAL PARAMETER ESTIMATE THETA VECTOR OF FIXED EFFECTS PARAMETERS TH 1 9 94E 00 OMEGA COV MATRIX FOR RANDOM EFFECTS ETAS ETA1 ETA2 ETA3 ETA1 1 18E 00 ETA2 0 00E 00 2 66E 01 ETA3 0 00E 00 0 00E 00 1 38E 01 SIGMA COV MATRIX FOR RANDOM EFFECTS EPSILONS EPS1 EPS1 1 08E 01 1 STANDARD ERROR OF ESTIMATE THETA VECTOR OF FIXED EFFECTS PARAMETERS TH 1 1 13E 01 OMEGA COV MATRIX FOR RANDOM EFFECTS ETAS ETA1 ETA2 ETA3 ETA1 1 69E 01 ETA2 8 26E 02 ETA3 7 56E 02 SIGMA COV MATRIX FOR RANDOM EFFECTS EPSILONS EPS1 EPS1 7 38E 03 1 COVARIANCE MATRIX OF ESTIMATE TH 1 OM11 OM12 OM13 OM22 OM23 OM33 SG11 TH 1 1 28E 02 OM11 1 93E 03 2 85E 02 OM12 OM13 OM22 1 41E 03 1 78E 03 6 82E 03 OM23 OM33 1 12E 03 4 00E 03 3 90E 03 5 71E 03 SG11 3 28E 05 5 30E 05 3 04E 05 3 94E 06 5 45E 05 1 CORRELATION MATRIX OF ESTIMATE TH 1 OM11 OM12 OM13 OM22 OM23 OM33 SG11 TH 1 1 00E 00 OM11 1 01E 01 1 00E 00 OM12 OM13 OM22 1 51E 01 1 28E 01 1 00E 00 OM23 OM33 1 31E 01 3 14E 01 6 25E 01 1 00E 00 SG11 3 93E 02 4 25E 02 4 99E 02 7 05E 03 1 00E 00 1 INVERSE COVARIANCE MATRIX OF ESTIMATE TH 1 OM11 OM12 OM13 OM22 OM23 OM33 SG11 TH 1 8 07E 01 OM11 4 18E 00 3 95E 01 OM12 OM13 OM22 1 32E 01 9 44E 00 2 46E 02 OM23 OM33 3 86E 00 3 33E 01 1 72E 02 3 17E 02 SG11 4 56E 01 3 32E 01 1 33E 02 8 90E 01 1 85E 04 1 EIGENVALUES OF COR MATRIX OF ESTIMATE 1 2 3 4 5 3 43E 01 8 64E 01 9 40E 01 1 04E 00 1 82E 00 From Nick Holford Subject RE NMusers BOV Date Wed September 22 2004 4 30 pm Hi Thank you Mats for simulating the problem that Ken suggested With regard to Ken s prediction that this model Model 1 is overparameterized and ill conditioned it would seem that NONMEM falsifies the prediction It does seem to be possible to estimate BOV on each occasion without running into the numerical problems that Ken expected The bias and imprecision of the estimates is not shown in the results from just one simulation run but while Mats was simulating with NONMEM I was simulating with Excel If you go to this page http www health auckland ac nz pharmacology staff nholford pkpd you can download an Excel sheet that simulates the thought experiment I proposed for upto 10 occasions and upto 2000 subjects The Excel simulation demonstrates how to calculate BSV and BOV for each occasion However as Ken pointed out the estimate of BSV is an asymptotic estimate we can still obtain an unbiased estimate of BSV we just can t do it the way Nick has suggested unless the number of occasions is large When the number of occasions is not infinite the individual estimates of average clearance CLAVGi are not exact estimates of the true clearance CLi They have additional error due to BOV not being averaged out to zero The estimate of BSV is therefore upwardly biased However if we accept the bias in BSV the estimates of BOV for each occasion are still reasonably close to the true BOV values when the number of occasions is 10 and number of subjects is 2000 Here are some estimates I obtained using Excel True Estimates Nocc 10 10 Nsub 2000 20 BSV 0 2 0 22 0 20 BOV1 0 2 0 17 0 20 BOV2 0 3 0 28 0 24 BOV3 0 4 0 38 0 47 Note that these numbers will vary every time you open the Excel file or make any change so don t expect to see exactly the same values if you download the file My scepticism for statistics as noted by Ken seems to be supported by these results However it may be that there is some misunderstanding of the true nature of the problem that is causing the confusion Perhaps these explicit empirical examples from Mats and myself will focus the statistical theoreticians and allow them to propose some resolution Nick Nick Holford Dept Pharmacology Clinical Pharmacology University of Auckland 85 Park Rd Private Bag 92019 Auckland New Zealand email n holford auckland ac nz tel 64 9 373 7599x86730 fax 373 7556 http www health auckland ac nz pharmacology staff nholford From Liang Zhao zhao 80 osu edu Subject RE NMusers BOV Date Wed September 22 2004 4 56 pm Hi Qi In my understanding if the variables are RANDOM by way of viewing the regression as orthogonal projections with condition that the sum of residual distances to be 0 another view point for the techniques used in least square simple linear nonlinear regressions you can make these assumptions In addition the distribution of BSV and BOV do follow normal distributions with mean 0 by assumption in this case The calculations based on weighted least square or maximum likelihood approach for PPK are equivalent if the RANDOM variables are assumed to be normally distributed Please refer to some nonlinear regression books by Bates for the concept of orthogonal projection In fact a trick to validate the NONMEM outputs is to make sure the sum of weighted residual is 0 if everything is normally distributed Point out if I am wrong Liang Zhao PhD Division of Pharmaceutics The Ohio State Univ From Nick Holford n holford auckland ac nz Subject RE NMusers BOV Date Wed September 22 2004 4 56 pm Ken Thanks for this additional result showing that NONMEM appears to be able to estimate 3 levels of random effect for this design There is no need to offer any apologies This discussion has been most helpful in clarifying ideas and understanding the limitations and opportunities for BOV You and Yaning were certainly right in predicting that the estimate of BSV is biased upwards A point I did not appreciate myself until I looked at the Excel simulations and realized from the numerical example what was happening Yaning I am still puzzled by your theoretical comments 2 Complex scenario When we assume BOV is different for all occasions this leads to a quite unusual assumption in the ANOVA setting as demonstrated by the following derivation CLij CL ai bij CL is the true CL for the whole population ai is the random subject effect bij is the random occasion effect within a subject ai N 0 BSV i 1 t bij N 0 BOVj j 1 r Note BOV has a subscript now In this case the replicates occasions come from different distributions I went through some math stat derivation and found the following conclusions The individual BOVj is not estimable The way you have written the model seems to be the same as the way it was simulated by Mats NONMEM and myself Excel We both claim empirically that BOVj values are estimable Yet you conclude individual BOVj is not estimable Can you please explain Nick Nick Holford Dept Pharmacology Clinical Pharmacology University of Auckland 85 Park Rd Private Bag 92019 Auckland New Zealand email n holford auckland ac nz tel 64 9 373 7599x86730 fax 373 7556 http www health auckland ac nz pharmacology staff nholford From Mats Karlsson Subject RE NMusers BOV Date Wed September 22 2004 5 10 pm Nick I understand that you get a biased estimate of BSV if you do it the way you do it in Excel taking the mean of each subject s CL values to be the true value of CL Fortunately in mixed effects models that s not what happens at least not should happen My prediction is that no bias will occur in the examples run by Ken and me The show must go on Mats Mats Karlsson PhD Professor of Pharmacometrics Div of Pharmacokinetics and Drug Therapy Dept of Pharmaceutical Biosciences Faculty of Pharmacy Uppsala University Box 591 SE 751 24 Uppsala Sweden phone 46 18 471 4105 fax 46 18 471 4003 mats karlsson farmbio uu se From Nick Holford n holford auckland ac nz Subject RE NMusers BOV Date Wed September 22 2004 6 15 pm Mats Your prediction seems to be confirmed by simulation 100 replications from your example CL BSV BOV1 BOV2 BOV3 TRUE 10 000 1 000 0 316 0 316 0 316 average 9 976 0 994 0 319 0 322 0 311 bias 0 2 0 6 1 0 1 8 1 6 and from Ken s CL BSV BOV1 BOV2 RUV TRUE 10 000 1 000 0 447 0 447 0 316 average 10 004 0 987 0 438 0 443 0 317 bias 0 0 1 3 2 1 0 9 0 2 Nick Nick Holford Dept Pharmacology Clinical Pharmacology University of Auckland 85 Park Rd Private Bag 92019 Auckland New Zealand email n holford auckland ac nz tel 64 9 373 7599x86730 fax 373 7556 http www health auckland ac nz pharmacology staff nholford From Wang Yaning WangYA cder fda gov Subject RE NMusers BOV Date Wed September 22 2004 9 57 pm Dear all First of all I have to appologize for giving the wrong comments especially to Ken If Ken had done the derivation he would not have missed this Then I would like to say individual BOVj is estimable even if there is no replicates of occasions within a subject Just my personal opinion based on my own derivation I may be wrong In my previous derivation I had to admit that I didn t try hard enough to get the estimates for BOVj Once I saw BSV could not be estimated by Nick s proposal SD2avg I stopped and assumed BOVj certainly could not be estimated by his next step But Nick s intuition is right If BSV is estimated by SD2avg BOVavghat r unbiased for BSV as shown in my detailed derivation the estimate BSVhat can then be used to estimate BOVj based on Nick s logic Define CLjavg as the mean CL across subjects for occassion j If SD2j sum i t CLij CLjavg 2 t 1 then BOVjhat SD2j BSVhat BOVjhat is also an unbiased estimate for BOVj see the derivation Detailed derivation can be found here http www geocities com wangyaning2004 unequalbov pdf Summary of the derivation CLij CL ai bij CL is the true CL for the whole population ai is the random subject effect bij is the random occasion effect within a subject ai N 0 BSV i 1 t bij N 0 BOVj j 1 r N t r BOVavghat sum i t sum j r CLij CLavgi 2 N t unbiased estimate SD2avg sum i t CLavgi CLavgall 2 t 1 BSVhat SD2avg BOVavghat r unbiased estimate SD2j sum i t CLij CLjavg 2 t 1 BOVjhat SD2j BSVhat unbiased estimate This is really an exciting discussion I learned a lot Again my appologies for sending the previous misleading comments Thanks to Matts

Original URL path: http://nonmem.org/nonmem/nm/99sep202004.html (2016-04-25)

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