zan Junior US, 20140129 23:58 Posting: # 12289 Views: 11,028 

All, I encountered a negative Var(residual) for Cmax in PHX winnonlin when I run the 2x2 crossover test for intersubject and intrasubject CV% for Cmax and AUC. I was able to obtain the intrasub CV for both parameters but the intersub CV for Cmax is missing. However I would still like to get the estimate for this intersub CV, I was wondering how can I calculate this value out in this case. My limited searching tells me that this might be due to intersub CV% < intrasub CV%. What is the caution and steps to do when seeing this phenomena in the results? Many thanks zan Edit: Category changed. [Helmut] 
Helmut Hero Vienna, Austria, 20140130 01:16 @ zan Posting: # 12291 Views: 10,288 

Hi Zan, » I encountered a negative Var(residual) for Cmax in PHX winnonlin […] » My limited searching tells me that this might be due to intersub CV% < intrasub CV%. What is the caution and steps to do when seeing this phenomena in the results? Did you find this thread? A workaround for PHX at the end. If you want you can post your data set here (variables separated by blanks, please). I have the latest betaversion of the new release of PHX on my machine. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
zan Junior US, 20140130 18:11 @ Helmut Posting: # 12296 Views: 10,144 

Thank you, Helmut! The thread really helps (although no clear answer as to how this happens). I will play with the workaround in PHX and calculate the CVinter from this. Best regards Edit: Full quote removed. Please delete everything from the text of the original poster which is not necessary in understanding your answer; see also this post! [Helmut] 
zan Junior US, 20140131 00:16 @ Helmut Posting: # 12299 Views: 10,149 

Hi Helmut, I played with the workaround method in PHX but came up with invalid CVinter. Based on the suggested formula for PHX: if(Hypothesis = 'Sequence*Subject', 100*sqrt(exp((MSMSerror)/2)1), ''), in my data MS is smaller than MSerror hence the resultant number before taking last step squareroot becomes negative. Is it true that in the case the intersubject CV is considered nonestimable? Or is there other way to calculate this out? Many thanks, zan » Did you find this thread? A workaround for PHX at the end. If you want you can post your data set here (variables separated by blanks, please). I have the latest betaversion of the new release of PHX on my machine. 
ElMaestro Hero Denmark, 20140131 08:20 @ zan Posting: # 12300 Views: 10,110 

Hi, » if(Hypothesis = 'Sequence*Subject', 100*sqrt(exp((MSMSerror)/2)1), ''), in my data MS is smaller than MSerror hence the resultant number before taking last step squareroot becomes negative. » Is it true that in the case the intersubject CV is considered nonestimable? Or is there other way to calculate this out? I think PHX is in mixed mode here. I'd switch to an allfixed model. The results is the same as long as we talk standard 2,2,2BE. If you really want to apply a mixed model for the result, then you can probably first do the allfixed trick to get estimates of effects and between + within variances, then use the results coming from the allfixed analysis as starter guess for the optimizer in the mixed model. That also puts less stress on the optimiser so your risk of getting trouble with the optimizer worker's union is low I am not a PHX/winnonlin user so I do not know the syntax for this approach. Finally, without knowing anything about PHX/winnonlin, how about trying Subject everywhere rather than Sequence*Subject or Subject*Sequence? — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
yjlee168 Senior Kaohsiung, Taiwan, 20140131 10:26 @ zan Posting: # 12302 Views: 10,115 

Dear all, Sorry to cut in. Yes, nonestimable CV_{inter} could happen, I guess. In bear, we had a dataset for demo run purpose (singledose, 2x2x2 design; and the dataset can be obtained from the top menu of bear ('Generate/export all demo datatsets'; it's called 'Single2x2x2_demo.csv' or 'Single2x2x2_demo.RData'.) ln(Cmax) is OK, but for ln(AUC_{0t}) and ln(AUC_{0inf}), we got for ln(AUC_{0t})... and for ln(AUC_{0inf})... Happy Chinese Lunar New Year (today)! » ...for PHX: » if(Hypothesis = 'Sequence*Subject', 100*sqrt(exp((MSMSerror)/2)1), ''), in my data MS is smaller than MSerror hence the resultant number before taking last step squareroot becomes negative. — All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
Helmut Hero Vienna, Austria, 20140201 16:03 @ yjlee168 Posting: # 12305 Views: 10,057 

Hi Yungjin, wonderful! Below the data set for nonRusers. No way in PHX (neither subjects random or fixed + my workaround). Subject Period Formulation Sequence Cmax AUCt AUCinf My post #3000. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yjlee168 Senior Kaohsiung, Taiwan, 20140201 17:40 @ Helmut Posting: # 12307 Views: 10,004 

Dear Helmut, Thanks a lot for your help. Could you present the results (part of it will be good enough) from running PHX (or its beta)? I don't have PHX. » ... No way in PHX (neither subjects random or fixed + my workaround). » ... My post #3000. Amazing and thanks for sharing. — All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
Helmut Hero Vienna, Austria, 20140202 02:04 @ yjlee168 Posting: # 12310 Views: 10,036 

Hi Yungjin, » […] Could you present the results (part of it will be good enough) from running PHX (or its beta)? There are small differences to bear, since I started from the raw data and performed NCA first. This is a complete, balanced data set; therefore, the same results for subject(sequence) random or fixed are expected.Table Partial SS Dependent Hypothesis DF SS MS F_stat P_value This table is missing for the fixed effects model in the current release 6.3 (build 6.3.0.395) – therefore my workaround, but available in prerelease 1.4 (build 6.4.0.511). Of course in the mixed model for AUCt and AUCinf:
Table Final Variance parameters (mixed)Dependent Parameter Estimate Table Final Variance parameters (fixed)Dependent Parameter Estimate Note the CV_{intra} is not reported (why not?)… — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yjlee168 Senior Kaohsiung, Taiwan, 20140202 07:54 @ Helmut Posting: # 12313 Views: 9,971 

Dear Helmut, Great post and thanks for sharing again. This allows me have a chance to compare the differences between bear and PHX (and its prerelease also). » [...] There are small differences to bear, since I started from the raw data and performed NCA first. [...] — All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
ElMaestro Hero Denmark, 20140201 16:31 (edited by ElMaestro on 20140201 16:46) @ zan Posting: # 12306 Views: 10,044 

Hi all, how did » if(Hypothesis = 'Sequence*Subject', 100*sqrt(exp((MSMSerror)/2)1), '') or "MSSubject(seq)MSResidual" enter the game? Doesn't it appear funny, given SS_{total}=SS_{within}+SS_{between} ? With MSE for Cmax being much lower than MSE for AUC's and because the MS for subject is lower than the EMS I'd be inclined to think the Bear dataset itself is also a bit ... well ... deserving an audit — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
yjlee168 Senior Kaohsiung, Taiwan, 20140201 17:47 @ ElMaestro Posting: # 12308 Views: 10,134 

Dear Elmaestro, » ... » "MSSubject(seq)MSResidual" enter the game? Should be this (as presented values in my previous post), I guess. » Doesn't it appear funny, given SS_{total}=SS_{within}+SS_{between} ? It's true. But I don't have any explanation for this. » ... I'd be inclined to think the Bear dataset itself is also a bit ... well ... deserving an audit Though it's demo dataset for bear, it is real data. — All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
ElMaestro Hero Denmark, 20140201 19:02 (edited by ElMaestro on 20140202 01:27) @ yjlee168 Posting: # 12309 Views: 9,978 

Thanks Yungjin, » » "MSSubject(seq)MSResidual" enter the game? » » Should be this (as presented values in my previous post), I guess. Here I am thinking loud, and usually nothing good results when I do it. But here goes: By way of a typical anova (forget for a moment the case of imbalance and type III SS which is irrelevant anyway for the actual dataset example) we have: SS_{tot}=SS_{trt}+SS_{seq}+SS_{per}+SS_{subj}+SS_{res} where MS_{subj}=SS_{subj}/(n2) [n=total number of subjects counting both sequences] and MS_{res}= SS_{res}/(n2). I want to know what the color and taste of "MS_{subj}MS_{res}" as prescribed above is: MS_{subj}=SS_{subj}/(n2) or MS_{subj}=(SS_{tot}SS_{trt}SS_{seq}SS_{per}SS_{res})/(n2) Then "MS_{subj}MS_{res}" = (SS_{tot}SS_{trt}SS_{seq}SS_{per}SS_{res})/(n2)  SS_{res}/(n2) = (SS_{tot}SS_{trt}SS_{seq}SS_{per}2*SS_{res})/(n2) This is truly a mindf%cker. My brain refuses to cooperate. I am experiencing the cerebral equivalent of a Proton M rocket launch. Actually, I am inclined to think there is something wrong with that subtraction in the first place. — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
Helmut Hero Vienna, Austria, 20140202 02:31 @ ElMaestro Posting: # 12312 Views: 10,004 

Hi ElMaestro, » Actually, I am inclined to think there is something wrong with that subtraction in the first place. I told you on the phone that I’m going to meet Martin. He said: “Maybe the model is wrong.” Fuck. In Chow/Liu Chapter 7.3.1 (p192 last edition) I read: A negative estimate may indicate that model 3.1.1 is incorrect or sample size is too small. More details on negative estimates in analysis of variance components can be found in Hocking (1985). My emphasis. 3.1.1 is the usual 2,2,2 (though with carry over).So if this model is wrong, which one is correct? I’m not sure whether I shall invest in a book I likely will not understand anyway. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yjlee168 Senior Kaohsiung, Taiwan, 20140202 08:07 (edited by yjlee168 on 20140202 16:03) @ Helmut Posting: # 12314 Views: 10,128 

Dear Helmut and Elmaestro, As I read from Faraway JJ's textbook (Extending the Linear Model with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Julian J. Faraway, Chapman & Hall/CRC, 2006 by Taylor & Francis Group, LLC., ISBN 158488424X., pp. 1704), it said (p.171) '...The estimates (ANOVA estimator from glm()) can take negative values... This is rather embarrassing since variances cannot be negative. Various fixes have been proposed, but these all take away from the original simplicity of the estimation method...' there are some discussions about this in the text, including using the linear mixed effect model (lme or lmer). Will lme/lmer be the answer for this if we are using a wrong model when doing a 2x2x2 BE study for this situation only?  [edited] The problem of negative variance components seems commonly seen with ANOVA. When googling the website, we can find a lots about this information from user forums of some other big stat apps, such as SAS, SPSS and MINITAB. Here is one of them from MINITAB. » [...] I’m not sure whether I shall invest in a book I likely will not understand anyway. — All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
Helmut Hero Vienna, Austria, 20140202 02:19 @ ElMaestro Posting: # 12311 Views: 10,000 

Hi ElMaestro, » how did » » if(Hypothesis = 'Sequence*Subject', 100*sqrt(exp((MSMSerror)/2)1), '') » or » "MSSubject(seq)MSResidual" enter the game? To name some:
— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
ElMaestro Hero Denmark, 20140202 09:56 @ Helmut Posting: # 12315 Views: 9,916 

Thanks Helmut, once again I am sort of baffled. I have to admit that I actually thought MS_{subj} was a direct measure of intersubject variability. Plenty of room for improvement at my end, it seems. RCA: I don't understand because my brain is walnutsized. CAPA: I shall stop trying to understand. Can we possibly do an lm on Test only with Sequence and Period as fixed and take the MSE as some measure of total variance (between+within), then do the same for Ref only, then at the end pool (or average) the two variance estimates to obtain some kind of total variability, from which we then derive a between by subtracting the within stemming from the grand analysis with subj, seq, per, and trt? — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
d_labes Hero Berlin, Germany, 20140203 09:02 @ zan Posting: # 12318 Views: 9,861 

Dear "discutanten"! Did you remember the Chow, Liu book, Chapter 7.3? There is an in depth discussion of the possibility of σ^{2}_{S} becoming negative if estimated via ANOVA mean squares. There is also a formula giving the probability for obtaining a negative estimate, which is (was?) available in bear, I think. Ways out? Just to cite Chow and Liu (without the 'hat' above the σ^{2}): "To avoid negative estimates a typical approach is to consider the following estimator σ^{2}_{S}=max(0,σ^{2}_{S}) The above estimators are known as restricted maximum likelihood (REML) estimators". End of citation. In SAS a Proc MIXED call with subject as random should do that, I think. Will check it for the example later. — Regards, Detlew 
ElMaestro Hero Denmark, 20140203 10:22 @ d_labes Posting: # 12319 Views: 9,975 

Hi Detleffff, » Ways out? Just to cite Chow and Liu (without the 'hat' above the σ^{2}): » "To avoid negative estimates a typical approach is to consider the following estimator » σ^{2}_{S}=max(0,σ^{2}_{S}) » σ^{2}_{e}=σ^{2}_{e} if MS_{inter}≥MS_{intra} » The above estimators are known as restricted maximum likelihood (REML) estimators". End of citation. Yes, indeed the holy scripture says so; I think much of the confusion hinges on eq.7.3.3 saying E(V_{inter})=V_{e}+2V_{S} I think I do not follow it. When PROC MIXED or R's LME/LER fit a true MM with REML, the Al Gore Rhythm does not derive the sigmas via any of these equations but from iterartively maximising the likelihoood of the V matrix with the fixed effects. It may be that the result ends up being these same as one of the REML estimators above. But are these estimates really "maximum likelihood"related (however restricted they are), or are they just cheap ways out of an annoying situation?? After all, the residual of an LM/GLM (traditional ANOVA) is a decomposition of the entire variability into avialable factors, so if we e.g. set Ve=V as 7.3.3 suggests on the odd occasion then I think we are solving one problem in a quick and dirty fashion and at the same time doing something that appears very dubious. I guess my confusion boils down to something like "annoying negative values aside, where's the likelihood basis behind the idea of fiddling with the model's residual which truly is some kind of maximum likelihod estimator" ? (and if we manually tweak V_{e} would we then reflect that in our calc. of the CI for "likelihood" reasons?) If or when you test with PROC MIXED, can you paste the entire covariance matrix (not the Z or the G)? It will be the one with 14 columns if you use the dataset above; I'd expect a common sigma sq. on the diagonal and a single beweensigma sq. elsewhere in each row. — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
d_labes Hero Berlin, Germany, 20140203 11:58 (edited by d_labes on 20140203 13:11) @ ElMaestro Posting: # 12320 Views: 9,957 

Dear ElMaestro, » If or when you test with PROC MIXED, can you paste the entire covariance matrix (not the Z or the G)? It will be the one with 14 columns if you use the dataset above; I'd expect a common sigma sq. on the diagonal and a single beweensigma sq. elsewhere in each row. As requested: the V matrices using the following code Proc Mixed data=BEBAC12305; ln(AUCt) Covariance Parameter Estimates: ln(AUCt) Variance parameters are by default in SAS restricted to ≥0 in the maximization of the likelihood. Reasonable to me . I get negative variance for subject(sequence) in case of ln(AUCt) only if I use the nonstandard NOBOUND option in the Proc MIXED call: ln(AUCt) Seems the same as PHX build 6.3.0.395 / 6.4.0.511 results. See Helmut's post above.Edit: Interesting! Here the 90% CI's for AUCt (PE=96.14%):
Proc GLM 85.02% ... 108.71% Our (at least my own ) belief "Proc GLM and Proc MIXED give the same results for a complete, balanced data set" has to be modified! — Regards, Detlew 
ElMaestro Hero Denmark, 20140203 12:58 @ d_labes Posting: # 12321 Views: 9,984 

Haha, thanks Detlefffff, » Variance parameters are by default in SAS restricted to ≥0 in the maximization of the likelihood. » Reasonable to me . » I get negative variance for subject(sequence) in case of ln(AUCt) only if I use the nonstandard NOBOUND option in the Proc MIXED call: » ln(AUCt) » V(subject(sequence))= 0.00609 » V(residual) = 0.03329 » Seems the same as PHX build 6.3.0.395 / 6.4.0.511 results. See Helmut's post above. This is mindblowing. I can't say that I understand in any way, but it is clear that the unbounded (=unfiddled, native and pure) optimisation analysis results in the same residual as the allfixed lm/anova. The milliondollar question asked in the nastiest fashion: Do you either believe in negative variances between subjects or would you inflate the MSE and get wide confidence intervals? An agonising choice indeed. Another wrong question: Why care about betweenVars in a 2,2,2BE? Why not just do the anova, fetch the residual, calculate a CI on basis of it and punch any guy who asks about betweens hard in the face? I wonder how the PKworkgroup at EMA would deal with this. I can't say I understand any details of the stats but this thread opened my eyes to an issue that I had no idea existed. Thanks. — I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
d_labes Hero Berlin, Germany, 20140203 13:16 @ ElMaestro Posting: # 12322 Views: 9,887 

Dear ÖbersterGrößterMeister! » Do you either » » believe in negative variances between subjects » » or » » would you inflate the MSE and get wide confidence intervals? See my edit above . — Regards, Detlew 
Helmut Hero Vienna, Austria, 20140203 14:14 @ ElMaestro Posting: # 12323 Views: 9,943 

Dear all, » This is mindblowing. I can't say that I understand in any way, but it is clear that the unbounded (=unfiddled, native and pure) optimisation analysis results in the same residual as the allfixed lm/anova. I followed Yungjin’s suggestions; _{} comes up with 1.78 mio hits. Amazing this one – especially the “ways out” mentioned on page 130. » An agonising choice indeed. Yep. » Why care about betweenVars in a 2,2,2BE? The only possible reason I can imagine: The crossover turned out to be not such a good idea and you want to plan the next study in a parallel design. Then you would need the total CV for sample size estimation. The common formula CV_{p} = 100 x √(ℯ^{(MSs + MSe)/2)} – 1) would “work”, but result in values smaller than CV_{intra}. Forget it. MSe MSs CVintra CVinter CVpooled » Why not just do the anova, fetch the residual, calculate a CI on basis of it… Sure. » …and punch any guy who asks about betweens hard in the face? That’s Zan’s business. » I wonder how the PKworkgroup at EMA would deal with this. Not a problem for them, I guess. Doesn’t appear in their mandatory all fixed effects model (PHX) or Proc GLM . For the rest of the world (if running Proc MIXED ) I would go with the UNBOUND option (see Detlew’s post). But – hey! – that’s not the code given in FDA’s guidances. Reading a lot of stuff it’s evident that the restriction to ≥0 results in biased estimates. With Yungjin’s data set the resulting CI turned out to be liberal. Keeping patient’s risk in mind that’s not a good idea. Is the unrestricted method (accepting negative variances) always conservative? I think so, but I’m lacking the intellectual horsepower to prove it. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
d_labes Hero Berlin, Germany, 20140203 15:54 @ Helmut Posting: # 12324 Views: 9,790 

Dear Helmut, » ... But – hey! – that’s not the code given in FDA’s guidances. where does your opinion came from? So far as I know there is no code given in the FDA's guidances for nonreplicate crossover studies. Moreover on page 10 of the 2001 Statistical guidance they recommend Proc GLM: "General linear model procedures available in PROC GLM in SAS or equivalent software are preferred, although linear mixedeffects model procedures can also be indicated for analysis of nonreplicated crossover studies. For example, for a conventional twotreatment, twoperiod, twosequence (2 x 2) randomized crossover design, the statistical model typically includes factors accounting for the following sources of variation: sequence, subjects nested in sequences, period, and treatment. The Estimate statement in SAS PROC GLM, or equivalent statement in other software, should be used to obtain estimates for the adjusted differences between treatment means and the standard error associated with these differences." — Regards, Detlew 
Helmut Hero Vienna, Austria, 20140203 16:16 @ d_labes Posting: # 12325 Views: 9,747 

Dear Detlew, » » ... But – hey! – that’s not the code given in FDA’s guidances. » » where does your opinion came from? » So far as I know there is no code given in the FDA's guidances for nonreplicate crossover studies. Correct. Fingers faster than brain. In the obsolete (July 1992) guidance “Statistical Procedures for Bioequivalence Studies using a Standard TwoTreatment Crossover Design” FDA recommended that An analysis of variance (ANOVA) should be performed […] using General Linear Models (GLM) procedures of SAS or an equivalent program. — Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yjlee168 Senior Kaohsiung, Taiwan, 20140203 20:43 @ Helmut Posting: # 12327 Views: 9,826 

Dear Helmut, Yes, I noticed that too. » [...] but result in values smaller than CV_{intra}. Forget it. » MSe MSs CVintra CVinter CVpooled » Cmax 0.0178034 0.0236397 13.40% 5.41% 14.47% » AUCt 0.0332878 0.0211136 18.40% NA 16.61% » AUCinf 0.0311744 0.0188434 17.79% NA 15.91% » [...] Not a problem for them, I guess. Doesn’t appear in their mandatory all fixed effects model (PHX) or Proc GLM . For the rest of the world (if running Proc MIXED ) I would go with the UNBOUND option (see Detlew's post).Sorry but I think it should be NOBOUND option with Proc MIXED .— All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
Helmut Hero Vienna, Austria, 20140203 22:08 @ yjlee168 Posting: # 12328 Views: 9,833 

Hi Yungjin, » Sorry but I think it should be NOBOUND option with Proc MIXED .Absolutely right – I dabble in SAS. I just have the 6.3Manual (a verbose 8640 pages): NOBOUND requests the removal of boundary constraints on covariance parameters. For example, variance components have a default lower boundary constraint of 0, and the NOBOUND option allows their estimates to be negative. Parameter Constraints By default, some covariance parameters are assumed to satisfy certain boundary constraints during the NewtonRaphson algorithm. For example, variance components are constrained to be nonnegative […]. You can remove these constraints […] with the NOBOUND option in the PROC MIXED statement, but this can lead to estimates that produce an infinite likelihood. […]
Convergence Problems
— Regards, Helmut Schütz The quality of responses received is directly proportional to the quality of the question asked. ☼ Science Quotes 
yjlee168 Senior Kaohsiung, Taiwan, 20140203 20:22 (edited by yjlee168 on 20140203 21:55) @ d_labes Posting: # 12326 Views: 9,796 

Dear Detlew and all, Thanks for your messages. Great discussions. » ... » There is also a formula giving the probability for obtaining a negative estimate, which is (was?) available in bear, I think. Do you mean VarCorr() in lme()? yes, but I didn't use it any more. The question is that in bear we use lm() first, and get the negative variance. Then we can switch to use lme(..., method="REML") to redo it for that negative variance (i.e., when CV_{inter} is NaN, if(is.nan(CV_{inter}){do lme()} ). Why do we need to know the probability for obtaining a negative estimate? BTW, should we consider to use lme() instead if lm() for all 2x2x2 BE study since there seems no regulatory consideration? That really can avoid negative variances, though it happens occasionally.— All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
ElMaestro Hero Denmark, 20140203 22:11 @ yjlee168 Posting: # 12329 Views: 9,801 

Hi Yungjin, EU: All fixed, no discussion. US: All fixed, but lots of confusion because the SAS PROC GLM has the random statement, giving users the impression that subject is treated as a random effect in the model.Other places: Same, as far as I know. Some places might accept lme, but would probably at the outset nevertheless expect a simple linear model. So lm and not lme for 2,2,2BE.— I could be wrong, but… Best regards, ElMaestro  Bootstrapping for dissolution data is a relatively new hobby of mine. 
yjlee168 Senior Kaohsiung, Taiwan, 20140204 13:09 (edited by yjlee168 on 20140204 17:06) @ ElMaestro Posting: # 12335 Views: 9,741 

Dear ElMaestro and all, Thanks for your messages and good to hear that. The reason I asked was that it would be related to how I would modify bear later. BTW, results obtained from R's lme() may differ from that from SAS's PROC MIXED. As I ran lme() with the dataset that I provided before, I got different MSE (0.0244=0.1562085^{2}), CV_{intra}(15.7%) and V(subj(seq)) (1.11*10^{06})^{2} for AUC_{0t}from that using SAS's PROC MIXED as posted by Detlew. I still check with my codes to see if I do anything wrong. » [...] » So lm and not lme for 2,2,2BE.— All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 
yjlee168 Senior Kaohsiung, Taiwan, 20140205 19:12 (edited by yjlee168 on 20140206 08:02) @ yjlee168 Posting: # 12349 Views: 9,669 

Dear all, Using lme() to a 2x2x2 BE study, we can code with R (taking AUC_{0t} as example of the dataset in this thread) something like
modlnAUC0t<lme(log(AUC0t) ~ drug + seq + prd, Then outputs will be
Linear mixedeffects model fit by REML Since we will still stick on lm() with 2x2x2 study, so bear will show the outputs as
... Therefore, the CV_{intra} from lme() will not be calculated in this case. But luckily for us, Detlew has showed us that V(subject(seq)) is zero (or should be close to zero) and the 90%CI was the same as what we got from lm() using SAS PROC MIXED. Sorry for this lengthy post. — All the best, Yungjin Lee bear v2.8.3: created by Hsinya Lee & Yungjin Lee Kaohsiung, Taiwan http://pkpd.kmu.edu.tw/bear Download link (updated) > here 