It seems my mails are not appearing on nmusers – maybe a sign that the thread has gone on too long. Anyway the one below is from yesterday.
/Mats Mats Karlsson, PhD Professor of Pharmacometrics Dept of Pharmaceutical Biosciences Uppsala University Box 591 751 24 Uppsala Sweden phone: +46 18 4714105 fax: +46 18 471 4003 From: Mats Karlsson [mailto:mats.karls...@farmbio.uu.se] Sent: Tuesday, June 01, 2010 4:03 PM To: 'Nick Holford'; 'nmusers@globomaxnm.com' Subject: RE: [NMusers] distribution assumption of Eta in NONMEM Nick, I don’t think the design was bad at all. Two very precisely measured observations per subject with 100 subjects for determining one THETA, one OMEGA and one sigma is indeed a much more informative design than we ever get in real life. I’m not sure what you try to achieve with these simulations. The question of sensitivity to the underlying distribution and a preference for transformations that result in normally distributed ETAs (ie differences between the individual parameters and the typical parameters under the model) I think has been shown. You may find situations where it is more or less sensitive, but that does not alter the fact. You don’t provide information about estimated sigma in your example below. Was the estimate unbiased? When you compare your original uniform eta distribution with the logit-transformation, you have to look at the transformed etas. Mats Mats Karlsson, PhD Professor of Pharmacometrics Dept of Pharmaceutical Biosciences Uppsala University Box 591 751 24 Uppsala Sweden phone: +46 18 4714105 fax: +46 18 471 4003 From: Nick Holford [mailto:n.holf...@auckland.ac.nz] Sent: Tuesday, June 01, 2010 3:23 PM To: Mats Karlsson; nmusers@globomaxnm.com Cc: 'Marc Lavielle' Subject: Re: [NMusers] distribution assumption of Eta in NONMEM Mats, Thanks for the suggestion to try a more complex model. I agree there might be some bias in the OMEGA(1,1) estimate from uniform simulated ETA when SIGMA is estimated with 2 obs/subject. In case this was due to a rather poor design (which is not what we are trying to test) I tried your example with 10 obs/subject. Although the OMEGA(1,1) (PPV_HILL) is indeed larger than the true value the 95% parametric bootstrap confidence interval includes the true value so I would not conclude this was a significant bias. Uniform Statistic HILL PPV_HILL Obj TRUE 5 0.083333 . average 4.9583 0.093377 -16926.4 CV 0.033317 0.102836 -0.00066 0.025 4.66 0.074833 -16950.2 0.975 5.25 0.11005 -16907.7 SD 0.165194 0.009603 11.15514 N 100 I also tried using the logistic transform you suggested and got these estimates: Logistic Statistic HILL LGPAR1 LGPAR2 PPV_HILL OBJ TRUE . . . . . average 5.0926 0.58006 1.6117 1.214079 -16938.7 CV 0.049328 0.121019 0.678749 0.432531 -0.00059 0.025 4.65475 0.47075 1.15475 0.321125 -16959.9 0.975 5.45575 0.6923 2.68925 2.1435 -16920.7 SD 0.251206 0.070198 1.09394 0.525127 10.05781 N 100 As you noted the OBJ was lower on average (12.3) with the LGST model. I tried simulating from the average estimates above using these two models. The distribution for the simulated uniform UNIETA value looked reasonably flat and within -0.5 to 0.5 as expected. The ETA1 distribution simulated from the uniform model was more or less normal with most of the values between -0.5 and 0.5. However the ETA1 distribution simulated from the logistic estimation model, while also more or less normal, had most of the values lying between -2 and 2 and more than 66% outside the range -0.5 to 0.5. So although the OFV was lower with the logistic transformation this would not be a good way to simulate the original data.
