RE: BOV

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/