Re: posthoc step

From: "Nick Holford" n.holford@auckland.ac.nz Subject: Re: [NMusers] posthoc step Date: Wed, December 8, 2004 2:34 pm Leonid, I have also done something similar and found similar results. Without relying on any explicit calculation it seems that if the prior for K is 10 with a SD of 2 and data of 3 observations simulated with K=1 that the posterior estimate of K might be much closer to 10 than to 1. A value of 1 drawn from N(10,SD=2) is quite unlikely (NORMDIST(1,10,2,TRUE) is 3E-6). The POSTHOC estimate of 9.78 which is obtained using the NM-TRAN code and data Jerry supplied supports this. The SAS MAP estimate of 0.9437 that Jerry reported seems unreasonable given such a strong prior of SD=2 for K=10. I have used NONMEM with both the pseudo-observation (DATA) method which Jerry mentioned and the undocumented PRIOR method in NONMEM V (METHOD=ZERO and METHOD=COND). The estimate of Khat for all methods remains stubbornly at 10 with SD of 2. When the SD for the prior on K was increased to 9 then Khat changes abruptly from 10 to 0.94. I was rather surprised not to find a gradual change in Khat as the SD for the prior on K was increased. As Leonid shows below the transition from Khat of ~10 to Khat ~ 1 happens over a very narrow range (between SD=8 and SD=9). In addition to this sharp transition I also found 'spikes' of Khat dropping to ~1 at certain values for the SD of K. These spikes were not present when I used NONMEM VI with the DATA method of Bayesian estimation and the transition SD was at a lower value (7.35). (see attached PDFs). Bayesian Estimation with NONMEM V.pdf Bayesian Estimation with NONMEM VI.pdf 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/