RE: SAEM and IMP

Bob: Yes, when I was developing the code for using the Sobol method in NONMEM, I too found that using the t-distribution with Sobol/Quasi normal method resulted in biased assessments of the objective function, when I used the unmodified standard technique of generating t-samples. So, I experimented with various alternative methods like you did, and the final algorithms used in NONMEM 7.2 and 7.3 appear to avoid the bias, at least when I tried some simple models, such as the example1 problem in the NONMEM ..\examples directory. For such a problem, I tried the following DF settings, with and without using the SOBOL method (RANMETHOD=3 (default), or RANMETHOD=3S2), DF=0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, and 12. I think beyond 12 DF is sufficiently normal like, and not much use. In all cases, the OBJF was within 1 unit of each other, and always within a STD of the Monte Carlo noise to the OBJF (I used EONLY=1, 20 iterations to obtain OBJFV replicates for each setting). By the way, the .cnv file publishes the mean and standard deviation of the last CITER objective function values (see nm730.pdf manual on root.cnv). Certainly it is worth assuring this lack of bias under other kinds of, and more complex, models, just to make sure, so it is worth while for modelers to use caution when mixing Sobol with DF>0. I should point out that odd-number DF’s such as 7 makes the corrective algorithm for Sobol with t-distributions work harder, whereas even-numbered DF’s are a little cleaner. So I recommend even-numbered DF’s, or 1, up to 10 to work with Sobol, at least as far as my algorithm is concerned (so DF=1,2,4,6,8,10 seem most efficient to use with Sobol). The algorithm I use for t-distributions is in the subroutine TDEV2, and is in ..source\general.f90. I publish it because I borrowed freely from the literature, and I consider it therefore “open-source”. Just a note for orienting you to the code, IRANM=5 refers to the Sobol method. I am afraid my theoretical expertise in the Sobol/Quasi random methods is not as good as yours, so please feel free to review the code, and perhaps let me and the modeling community know if there may be any potential pitfalls in using this t-distribution algorithm with Sobol. I am also happy to consider improvements you may come up with on this matter. Robert J. Bauer, Ph.D. Vice President, Pharmacometrics, R&D ICON Development Solutions 7740 Milestone Parkway Suite 150 Hanover, MD 21076 Tel: (215) 616-6428 Mob: (925) 286-0769 Email: [email protected]<mailto:[email protected]> Web: http://www.iconplc.com/