From Wed Nov 27 04:47:43 1996
Subject: Discrete parameters

Dear users:

Has anyone evey tried to use NONMEM to optimize a system the includes discrete parameters? I'm trying to use a function that includes a factorial (i.e., K**n*T**(n-1)*exp(-K*t)/(n-1)! (obviously I'll need an expression for the factorial). But n can only have integer values, and I'd like to optimize it. Any ideas?

Mark Sale M.D.


From Wed Nov 27 15:15:39 1996
Subject: Re: Discrete parameters


I presume you would limit your search for n to a finite range. That being the case, you could always do it by brute force, i.e., optimize for all possible values of n. (Yeah, I know you already thought of that one.) Another alternative that would allow partial automation of the problem might be to do an initial fit using a continuous analog for the factorial, e.g., the gamma function or a series approximation of it. Then you could probably limit your discrete search of n to 2 values---the integers immediately greater than and less than the real value obtained with the continuous search.

When I wrote the above I assumed you were using the same value of n for all individuals. If you're actually planning to allow n to vary among the individuals and estimate its distribution, then I don't have any great ideas. I suppose the second approach could be used in a relatively crude way.

Best Regards,
Bill Gillespie
Office of Clinical Pharmacology and Biopharmaceutics
Food and Drug Administration
5600 Fishers Lane (HFD-855)
Rockville, MD 20857
1-301-443-1640 / Fax: 1-301-480-6645