**From msale01@medlib.iaims.georgetown.edu Wed Nov 27 04:47:43 1996
**

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.

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**From GILLESPIEW@cder.fda.gov Wed Nov 27 15:15:39 1996
**

Mark,

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

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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

gillespiew@cder.fda.gov

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