Re: Computing std for secondary parms
Date: Fri, 12 Nov 1999 09:40:31 -0800
From: LSheiner <lewis@c255.ucsf.edu>
Subject: Re: Computing std for secondary parms
Yes, although it still takes some algebra, which is all the usual approximation using first derivatives takes, and it can be tricky.
You must reparameterize in the "dervied parameter" of interest and re-run.
In general, if you want the SE of s = g(theta), then you must reparameterize the model in s, deleting one of the current thetas. For example, you used
Cl = theta(1),
V = theta(2)
...
but now and you want SE(t1/2). Recognizing that s = t1/2 = .693Cl/V, so that V = .693CL/s, one rewrites PK as:
Cl = theta(1)
s = theta(2)
V = .693*Cl/s
...
The SE oth theta(2) is the SE of t1/2.
CAUTION: if, in the above exampe, Cl or V in the original code have etas attached, then this gets very very tricky if you redally beieve in the original model. That is, the following 2 models are NOT identical:
Cl = theta(1)+eta(1)
V = theta(2)+eta(2)
and
Cl = theta(1)+eta(1
s = theta(2)+eta(2
V = .693*Cl/s
ESPECIALLY if a diagonal OMEGA is used. Hence they may yield different obj fun values, parameter estimates (even for Cl), and predictions of y.
LBS.
--
Lewis B Sheiner, MD Professor: Lab. Med., Biopharm. Sci., Med.
Box 0626 voice: 415 476 1965
UCSF, SF, CA fax: 415 476 2796
94143-0626 email: lewis@c255.ucsf.edu