From: "Jiao Zheng" <jiaozhen@online.sh.cn>
Subject: negative objective value
Date: Tue, 17 Apr 2001 07:34:22 +0800
Dear All:
I am a new user in NONMEM and trying to model parent compound and metabolite seperately. I only got negative objective value in my metabolite modeling. I would be interested in why on how to take this problem.
My situation is: mutiple-trough sampling design one compartemnt open kinetic model with first order absorption and elimination in both parent and metabolite drug according to reference (ADVAN 2 TRANS 2) Ka was fixed to 0.05 from the parent drug's mean value of K.
thanks in advance
Jiao Zhen
Clin Pharm Dept. Hua Shan Hosptial Shanghai, P.R.China
negative objective value
From: SMITH_BRIAN_P@Lilly.com
Subject: Re: negative objective value
Date: Mon, 23 Apr 2001 10:02:10 -0500
A negative objective function is not a problem. Remember that the objective function is -2*ln(Likelihood). This is negative if the ln(Likelihood) is positive or when the Likelihood is greater than 1. There is no restriction in the likelihood that would restrict it to be less than 1. In fact, a negative objection function could be expected if your fit is very good.
Example 1: Assume a normal distribution with unknown mean and variance. You have 3 observations 0.9, 1, and 1.1. The maximum likelihood estimates of the mean and varaiance are 1 and 0.006667 respectively. The objective function is -21.5.
Example 2: Same assumptions. You have 3 observations 0, 1, and 2. The maximum likelihood estimates of the mean and variance are 1 and 0.6667 respectively. The objective function is 6.1.
(Note: there is a constant sqrt(2*pi) that sometimes is and sometimes is not used in the objective function calculation. I assumed that it was included, but either way the first example has a negative objective function and the second has a positive objective function.)
Conclusion: A negative objection function indicates a good fit, not that there is a problem.
Sincerely,
Brian Smith
From: SMITH_BRIAN_P@Lilly.com
Subject: Re: Negative OFV
Date: Mon, 23 Apr 2001 12:48:18 -0500
I made a stupid mistake in the calculation of the objective functions. Thanks go to Peter Bonate for finding the error. My face is red. :)
The correct values are -6.5 and 7.3 respectively.
Regardless, the message is the same. Negative objective functions are possible and indicate good fit rather than a problem with the model.
Sincerely,
Brian Smith