Re: Minimisation problem...
Gavin,
I think polynomial is the wrong function to study this problem. It would be better to use something more mechanistic that intrinsically reflects the expected behavior. I would start with simple linear model
A = THETA(1)+ETA(1)
B = THETA(2)+ETA(2)
TEST = 0 for control, THETA(3) for test
Y=A+(B+TEST)*TIME
(assuming that at time zero both groups are identical).
Then move to Emax model
Y = A + (B+TEST)*TIME/(TIME50 + TIME), TIME50=THETA(4)
These two models test whether observations increase with time. If you think that the response can go up and down, then you may try to use more complex functions, like difference of two EMAX values where TEST influences EMAX or TIME50 values
(see http://www.go-acop.org/sites/default/files/webform/Joy_Hsu.doc)
FOCEI should be as good as any other methods for this problem. To test the quality of the fit it is better to plot DV versus PRED, not IPRED, since with enough ETAs you can fit DV almost exactly, even if your model fits only noise.
To get the idea of the appropriate function, you can compare means of two groups (plots mean for each group by time versus time): the model can help to quantify the dependence but if there is any trend, it should be clearly visible on the plot.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Quoted reply history
On 1/9/2013 5:19 AM, Gavin Jarvis wrote:
> Dear NMusers
>
> I am trying to analyse data from a study in which samples were taken
> from each subject at 4 different time points (t=0,5,10,14). The problem
> with the data is that there are many missing data points and there is
> considerable variation between the subjects.
>
> The subjects are in either a control or a test group, and I want to
> determine whether there is any difference in the data values between
> these groups.
>
> Overall, it looks like the data values increase with time, but there is
> a suggestion that in the test group the increase is not sustained but
> returns to baseline levels by t=14, whereas the control group is either
> levelled off or possibly still rising.
>
> I have used a polynomial model to fit the data up to the 3rd power
> (which I think is probably too much) and included additive parameters to
> modify each of the coefficients from the polynomial model.
>
> The problem I have is as follows:
>
> When I use the FOCE method the ETA terms collapse towards zero. The
> quality of the fit looks poor when judged by a plot of DV against
> individual predicted values.
>
> When I use the BAYES method, I get credible ETA values and a much better
> fit (i.e., DV vs ipred clusters sensibly around a line of unity).
>
> However, I cannot use the OBJV value from the BAYES method to carry out
> hypothesis testing. The final reported parameter estimates following the
> BAYES method are sensitive to initial starting values and the number of
> iterations performed. If I use the parameter values obtained with the
> BAYES method I can determine an accurate OBJV for those parameter values
> using FOCE with just 1 evaluation. However, if I perform a minimisation
> with FOCE starting with those values, the ETA values collapse and the DV
> vs ipred plot looks awful again.
>
> I hope this makes some sense to someone out there – I’m a bit of a
> novice at NONMEM. I realise the data is far from ideal, but it would be
> great to get some statistical information about the difference between
> the two groups. If anyone had any suggestions I would be grateful. The
> biological interpretation of the experiment will change significantly
> depending on which way this goes!
>
> Thanks
>
> Gavin
>
> __________________________________________________
>
> *Dr Gavin E Jarvis MA PhD VetMB MRCVS*
>
> University Lecturer
>
> Department of Physiology, Development & Neuroscience
>
> Physiological Laboratory
>
> Downing Street
>
> Cambridge
>
> CB2 3EG
>
> Tel: +44 (0) 1223 333745
>
> Email: [email protected] <mailto:[email protected]>