From Thu Aug 17 10:06:40 1995
Subject: determination of Cmax and formulation effects

Hello NONMEM users,

I have been using NONMEM to determine the relative bioavailability of two different formulations in a population mode. Essentially what was done was to collect all phase I studies in which either or both formulations of interest were administered and then compare that information to a standard two-way cross-over study (n=24). Then 90% confidence intervals were determined for the point estimate of relative F. Advan 4, trans 3 was utilized.

Now it is of interest to determine a population estimate of Cmax for each formulation and also calculate a 90% confidence interval. Since Tmax and hence Cmax cannot be determined explicitly, can anyone suggest a sequence of code that can implicitly solve for these two terms so that a theta for formulation can be added and a 90% CI constructed.

thank you in advance for your suggestions

Gary Maier


From lewis Sat Aug 19 13:14:58 1995
Subject: Re: determination of Cmax and formulation effects

Explicitly parameterizing in the population parameters of interest is one way to go, and you may be able to come up with the desired code. Another way to go is to use a bootstrap approach, which might prove simpler intellectually, although more costly of computer time.

The ML estimates of CMAX abd TMAX are simply the solutions (which you can obtain numerically) for TMAX and the CMAX using the model equations and the population parameters determined from your NONMEM run. So, getting point estimates is no problem; it is estimating the variability that is the problem.

Assuming that your meta-analysis included K studies, with n(k) individuals in the kth study, the simplest Bootstrap approach to getting variability estimates that I can think of off the top of my head (that seems to make sense) would be to proceed according to the following algorithm, or something like it.

For m = 1 to M do:
For k = 1 to K do:
For j = 1 to n(k) do:
sample another individuals' data (with replacement) from the
individuals of study k, and add this individual to the mth
simulation of study k
Analyse the (mth) simulated set of K studies with NONMEM according to your model; compute the ML estimates of CMAX and TMAX, as above.
Population average CMAX and TMAX = average of M estiamates from the simulated data set analyses;
Std error of each is the SD of the M estimates;
95% confidence interval for each is the estimate values delineating the central 95% of the M separate estimates; etc.
One usually chooses M at about 1000. If standard errors are all you want, then M = a few hundred might work.

Good luck,