Date: Fri, 16 Jul 1999 16:24:59 -0400 (EDT)
Subject: Analysis of sparse data

Dear NM users

We have been encountering a problem with fitting a sparse data set (45 subjects, 77 concentrations) using ADVAN2 TRANS2.

The initial estimates for this study were obtained from the analysis of a rich data set (5 subjects, 45 concentrations). The rich data provided estimates of CL, V and Ka with interind variabilities of 30%, 2% and 70% and a residual var of 13%.

Consequently, we have been trying to fit the sparse data using these estimates but the ETAS for CL and Ka come out to be 0.002% and 175% respectively with a 42% residual variability. The estimates of CL, V and Ka seem to be OK eventhough the variabilites are high. But the Plot of IPRED vs DV shows distinct bias with higher predicted concentrations at the lower end and relatively flat at the higher end of DV. We are using FOCE to analyze the data. WRES vs DV plot also shows a bias (almost like a linear relationship) whereas WRES vs TIME plot shows no bias.

As a result, we are exploring the possibility of joining the two data sets in an effort to obtain decent estimates of the inter and intra variabilities. The estimates have turned out to be reasonable with interindividual variabilites for CL, V and Ka of 40%, 16% and 70% and residual var of 37%. Moreover, the IPRED vs DV plots look much better now.

The question is: Is this approach a viable or a reasonable option? and what are some of the downsides of it?

The sparse data is from patients and the rich from healthy volunteers. The overall goal is to evaluate CL against some covariates such as concomitant medication and other patient related parameters. Healthy versus patients could just be one among them.

Suggestions on alternative approaches are also most welcome.






Date: Mon, 19 Jul 1999 13:04:18 -0700
From: LSheiner <>
Subject: Re: Analysis of sparse data

Joining the data sets (if you think the populations are the same) is the right thing to do. Interindividual variability cannot in general be estimated from data sets unless a significant number of individuals have at least as many observations as there are distinct parameters in the individual model. There has been considerable simulation work verifying this.

In your case, the 2 populations are not necesarily the same (normals vs patients). The estimates you get are then some hybrid of the approriate values

for the 2 populations (which, of course, are not necessarily different, regarding PK).

The only alternative to merging the data sets is using a prior distribution on the popualtion paramters, notably the elements of OMEGA. Unfortunately, the NONMEM feature allowing you to do this conveniently is not part of the currently distributed verion.


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:






From: "Piotrovskij, Vladimir [JanBe]" <>
Subject: RE: Analysis of sparse data
Date: Mon, 2 Aug 1999 13:35:42 +0200

Dear Sriram,
Your problem is quite typical. The two data sets you have, apparently, differ not only in the number of plasma samples per subject and in that they came from distinct populations. Most probably, your rich data set was obtained in a well-controlled Phase I study whereas the sparse data set was from a Phase II or III trial. Hence, the residual error could not be the same. So, when you merge the two data sets you should create an indicator variable to distinguish them and include two ERRs in $ERROR block. To avoid merging you can fix some of PK parameters, particularly, KA to the estimates obtained with the rich data set. As to the random effect parameters (ETAs) I would suggest using the full variance-covariance matrix (the BLOCK option in the $OMEGA block).

Hope this helps,

Vladimir Piotrovsky, Ph.D.
Janssen Research Foundation (5463)
Clinical Pharmacokinetics
B-2340 Beerse