RE: posthoc step

From: "Kowalski, Ken" Ken.Kowalski@pfizer.com Subject: RE: [NMusers] posthoc step Date: Wed, December 8, 2004 9:05 am Marc, NMusers, I agree with your comments. I was not suggesting that the number of observations is the only factor that determines the amount of shrinkage. When OMEGA>>SIGMA, MAP Bayes will have less shrinkage even with sparse data but there will still be some shrinkage. The degree of shrinkage will also be influenced by the design (times at which samples are taken). For example with sparse PK during a steady state dosing interval following oral administration, there is more shrinkage for the ETAs on ka and V/F than there is for CL/F since we often don't have rich information during the absorption phase and V/F is better estimated during non-steady-state conditions. So, with sparse data, depending on the placement of the time points, there can still be a fair amount of shrinkage in one or more of the ETAki. I don't think you were implying this but just to be clear, the IPREDs can fit the observations very well under sparse conditions even when there is significant shrinkage in one or more of the individual parameter estimates. With sparse data (e.g., fewer observations than number of parameters) if we fit the individual model using WLS we will have over-parameterization as the estimates will not be unique in that we can have an infinite set of solutions that will result in essentially the same minimum value of the WLS objective function. MAP Bayes estimates on the other hand, although they shrink the estimates to mean (perhaps some parameters more than others) will be unique. A simple exercise one can do to assess the degree of shrinkage is to calculate the sample variance for ETAki and compare that to the estimate of OMEGAk from the population model fit. The sample variance should be smaller and the greater the discrepancy the more shrinkage there is. Ken