Identifiability of random effects parameters in mixed effects models In-Sun Nam Knutsson and Leon Aarons School of Pharmacy and Pharmaceutical Sciences The University of Manchester Manchester, U.K. Structural identifiability deals with the ability to uniquely identify parameters given perfect data. A model is said to be globally identifiable if only one set of parameters uniquely describes a perfect set of data. On the other hand if a finite number of sets of parameters reproduce identical input-output behaviour for a model it is said to be locally identifiable. The best known example in pharmacokinetics is the flip-flop behaviour of the one compartment first order absorption model whereby two sets of parameters give exactly the same model prediction. Finally a model is said to be unidentifiable if certain parameters can take on an infinite set of values. Again the best known pharmacokinetic example is the one compartment first order absorption model, whereby only the ratios CL/F and V/F can be identified but the individual parameters can take any value that gives the correct quotient. There is an extensive literature, particularly in the engineering field, that deals with the identifiability of fixed effects models, for example nonlinear regression models for single subject data. On the other hand there is nothing in the literature – that we can find – that deals with random effects parameters in a mixed effects model, such as a population PK model. We have investigated the one compartment first order absorption mixed effects model. From simulation it appears that whereas the PK structural parameters obey the same rules as those for the fixed effects model, for particular covariance structures the random effects parameters appear to be identifiable when the fixed effects parameters are not. This talk will describe our attempt to understand this problem and we have derived some preliminary results. It is very much a work in progress and we are looking for some feedback.
