Methods of parameter estimation for nonlinear models have generally been based on appropriate least squares procedures. The authors have presented previously, for the one compartment open model, a marginal likelihood approach which obviates some of the difhcuhies encountered in the nonlinear least squares technique. This note is a consideration of the model when a time lag is present in the system. The calculation procedure is discussed in detail and applied to a set of pharmacokinetic data.
MODEL
The usual one compartment open model Cc = (Ak,/(k, -k.J)(evkzf -eeklt)
[II describes the concentration of substance in a compartment at time t with incoming and outgoing flow rates of k, and $, respectively. This model assumes that movement of material begins at t = 0 but it is sometimes desirable to incorporate a lag time (to) into the model to allow for some delay at the beginning of the process. Such a situation would pertain to ingestion of a drug capsule, for example, where there may be some appreciable delay before the absorption of the drug commences. The model now becomes C, = (&/(k, -k2))(e-kN-b) -e-kl(t-to)). VI Estimation of the parameters in this model by a least squares procedure involves successive iterations relying on linear approximations to [2] until some convergence criteria are met. The accuracy of the estimates and the rate of convergence depend on the goodness of fit of the model to the observed data.