Application of ridge regression for improved estimation of parameters in compartmental models

Ridge regression is a technique of fitting parametric models to the data arising from scientific experiments. A standard method of achieving this is the least squares technique. In ridge regression, the least square criterion is augmented by a penalty term which penalizes the parameter estimates which are too different from some specified value. Finding out the optimal value for the ridge parameter in a given problem is of great importance because desirable properties of the parameter estimates crucially depend on this choice.;The subject of this work is the application of ridge regression to a particular class of compartmental models and the design of good strategies for determination of ridge parameter. In this work attention has been devoted to the radiotracer models arising from the kinetic analysis of data obtained from Positron Emission Tomography (PET) studies. These are compartmental models describing the uptake and metabolism of the radiotracers injected in subject's body during a PET study. Currently nonlinear least squares (NLS) technique is used for the parameter estimation. This work has applied ridge regression, which is usually used for linear models, to this area of nonlinear models. Extensive simulation studies with different radiotracer models have shown that one particular strategy of Ridge regression has a great potential to improve upon NLS. Accurate estimation of parameters of these models are of great interest to the doctors dealing with nuclear medicine because that information is valuable for understanding of complex biochemical processes inside both normal and pathological tissues.;The main contribution of this work is the extension of an existing methodology like ridge regression to the area of estimation of parameters of an important class of nonlinear models. In context of nuclear medicine, integration of this methodology with the existing ones might prove to be very useful in diagnosis of diseases and clinical management of patients.