Classical and Bayesian approaches to compartment models based on in vivo cadmium data

Four-compartment models in the form of a system of linear differential equations, associated with in vivo cadmium data, have been constructed to describe a particular biological phenomenon of cadmium metabolism in the human body. Since it is quite technically expensive to make in vivo measurements and also difficult to collect data over a period of a decade, the data analyzed in this paper are quite precious, and in fact, one of very few such existing data sets in the area of cadmium research. Cadmium researchers are very much interested in drawing as much information as possible from these data. Methods are developed here for deriving the expectation functions and for using them to analyze this special data set. The parameter estimation for compartment models discussed next uses classical as well as Bayesian approaches. This is the first time that a whole system of the human body is analyzed simultaneously, instead of discussing each compartment separately with a large number of assumptions from different sources on Kjellstrِmʹs model, without any additional assumption on the derived compartment models. The results, obtained from these statistical approaches on simple as well as more direct mathematical models, are not only interpretable very reasonably in terms of biological phenomena, but also reveal interesting patterns and show a great consistency with previous studies.