In Pharmacokinetic (PK) studies, inference is made on the absorption, distribution, metabolism and excretion (ADME) of an externally administered compound within the body. This is done by measuring the concentration of the compound in some form of bodily tissue (such as whole blood or plasma) at a number of time points after administration. There are two approaches to PK analysis, modelling and non-compartmental (NCA). The modelling approach uses assumptions of the behaviour of the compound in the body to fit models to the data in order to approximate the concentration versus time curve. Whereas in NCA, no such assumptions are made, and numerical methods are used to approximate this curve. The PK behaviour is summarised by PK parameters that are derived from this approximation, such as the area under the curve (AUC), the maximum concentration (Cmax) and the time at which this maximum occurs (tmax).
In this thesis, three separate topics in the area of PK studies are explored. The first two are motivated by the new blood sampling method of microsampling, which requires a smaller sample volume than traditionally used. Firstly, a methodology is introduced for comparing microsampling to traditional sampling using the derived PK parameters from PK modelling, to find evidence of equivalence of the two sampling methods. The next topic establishes an algorithm for choosing an optimal sparse sampling scheme for PK studies that use microsampling using NCA, developing a two-stage procedure that minimizes bias and variance of the PK parameter estimates. The final topic concerns how PK analysis can be conducted when some measurements are too low to be reliably detected, again using NCA. Seven methods are explored, with the introduced method of using kernel density estimation to impute values onto censored responses using an iterative procedure showing.