Inference for intraclass correlations and drug interaction studies: fiducial approach and small sample asymptotics

Abstract

This thesis addresses two topics, the first topic is the interval estimation of the intraclass correlation coefficient under two scenarios: a general linear mixed model, and a nonlinear mixed model. The second topic is on the interval estimation of the drug interaction index under two popular models available in the literature: the Loewe additivity model and the Bliss independence model. For solutions to both problems, accurate small sample procedures is a major goal, and the methodologies used are meant to provide confidence intervals that maintain the coverage probabilities in small sample scenarios. The methodologies used include small sample asymptotic procedures and the fiducial approach. The models and the problems investigated are described in detail, followed by a summary of the small sample asymptotic procedures and the fiducial approach. These methodologies are then applied to obtain accurate confidence intervals for the intraclass correlation coefficient and the drug interaction index. Extensive simulation results are provided to assess the performance of the proposed confidence intervals, especially in small samples. The simulation results have demonstrated the accuracy of the proposed solutions. The results are also illustrated with examples.