Optimal designs in the presence of missing responses

Design of experiments is an approach that could minimise the costs of conducting experiments by maximising the information that could be obtained from the study prior to the implementation. It is crucial that the experimenters consider the impact of the presence of missing observations on the statistical power of the study and the precision of the inferences. This research incorporates the features of some missing data analysis approaches into the experimental design framework for finding a design that is robust to the presence of missing responses.We propose optimal design framework for the linear regression models and the linear mixed models respectively. Assuming that missing responses are generated by a monotone missing at random (MAR) mechanism, we consider the features of complete case analysis and a multiple imputation respectively in the design framework for the linear regression models, and of available case analysis in the cohort design framework for the linear mixed models.The optimal design framework for the linear regression models with complete case analysis is a generalisation to the work that is proposed by Imhof et al. (2002). Besides that, we believe we are the first who consider a multiple imputation approach at the design stage of an experiment. Moreover, having accounted for the presence of dropouts, we introduce two types of design regime in the cohort design framework for the linear mixed models.Throughout this project we show that using the optimal designs that assume completely observed responses or the naive designs may not be the best option. There are statistical gains in accounting for the features of missing data analysis approaches at the design stage of an experiment, especially for the study that involves a small sample size and high costs. This novel research provides a new tool to tackle the presence of missing data in future experimental studies