No abstract

The concepts of D-, A-and E-minimax optimality criteria of designs for estimating the slopes of a response surface are considered for situations where the region of interest may not be identical to the experimental region. Optimal second-order designs are derived for the situation where the experimental region and the region of interest are both hyperspherical with a common centre. The dependence of the optimal design on the relative sizes of the regions is investigated. Further, the perfomance of designs optimal for one region in estimating slopes in other regions is also examined.

In any longitudinal study, a dropout before the final timepoint can rarely be avoided. The chosen dropout model is commonly one of these types: Missing Completely at Random (MCAR), Missing at Random (MAR), Missing Not at Random (MNAR), and Shared Parameter (SP). In this paper we estimate the parameters of the longitudinal model for simulated data and real data using the Linear Mixed Effect (LME) method. We investigate the consequences of misspecifying the missingness mechanism by deriving the so-called least false values. These are the values the parameter estimates converge to, when the assumptions may be wrong. The knowledge of the least false values allows us to conduct a sensitivity analysis, which is illustrated. This method provides an alternative to a local misspecification sensitivity procedure, which has been developed for likelihood-based analysis. We compare the results obtained by the method proposed with the results found by using the local misspecification method. We apply the local misspecification and least false methods to estimate the bias and sensitivity of parameter estimates for a clinical trial example.