ABSTRACT
This paper discusses the problem of determining optimal designs for regression models, when the observations are dependent and taken on an interval. A complete solution of this challenging optimal design problem is given for a broad class of regression models and covariance kernels. We propose a class of estimators which are only slightly more complicated than the ordinary least-squares estimators. We then demonstrate that we can design the experiments, such that asymptotically the new estimators achieve the same precision as the best linear unbiased estimator computed for the whole trajectory of the process. As a by-product we derive explicit expressions for the BLUE in the continuous time model and analytic expressions for the optimal designs in a wide class of regression models. We also demonstrate that for a finite number of observations the precision of the proposed procedure, which includes the estimator and design, is very close to the best achievable. The results are illustrated on a few numerical examples.
ABSTRACT
The three fixed effects estimators of a treatment,difference are compared under conditions of random enrollment in a multicenter clinical trial. These comparisons are performed by assuming five different enrollment schemes. The estimators are compared via simulation using their expected mean squared errors. Unlike previous discussions of these three estimators, we take explicit account of the effect of centers that fail to enroll patients to one or both treatment arms. Within each center, we assume enrollment follows a Poisson process and consider the two situations in which the mean rate of this process is the same in every center and in which the mean rates are sampled from a gamma distribution. The effect of patient dropout is studied as well as the effect of increasing the number of centers. Simulations show that for many sound scenarios, the simpler estimator corresponding to the simplest model works better, even for the cases when data are generated by more complex models.
