Some families of optimal and efficient repeated measurements designs

Optimal Designs for Carry Over Effects the Case of Two Treatment and Four Periods

The optimal cross-over experimental designs are derived in experiments with two treatments, four periods, and an experimental unit. The results are given for the values n = 0mod4, 1mod4, 2mod4 and 3mod4. The criterion being the minimization of the variance of the estimated carry over effect.

Optimal Repeated Measurements for Two Treatment Designs with Dependent Observations: The Case of Compound Symmetry

In this paper, we construct optimal repeated measurement designs of two treatments for estimating direct effects, and we examine the case of compound symmetry dependency. We present the model and the design that minimizes the variance of the estimated difference of the two treatments. The optimal designs with dependent observations in a compound symmetry model are the same as in the case of independent observations.

Optimal and efficient crossover designs under different assumptions about the carryover effects

In certain studies it is desirable or necessary that a subject, such as a patient in a medical trial, receive a treatment in each period. This facilitates a within-subject comparison of the treatments. Designs for studies of this type are called crossover designs or repeated measurements designs. If there are s subjects in p periods, the design should specify which of the t treatments is assigned to subject j in period i, i = 1,... ,p,j = 1,..., s. Equivalently we may think of a design as assigning each subject to one of the t(p) possible treatment sequences. The choice of a design will clearly depend on the values of p, s, and t, to which we will refer as the design parameters. But for any set of design parameters, we will typically still have many design choices. To distinguish between different designs for the same design parameters, we will compare the designs under criteria that are related to the objective of the study. Often the objective is a comparison of the treatments, and we would choose a design that, in some sense, provides good estimates of the treatment differences. For these criteria, a design that is optimal under one statistical model may not be optimal under another. It is therefore also of interest to identify designs that are efficient (relative to an optimal design) for more than one model. The main difference in the models that we will consider is in how the possible first-order carryover effects are modeled. This is a controversial issue, and it is by no means our intent to resolve this here. But a design that is efficient under a variety of plausible models is preferable to one that performs well under one model but poorly under another. Our main focus will be on two models. One of these models has been considered extensively in the literature, while the other is relatively new. For selected design parameters, we will compare selected designs under these models.

Regulatory affairs in biotechnology: optimal statistical designs for biomedical experiments

One of the major issues in all applications of biotechnology is how to regulate the process through which new technological information is produced. The end products of biotechnological applications are diverse (e.g., better drugs, better interventions, better fertilizers). Such applications should be properly regulated to obtain valid scientific findings in the most efficient way possible. Some statistically optimal designs are more popularly employed than others as regulatory tools in medical, pharmaceutical and clinical trials. The statistical and practical properties (strengths and weaknesses) are presented to better appreciate their optimality. Recent developments on some related issues are also reviewed.

Multi-period crossover trials

This paper presents a review of crossover designs for use in medical applications which have three or more treatment periods. Only outcomes which can be analysed as continuous variables are considered. Designs which purport to allow for carryover effects are reviewed in detail, as are methods for analysing data collected in such trials. In practice, it is often possible to eliminate carryover by interposing sufficiently long 'washout' periods between successive treatments, and suitable designs for this case are also mentioned. Much current practice revolves around a model which has been widely criticized: the shortcomings of this model and the implications of possible remedies, for design as well as analysis, are discussed.