Efficient Crossover Designs Research Articles

Algorithm-Based Optimal and Efficient Exact Experimental Designs for Crossover and Interference Models

The crossover models and interference models are frequently used in clinical trials, agriculture studies, social studies, etc. While some theoretical optimality results are available, it is still challenging to apply these results in practice. The available theoretical results, due to the complexity of exact optimal designs, typically require some specific combinations of the number of treatments (t), periods (p), and subjects (n). A more flexible method is to build integer programming based on theories in approximate design theory, which can handle general cases of $(t,p,n)$. Nonetheless, those results are generally derived for specific models or design problems and new efforts are needed for new problems. These obstacles make the application of the theoretical results rather difficult. Here we propose a new algorithm, a revision of the optimal weight exchange algorithm by [1]. It provides efficient crossover designs quickly under various situations, for different optimality criteria, different parameters of interest, different configurations of $(t,p,n)$, as well as arbitrary dropout scenarios. To facilitate the usage of our algorithm, the corresponding R package and an R Shiny app as a more user-friendly interface has been developed.

Optimal and/or Efficient Cross-Over Designs Balanced for Carry-Over of Active Treatments

Optimal and/or Efficient Cross-Over Designs Balanced for Carry-Over of Active Treatments

Efficient crossover designs for non-regular settings

Crossover designs are called for in situations when several subjects undergo a sequence of treatments. Though, usually, the model contains the direct effects of treatments as well as the carryover effects, the primary interest lies in the estimation of direct effects of the treatment. Most results in the literature on crossover designs are available for the situations where either the number of periods or the number of subjects is a multiple of the number of treatments. In this article, we consider crossover designs for the non-regular settings, that is, the situations when the number of treatments divides neither the number of periods nor the number of subjects. We provide a construction method to obtain highly E-efficient crossover designs for non-regular settings, while also providing a crude lower bound to E-efficiency of the designs constructed through our construction method. In a table, we provide E-efficiencies of a constructed design for the number of treatments up to 10 and the number of subjects up to 50.

Optimal and/or efficient three treatment crossover designs for five carryover models

ABSTRACTThe additional benefits in the analysis of crossover designs with two active treatments and a placebo motivated us to study these kinds of designs. These designs have been studied through a computer search algorithm, called 5M balanced algorithm, in two to four periods for different number of units, which resulted in optimal and/or efficient crossover designs. The new two periods crossover designs having two active treatments and a placebo, enables the estimation of treatment contrasts, unlike the classic two treatments two periods crossover which fails to estimate the treatment contrasts under self and mixed carryover model. The crossover designs having three or four periods in two active treatments and a placebo, estimate treatment contrasts more efficiently under self and mixed carryover model than the usual two treatments crossover designs. An exhaustive list of optimal and/or efficient crossover designs has been provided for designs in two periods having 6–21 subjects, three periods having 3–20 subjects and four periods having 3–14 subjects. In this list, 35 new designs are optimal for one of the established carryover models and 26 new designs are optimal and/or efficient to all four plausible carryover models.

Optimal and/or Efficient Two treatment Crossover Designs for Five Carryover Models.

Crossover designs robust to changes in carryover models are useful in clinical trials where the nature of carryover effects is not known in advance. The designs have been characterized for being optimal and efficient under no carryover-, traditional-, and, self and mixed carryover- models, however, ignoring the number of subjects, which has significant impact on both optimality and administrative convenience. In this article, adding two more practical models, the traditional, and, self and mixed carryover models having carryover effect only for the new or test treatment, a 5M algorithm is presented. The 5M algorithm based computer code searches all possible two treatment crossover designs under the five carryover models and list those which are optimal and /or efficient to all the five carryover models. The resultant exhaustive list consists of optimal and/or efficient crossover designs in two, three, and four periods, having 4 to 20 subjects of which 24 designs are new optimal for one of the established carryover models, and 34 designs are optimal for newly added models.

Efficient crossover designs in the presence of interactions between direct and carry-over treatment effects

Crossover designs, or repeated measurements designs, are used for experiments in which t treatments are applied to each of n experimental units successively over p time periods. Such experiments are widely used in areas such as clinical trials, experimental psychology and agricultural field trials. In addition to the direct effect on the response of the treatment in the period of application, there is also the possible presence of a residual, or carry-over, effect of a treatment from one or more previous periods. We use a model in which the residual effect from a treatment depends upon the treatment applied in the succeeding period; that is, a model which includes interactions between the treatment direct and residual effects. We assume that residual effects do not persist further than one succeeding period. A particular class of strongly balanced repeated measurements designs with n= t 2 units and which are uniform on the periods is examined. A lower bound for the A-efficiency of the designs for estimating the direct effects is derived and it is shown that such designs are highly efficient for any number of periods p=2,…,2 t.

Optimal and efficient crossover designs for comparing test treatments to a control treatment under various models

We study the optimality, efficiency, and robustness of crossover designs for comparing several test treatments to a control treatment. Since A-optimality is a natural criterion in this context, we establish lower bounds for the trace of the inverse of the information matrix for the test treatments versus control comparisons under various models. These bounds are then used to obtain lower bounds for efficiencies of a design under these models. Two algorithms, both guided by these efficiencies and results from optimal design theory, are proposed for obtaining efficient designs under the various models.

CONSTRUCTION OF CROSSOVER DESIGNS WITH CORRELATED ERRORS

SummaryCrossover experiments are widely used, particularly where a sequence of treatments is given to subjects. Correlations between observations on the same subject are therefore likely and should be considered in both the design and analysis of crossover experiments. This paper presents an algorithm for the generation of efficient crossover designs with autoregressive and linear variance structures. The algorithm has been implemented as a module in the experimental design generation package CycDesigN (Release 3.0; CycSoftware, Hamilton, New Zealand). Output from the algorithm is compared with earlier work. Some results are given from the analysis of a crossover experiment assuming correlated errors.

Efficient crossover designs for comparing test treatments with a control treatment

Within a large family of crossover designs this paper characterizes the mathematical structures of A-optimal and A-efficient crossover designs for the purpose of statistical comparison between t experimental treatments with a control (standard) treatment. It further guides the user how to go about the construction of these designs and if needed doing the last minute modifications. To demonstrate the ideas some very interesting optimal and efficient small designs are constructed. The mathematical and statistical tools developed here could be very useful in other areas of design of experiments. Many interesting and not yet solved design problems for further research are implicitly stated throughout the paper.

Efficient crossover designs for comparing test treatments with a control treatment when [formula omitted

Efficient crossover designs for comparing t test treatments to one control treatment with three periods is considered. Through this investigation and the characterization obtained for the A-optimal/efficient designs in the nearly entire class, the efficiency of a given design is evaluated and guidance for constructing highly efficient designs is provided.

Optimal and efficient crossover designs for comparing test treatments with a control treatment

This paper deals exclusively with crossover designs for the purpose of comparing t test treatments with a control treatment when the number of periods is no larger than t+1. Among other results it specifies sufficient conditions for a crossover design to be simultaneously A-optimal and MV-optimal in a very large and appealing class of crossover designs. It is expected that these optimal designs are highly efficient in the entire class of crossover designs. Some computationally useful tools are given and used to build assorted small optimal and efficient crossover designs. The model robustness of these newly discovered crossover designs is discussed.

CrossOver: an algorithm for the construction of efficient cross-over designs.

A cross-over experiment involves the application of sequences of treatments to several subjects over a number of time periods. It is thought that the observation made on each subject at the end of a time period may depend on the direct effect of the treatment applied in the current period, and the carry-over effects of the treatments applied in one or more previous periods. Various models have been proposed to explain the nature of the carry-over effects. An experimental design that is optimal under one model may not be optimal if a different model is the appropriate one. In this paper an algorithm is described to construct efficient cross-over designs for a range of models that involve the direct effects of the treatments and various functions of their carry-over effects. The effectiveness and flexibility of the algorithm are demonstrated by assessing its performance against numerous designs and models given in the literature.

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 ssubjects in pperiods, the design should specify which of the ttreatments is assigned to subject jin 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.

Efficient cross-over designs allowing a check on the assumption that direct and carry-over effects do not interact

In cross-over experiments, each subject receives a sequence of treatments, one in each of a number of consecutive time periods, and a response is measured at the end of each period. Traditional models for these experiments assume that the direct effect of the treatment applied in the current period and the carry¬over effect of the treatment applied in the previous period act additively on the response. Recently, models involving directxcarry-over interaction have been considered and universally optimal designs for investigating such an interaction have been presented. However, these designs require large numbers of subjects and time periods, and such resources are not always available. This paper presents construction methods for designs that permit a test of the interaction, but which require a small number of subjects and periods. The best designs obtained by these methods are given. The designs are also optimal or near-optimal in the absence of directxcarry-over interaction.