Maroussa Zagoraiou

Balance and randomness in sequential clinical trials: the dominant biased coin design.

Efrons biased coin design (BCD) is a well-known randomization technique that helps neutralize selection bias, while keeping the experiment fairly balanced for every sample size. Several extensions of this rule have been proposed, and their properties were analyzed from an asymptotic viewpoint and compared via simulations in a finite setup. The aim of this paper is to push forward these comparisons by taking also into account the adjustable BCD, which is never considered up to now. Firstly, we show that the adjustable BCD performs better than Efrons coin with respect to both loss of precision and randomness. Moreover, the adjustable BCD is always more balanced than the other coins and, only for some sample sizes, slightly more predictable. Therefore, we suggest the dominant BCD, namely a new and flexible class of procedures that can change the allocation rule step by step in order to ensure very good performance in terms of both balance and selection bias for any sample size. Our simulations demonstrate that the dominant BCD is more balanced and, at the same time, less or equally predictable than Atkinsons optimum BCD.

Covariate Adjusted Designs for Combining Efficiency, Ethics and Randomness in Normal Response Trials

This paper deals with the problem of allocating patients to two competing treatments in the presence of covariates in order to achieve a good trade-off between efficiency, ethical concern and randomization. We propose a compound criterion that combines inferential precision and ethical gain by flexible weights depending on the unknown treatment effects. In the absence of treatment-covariate interactions, this criterion leads to a locally optimal allocation which does not depend on the covariates and can be targeted by a suitable implementation of the doubly-adaptive biased coin design aimed at balancing the roles of randomization, ethics and information. Some properties of the suggested procedure are described.

On the almost sure convergence of adaptive allocation procedures

In this paper, we provide some general convergence results for adaptive designs for treatment comparison, both in the absence and presence of covariates. In particular, we demonstrate the almost sure convergence of the treatment allocation proportion for a vast class of adaptive procedures, also including designs that have not been formally investigated but mainly explored through simulations, such as Atkinsons optimum biased coin design, Pocock and Simons minimization method and some of its generalizations. Even if the large majority of the proposals in the literature rely on continuous allocation rules, our results allow to prove via a unique mathematical framework the convergence of adaptive allocation methods based on both continuous and discontinuous randomization functions. Although several examples of earlier works are included in order to enhance the applicability, our approach provides substantial insight for future suggestions, especially in the absence of a prefixed target and for designs characterized by sequences of allocation rules.

Computer Simulations for the Optimization of Technological Processes

This chapter is about experiments for quality improvement and the innovation of products and processes performed by computer simulation. It describes familiar methods for creating surrogate models of simulators (emulators), with particular reference to Kriging interpolation, and some new ways of fitting the models to the simulated data.

Is the classical Wald test always suitable under response-adaptive randomization?

The aim of this paper is to analyze the impact of response-adaptive randomization rules for normal response trials intended to test the superiority of one of two available treatments. Taking into account the classical Wald test, we show how response-adaptive methodology could induce a consistent loss of inferential precision. Then, we suggest a modified version of the Wald test which, by using the current allocation proportion to the treatments as a consistent estimator of the target, avoids some degenerate scenarios and so it should be preferable to the classical test. Furthermore, we show both analytically and via simulations how some target allocations may induce a locally decreasing power function. Thus, we derive the conditions on the target guaranteeing its monotonicity and we show how a correct choice of the initial sample size allows one to overcome this drawback regardless of the adopted target.

Choosing a covariate-adaptive randomization procedure in practice

ABSTRACT Pocock and Simon’s minimization method is a very popular covariate-adaptive randomization procedure intended to balance the allocations of two treatments across a set of covariates without compromising randomness. Additional covariate-adaptive schemes have been proposed in the literature, such as Atkinson’s -optimum Biased Coin Design and the Covariate-Adaptive Biased Coin Design (CA-BCD), and their properties were analyzed and compared in terms of imbalance and predictability. The aim of this paper is to push forward these comparisons by also taking into account other randomization methods, such as the Permuted Block Design, the Big Stick Design, a generalization of the CA-BCD that can be implemented when the covariate distribution is unknown, and the Covariate-Adaptive Dominant Biased Coin Design, which is a new class of stratified randomization methods that forces the balance increasingly as the joint imbalance grows and improves the degree of randomness as the size of every stratum increases. The performance of covariate-adaptive procedures is strictly related to the considered factors and the number of patients in the trial as well, which makes it hard to find a dominant rule, namely a design that is more balanced and less predictable with respect to other schemes. In general, stratified randomization methods perform very well when the number of strata is small, showing also some dominance structure with respect to the other designs. Nevertheless, the evolution and the performance of stratified designs are strictly related to the random entries of the subjects. Thus, these rules become less efficient in the case of both (i) limited samples and (ii) large number of factors/levels.

Exact optimum coin bias in Efron's randomization procedure

Efrons biased coin design is a restricted randomization procedure that has very favorable balancing properties, yet it is fully randomized, in that subjects are always randomized to one of two treatments with a probability less than 1. The parameter of interest is the bias p of the coin, which can range from 0.5 to 1. In this note, we propose a compound optimization strategy that selects p based on a subjected weighting of the relative importance of the two fundamental criteria of interest for restricted randomization mechanisms, namely balance between the treatment assignments and allocation randomness. We use exact and asymptotic distributional properties of Efrons coin to find the optimal p under compound criteria involving imbalance variability, expected imbalance, selection bias, and accidental bias, for both small/moderate trials and large samples.

Optimal designs for testing hypothesis in multiarm clinical trials

The present paper deals with the problem of designing randomized multiarm clinical trials for treatment comparisons in order to achieve a suitable trade-off among inferential precision and ethical concerns. Although the large majority of the literature is focused on the estimation of the treatment effects, in particular for the case of two treatments with binary outcomes, the present paper takes into account the inferential goal of maximizing the power of statistical tests to detect correct conclusions about the treatment effects for normally response trials. After discussing the allocation optimizing the power of the classical multivariate test of homogeneity, we suggest a multipurpose design methodology, based on constrained optimization, which maximizes the power of the test under a suitable ethical constraint reflecting the effectiveness of the treatments. The ensuing optimal allocation depends in general on the unknown model parameters but, contrary to the unconstrained optimal solution or to some targets proposed in the literature, it is a non-degenerate continuous function of the treatment contrasts, and therefore it can be approached by standard response-adaptive randomization procedures. The properties of this constrained optimal allocation are described both theoretically and through suitable examples, showing good performances both in terms of ethical gain and statistical efficiency, taking into account estimation precision as well.

Efficient statistical sample designs in a GIS for monitoring the landscape changes

The process of land planning, addressed to operate the synthesis between development aims and appropriate policies of preservation and management of territorial resources, requires a detailed analysis of the territory carried out by making use of data stored in Geographic Information Systems (GISs). A detailed analysis of changes in the landscape is time consuming, thus it can be carried out only on a sample of the whole territory and an efficient procedure is needed for selecting a sample of area units. In this paper we apply two recently proposed sample selection procedures to a study area for comparing them in terms of efficiency as well as of operational advantages, in order to set up a methodology which enables an efficient estimate of the change in the main landscape features on wide areas.

Space filling and locally optimal designs for Gaussian Universal Kriging

Computer simulations are often used to replace physical experiments aimed at exploring the complex relationships between input and output variables. Undoubtedly, computer experiments have several advantages over real ones, however, when the response function is complex, simulation runs may be very expensive and/or time-consuming, and a possible solution consists of approximating the simulator by a suitable stochastic metamodel, simpler and much faster to run. Several metamodel techniques have been suggested in the literature and one of the most popular is the Kriging methodology. In this paperwe study the optimal design problem for the Universal Kriging metamodel with respect to different approaches, related to prediction, information gain and estimation. Also we give further justifications and some criticism concerning the adoption of the space filling designs, based on theoretical results and numerical evidence as well.