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Covariate balance is one of the fundamental issues in designing experiments for treatment comparisons, especially in randomized clinical trials. In this article, we introduce a new class of covariate-adaptive procedures based on the Simulated Annealing algorithm aimed at balancing the allocations of two competing treatments across a set of pre-specified covariates. Due to the nature of the simulated annealing, these designs are intrinsically randomized, thus completely unpredictable, and very flexible: they can manage both quantitative and qualitative factors and be implemented in a static version as well as sequentially. The properties of the suggested proposal are described, showing a significant improvement in terms of covariate balance and inferential accuracy with respect to all the other procedures proposed in the literature. An illustrative example based on real data is also discussed.

The present paper discusses drawbacks and limitations of likelihood-based inference in sequential clinical trials for treatment comparisons managed via Response-Adaptive Randomization. Taking into account the most common statistical models for the primary outcome—namely binary, Poisson, exponential and normal data—we derive the conditions under which (i) the classical confidence intervals degenerate and (ii) the Wald test becomes inconsistent and strongly affected by the nuisance parameters, also displaying a non monotonic power. To overcome these drawbacks, we provide a very simple solution that could preserve the fundamental properties of likelihood-based inference. Several illustrative examples and simulation studies are presented in order to confirm the relevance of our results and provide some practical recommendations.

Multi-arm clinical trials are complex experiments which involve several objectives. The demand for unequal allocations in a multi-treatment context is growing and adaptive designs are being increasingly used in several areas of medical research. For uncensored and censored exponential responses, we propose a constrained optimization approach in order to derive the design maximizing the power of the multivariate test of homogeneity, under a suitable ethical constraint. In the absence of censoring, we obtain a very simple closed-form solution that dominates the balanced design in terms of power and ethics. Our suggestion can also accommodate delayed responses and staggered entries, and can be implemented via response adaptive rules. While other targets proposed in the literature could present an unethical behavior, the suggested optimal allocation is frequently unbalanced by assigning more patients to the best treatment, both in the absence and presence of censoring. We evaluate the operating characteristics of our proposal theoretically and by simulations, also redesigning a real lung cancer trial, showing that the constrained optimal target guarantees very good performances in terms of ethical demands, power and estimation precision. Therefore, it is a valid and useful tool in designing clinical trials, especially oncological trials and clinical experiments for grave and novel infectious diseases, where the ethical concern is of primary importance.

This paper develops a unified framework for deriving optimal designs for hypothesis testing in the presence of several heteroscedastic groups. In particular, the obtained optimal designs are generalized Neyman allocations involving only two experimental groups. In order to account for the ordering among the treatments, particularly relevant in the clinical context for ethical reasons, we provide the optimal design for testing under constraints reflecting their effectiveness. The advantages of the suggested allocations are illustrated both theoretically and through several numerical examples, also compared with other designs proposed in the literature, showing a substantial gain in terms of both power and ethics.

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.

The aim of the present paper is to provide optimal allocations for comparative clinical trials with survival outcomes. The suggested targets are derived adopting a compound optimization strategy based on a subjective weighting of the relative importance of inferential demands and ethical concerns. The ensuing compound optimal targets are continuous functions of the treatment effects, so we provide the conditions under which they can be approached by standard response-adaptive randomization procedures, also guaranteeing the applicability of the classical asymptotic inference. The operating characteristics of the suggested methodology are verified both theoretically and by simulation, including the robustness to model misspecification. With respect to the other available proposals, our strategy always assigns more patients to the best treatment without compromising inference, taking into account estimation efficiency and power as well. We illustrate our procedure by redesigning two real oncological trials.

The aim of this paper is to provide a new design strategy for response adaptive randomization in the case of normal response trials aimed at testing the superiority of one of two available treatments. In particular, we introduce a new test statistic based on the treatment allocation proportion ensuing the adoption of a suitable response adaptive randomization rule that could be more efficient and uniformly more powerful with respect to the classical Wald test. We analyze the conditions under which the suggested strategy, derived by matching an asymptotically best response adaptive procedure and a suitably chosen target allocation, could induce a monotonically increasing power that discriminates with high precision the chosen alternatives. Moreover, we introduce and analyze new classes of targets aimed at maximizing the power of the new statistical test, showing both analytically and via simulations i) how the power function of the suggested test increases as the ethical skew of the chosen target grows, namely overcoming the usual trade-off between ethics and inference, and ii) the substantial gain of inferential precision ensured by the proposed approach.

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 [Formula: see text]-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.

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 Atkinson's optimum biased coin design, Pocock and Simon's 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., Published at http://dx.doi.org/10.3150/13-BEJ591 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

Efron's 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 Efron's 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.

In this paper we provide some general asymptotic properties of covariate-adaptive (CA) randomized designs aimed at balancing the allocations of two treatments across a set of chosen covariates. In particular, we establish the central limit theorem for a vast class of covariate-adaptive procedures characterized by i) a different allocation function for each covariate profile and ii) sequences of allocation rules instead of a pre-fixed one. This result allows one to derive theoretically the asymptotic expressions of the loss of information induced by imbalance and the selection bias due to the lack of randomness, that are the fundamental properties for estimation of every CA rule, widely used in order to compare different CA procedures. Besides providing the proofs of unsolved conjectures about some CA designs suggested in the literature, explored up to now almost exclusively through simulations, our results provide substantial insight for future suggestions and represent an accurate tool for the large sample comparisons between CA designs. A numerical study is also performed to assess the validity of the suggested approach.

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.

The paper describes the main phases and results of a study which is part of a broader research programme aimed at assessing the changes that have occurred in Italian rural landscapes since the Second World War. The research deals with the definition of a methodology suitable for analysing the changes in the rural built environment over wide areas. This methodology focuses on the definition of representative sample areas aimed to reduce survey costs while allowing results to be characterised by a known and provable degree of reliability and precision. Based on the results of a previous work (Tassinari, Carfagna, Benni, & Torreggiani (2008). Biosystems Engineering, 100, 435–447), where the authors defined the first phases of the sampling methodology and surveyed some building-density test variables on a pilot sample, this paper focuses on optimising both the criteria for the stratification of the sampling frame and the estimator used to assess the changes in the built area, as well as testing the method on a super-municipal study area in northern Italy for the 1975–2005 time span. The results contribute new knowledge within the broader field of the analysis and interpretation of trends in rural areas, which is fundamental to support proper land-use and landscape planning through accurate and efficient tools.

Efron's 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 Efron's 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 Atkinson's optimum BCD.

The present paper deals with the problem of allocating patients to two competing treatments in the presence of covariates or prognostic factors in order to achieve a good trade-off among ethical concerns, inferential precision and randomness in the treatment allocations. In particular we suggest a multipurpose design methodology that combines efficiency and ethical gain when the linear homoscedastic model with both treatment/covariate interactions and interactions among covariates is adopted. The ensuing compound optimal allocations of the treatments depend on the covariates and their distribution on the population of interest, as well as on the unknown parameters of the model. Therefore, we introduce the reinforced doubly adaptive biased coin design, namely a general class of covariate-adjusted response-adaptive procedures that includes both continuous and discontinuous randomization functions, aimed to target any desired allocation proportion. The properties of this proposal are described both theoretically and through simulations., Published in at http://dx.doi.org/10.1214/12-AOS1007 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Simulation is a widely used tool to investigate real-world systems in a large number of fields, including clinical trials for drug development, since real trials are costly, frequently fail and may lead to serious side effects. This paper is a survey of the statistical issues arising in these simulated trials, with particular emphasis on the design of such virtual experiments, stressing similarities and differences with the design of real trials. We discuss the aims and peculiarities of the simulation models used in this context, including a brief mention of metamodels, and different validating techniques. We illustrate each specific issue through one or more studies recently reported in the medical and/or pharmaceutical literature. We end the paper with some challenging questions on the scientific rigour, ethics and effectiveness of simulation in clinical research, and the interesting research problem of how to integrate virtual and physical experiments in a clinical context., Statistica; Vol 72, No 1 (2012); 63-80

The process of land planning, addressed to operate the synthesis between development aims and appropriate policies of preservation and management of territorial resources, requires detailed analysis of the territory. Generally this analysis is carried out on the whole area of interest by making use of data stored in Geographic Information Systems (GIS), but a detailed analysis of changes in the landscape can be carried out only on a sample of the whole territory. A very efficient sample design is the adaptive sequential procedure with permanent random numbers (ASPRN) proposed by Carfagna and Marzialetti (2009). However, ASPRN obliges the environmental engineer to jump from one side to another of the study area. Carfagna (2007) proposed a two-steps selection procedure with permanent random numbers (TSPRN) which allows to overcome the operational drawbacks of the ASPRN. In this paper we apply both procedures to a study area, in order to compare them from an operational viewpoint and to set up a methodology which enables an efficient estimate of the change of main landscape features on large areas.

For clinical trials that compare two or more competing treatments, the literature proposes several randomization rules that aim at favouring, at each stage of the trial, the treatment that appears to be best. In two papers the present authors have suggested criteria of optimal allocation that combine inferential precision and ethical gain by means of flexible weights, in order to achieve a good trade-off between efficiency and ethical concerns. The ensuing optimal allocation of the treatments can be targeted by a suitable response- adaptive randomization rule. The purpose of this paper is to illustrate and extend the results previously obtained by the authors to a wider range of statistical models for comparative trials. Methods for implementing these designs are given. Some numerical examples are included in order to enhance the applicability., Statistica; Vol 72, No 4 (2012); 375-393

The present paper deals with sequential designs intended to balance the allocations of two competing treatments in the presence of prognostic factors. After giving a theoretical framework on the optimality of balanced designs that can arise when covariates are taken into account, we propose a new family of covariate-adaptive randomized designs that represents higher order approximation to balance treatments, both globally and also across covariates. We derive the theoretical properties of the suggested designs in terms of loss of precision and predictability. The performance of this proposal is illustrated through a simulation study and compared with those of other procedures suggested in the literature. Copyright 2011, Oxford University Press.

Simulation is widely used to investigate real-world systems in a large number of fields, including clinical trials for drug development, since real trials are costly, frequently fail and may lead to serious side effects. This paper is a survey of the statistical issues arising in these simulated trials. We illustrate the broad applicability of this investigation tool by means of examples selected from the literature. We discuss the aims and the peculiarities of the simulation models used in this context, including a brief mention of the use of metamodels. Of special interest is the topic of the design of the virtual experiments, stressing similarities and differences with the design of real life trials. Since it is important for a computerized model to possess a satisfactory range of accuracy consistent with its intended application, real data provided by physical experiments are used to confirm the simulator : we illustrate validating techniques through a number of examples. We end the paper with some challenging questions on the scientificity, ethics and effectiveness of simulation in the clinical research, and the interesting research problem of how to integrate simulated and physical experiments in a clinical context.

Nowadays it is common to reproduce physical systems using mathematical simulation models and, despite the fact that computing resources continue to increase, computer simulations are growing in complexity. This leads to the adoption of surrogate models and one of the most popular methodologies is the well-known Ordinary Kriging, which is a statistical interpolator extensively used to approximate the output of deterministic simulation. This paper deals with the problem of finding suitable experimental plans for the Ordinary Kriging with exponential correlation structure. In particular, we derive exact optimal designs for prediction, estimation and information gain approaches in the one-dimensional case, giving further theoretical justifications for the adoption of the equidistant design. Moreover, we show that in some circumstances several results related to the uncorrelated setup still hold for correlated observations.

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.

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 consist 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 paper we 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.

This paper deals with optimal designs for Gaussian random fields with constant trend and exponential correlation structure, widely known as the Ornstein–Uhlenbeck process. Assuming the maximum likelihood approach, we study the optimal design problem for the estimation of the trend and the correlation parameter using a criterion based on the Fisher information matrix. For the problem of trend estimation, we give a new proof of the optimality of the equispaced design for any sample size (see Statist. Probab. Lett. 2008; 78:1388–1396). We also show that for the estimation of the correlation parameter, an optimal design does not exist. Furthermore, we show that the optimal strategy for the latter conflicts with the one for the trend, since the equispaced design is the worst solution for estimating the correlation. Hence, when the inferential purpose concerns both the unknown parameters we propose the geometric progression design, namely a flexible class of procedures that allow the experimenter to choose a suitable compromise regarding the estimation’s precision of the two unknown parameters guaranteeing, at the same time, high efficiency for both.

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. It also deals with the advantages of computer experiments performed sequentially, and with computer experiments in which some of the random noise factors that affect the output of a process are simulated stochastically. As an example, an application to the integrated parameter and tolerance design of a high-precision space-measuring instrument is illustrated, and other potential applications are also mentioned.

Study objectives: Sleep-related complaints are common in adolescents, but their impact on the rate of motor vehicle crashes accidents is poorly known. We studied subjective sleep quality, driving habits, and self-reported car crashes in high-school adolescents. Methods: Self-administered questionnaires (with items exploring driving habits) were distributed to 339 students who had a driver's license and attended 1 of 7 high schools in Bologna, Italy. Statistical analysis were performed to describe lifestyle habits, sleep quality, sleepiness, and their relationship with the binary dependent variable (presence or absence of car crashes) to identify the factors significantly affecting the probability of car crashes in a multivariate binary logistic regression model. Results: Nineteen percent of the sample reported bad sleep, 64% complained of daytime sleepiness, and 40% reported sleepiness while driving. Eighty students (24%), 76% of which were males, reported that they had already crashed at least once, and 15% considered sleepiness to have been the main cause of their crash. As compared with adolescents who had not had a crash, those who had at least 1 previous crash reported that they more frequently used to drive (79% vs 62%), drove at night (25% vs 9%), drove while sleepy (56% vs 35%), had bad sleep (29% vs 16%), and used stimulants such as caffeinated soft drinks (32% vs 19%), tobacco (54% vs 27%), and drugs (21% vs 7%). The logistic procedure established a significant predictive role of male sex (p < 0.0001; odds ratio = 3.3), tobacco use (p < 0.0001; odds ratio = 3.2), sleepiness while driving (p = 0.010; odds ratio = 2.1), and bad sleep (p = 0.047; odds ratio = 1.9) for the crash risk. Conclusions: Our results confirm the high prevalence of sleep-related complaints among adolescents and highlight their independent role on self-reported crash risk