Optimal design for inference on the threshold of a biomarker

Enrichment designs with a continuous biomarker require the estimation of a threshold to determine the subpopulation benefitting from the treatment. This article provides the optimal allocation for inference in a two-stage enrichment design for treatment comparisons when a continuous biomarker is suspected to affect patient response. Several design criteria, associated with different trial objectives, are optimized under balanced or Neyman allocation and under equality of the first two empirical biomarker's moments. Moreover, we propose a new covariate-adaptive randomization procedure that converges to the optimum with the fastest available rate. Theoretical and simulation results show that this strategy improves the efficiency of a two-stage enrichment clinical trial, especially with smaller sample sizes and under heterogeneous responses.

New insights into adaptive enrichment designs

The transition towards personalized medicine is happening and the new experimental framework is raising several challenges, from a clinical, ethical, logistical, regulatory, and statistical perspective. To face these challenges, innovative study designs with increasing complexity have been proposed. In particular, adaptive enrichment designs are becoming more attractive for their flexibility. However, these procedures rely on an increasing number of parameters that are unknown at the planning stage of the clinical trial, so the study design requires particular care. This review is dedicated to adaptive enrichment studies with a focus on design aspects. While many papers deal with methods for the analysis, the sample size determination and the optimal allocation problem have been overlooked. We discuss the multiple aspects involved in adaptive enrichment designs that contribute to their advantages and disadvantages. The decision-making process of whether or not it is worth enriching should be driven by clinical and ethical considerations as well as scientific and statistical concerns.

Simulated annealing for balancing covariates

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.

A new inferential approach for response-adaptive clinical trials: the variance-stabilized bootstrap

This paper discusses disadvantages and limitations of the available inferential approaches in sequential clinical trials for treatment comparisons managed via response-adaptive randomization. Then, we propose an inferential methodology for response-adaptive designs which, by exploiting a variance stabilizing transformation into a bootstrap framework, is able to overcome the above-mentioned drawbacks, regardless of the chosen allocation procedure as well as the desired target. We derive the theoretical properties of the suggested proposal, showing its superiority with respect to likelihood, randomization and design-based inferential approaches. Several illustrative examples and simulation studies are provided in order to confirm the relevance of our results.

Optimal and ethical designs for hypothesis testing in multi-arm exponential trials

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.

Compound optimal allocations for survival clinical trials

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.

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.

Choosing a covariate-adaptive randomization procedure in practice

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.

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.

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

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.

Sleep quality and motor vehicle crashes in adolescents

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.