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When there is a predictive biomarker, enrichment can focus the clinical trial on a benefiting subpopulation. We describe a two-stage enrichment design, in which the first stage is designed to efficiently estimate a threshold and the second stage is a "phase III-like" trial on the enriched population. The goal of this paper is to explore design issues: sample size in Stages 1 and 2, and re-estimation of the Stage 2 sample size following Stage 1. By treating these as separate trials, we can gain insight into how the predictive nature of the biomarker specifically impacts the sample size. We also show that failure to adequately estimate the threshold can have disastrous consequences in the second stage. While any bivariate model could be used, we assume a continuous outcome and continuous biomarker, described by a bivariate normal model. The correlation coefficient between the outcome and biomarker is the key to understanding the behavior of the design, both for predictive and prognostic biomarkers. Through a series of simulations we illustrate the impact of model misspecification, consequences of poor threshold estimation, and requisite sample sizes that depend on the predictive nature of the biomarker. Such insight should be helpful in understanding and designing enrichment 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.

Most industrial processes are composed of multiple subsequent steps. In this article, we provide a statistical approach to design experiments and to define the manufacturing design space of multi-step processes by taking into account the complex system of interactions among steps. We consider each intermediate outcome as an additional input factor in the next step and we plan experiments following a particular sequential structure. To encompass the potential deviations from the target levels of such input factors, designs are selected according to the D-optimality in average criterion and, in order to assess their prediction capabilities, a suitable extension of the fraction of design space technique has been proposed. The manufacturing design space of the process is then defined by combining the interconnected manufacturing design spaces of the process steps and by deriving the linear combination of the process inputs that ensures the required quality standard for the final outcome. Appealing properties of this approach are also shown by the application to a three-steps biochemical process of expression and purification of a recombinant protein in which 10 input factors are included in the design.

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.

Background: The aim of the study was to compare the prognostic value of histological and endoscopic activity in patients with ulcerative colitis (UC). Methods: Patients in clinical remission for 1 year under treatment with mesalazine underwent a planned colonoscopy with biopsies. Histological activity was scored using the histological activity index (HAI). Endoscopic activity was scored using the Mayo endoscopic subscore (MES). The clinical course was evaluated measuring relapses needing steroids during a follow up of 3 years. Results: A total of 52 patients were enrolled into the study and followed up for 3 years. At baseline 29 patients (55.77%) had no endoscopic lesions, and 17 patients (32.69%) showed no histological alteration. At 3 years of follow up, overall, 26 patients (50%) were still in steroid-free remission. Using univariate logistic regression analysis, both histological (HAI ⩾ 1) and endoscopic activity (MES ⩾ 1) were significantly associated with outcome, showing, respectively, a relapse risk (odds ratio [OR]) 16.4 times higher than histological remission (HAI 0) (96% confidence interval [CI]: 3.2–84.3) and 6.3 times higher with respect to endoscopic remission (MES 0) (96% CI: 1.9–21.3). After multivariate logistic regression analysis, histological activity was the only factor significantly associated with outcome (OR 10.2; 95% CI: 1.7–59.4). Conclusions: Histological activity has the most powerful prognostic value in predicting the need for steroids in patients with UC in stable clinical remission on mesalazine. It could be considered as a target of therapy in UC.