Continual reassessment method for partial ordering

Summary Much of the statistical methodology underlying the experimental design of phase 1 trials in oncology is intended for studies involving a single cytotoxic agent. The goal of these studies is to estimate the maximally tolerated dose, the highest dose that can be administered with an acceptable level of toxicity. A fundamental assumption of these methods is monotonicity of the dose–toxicity curve. This is a reasonable assumption for single‐agent trials in which the administration of greater doses of the agent can be expected to produce dose‐limiting toxicities in increasing proportions of patients. When studying multiple agents, the assumption may not hold because the ordering of the toxicity probabilities could possibly be unknown for several of the available drug combinations. At the same time, some of the orderings are known and so we describe the whole situation as that of a partial ordering. In this article, we propose a new two‐dimensional dose‐finding method for multiple‐agent trials that simplifies to the continual reassessment method (CRM), introduced by O'Quigley, Pepe, and Fisher (1990, Biometrics 46 , 33–48), when the ordering is fully known. This design enables us to relax the assumption of a monotonic dose–toxicity curve. We compare our approach and some simulation results to a CRM design in which the ordering is known as well as to other suggestions for partial orders.     

Utility‐Based Optimization of Combination Therapy Using Ordinal Toxicity and Efficacy in Phase I/II Trials

Summary An outcome‐adaptive Bayesian design is proposed for choosing the optimal dose pair of a chemotherapeutic agent and a biological agent used in combination in a phase I/II clinical trial. Patient outcome is characterized as a vector of two ordinal variables accounting for toxicity and treatment efficacy. A generalization of the Aranda‐Ordaz model (1981, Biometrika 68 , 357–363) is used for the marginal outcome probabilities as functions of a dose pair, and a Gaussian copula is assumed to obtain joint distributions. Numerical utilities of all elementary patient outcomes, allowing the possibility that efficacy is inevaluable due to severe toxicity, are obtained using an elicitation method aimed to establish consensus among the physicians planning the trial. For each successive patient cohort, a dose pair is chosen to maximize the posterior mean utility. The method is illustrated by a trial in bladder cancer, including simulation studies of the method's sensitivity to prior parameters, the numerical utilities, correlation between the outcomes, sample size, cohort size, and starting dose pair.     

Risk‐Group‐Specific Dose Finding Based on an Average Toxicity Score

Summary We propose a Bayesian dose‐finding design that accounts for two important factors, the severity of toxicity and heterogeneity in patients' susceptibility to toxicity. We consider toxicity outcomes with various levels of severity and define appropriate scores for these severity levels. We then use a multinomial‐likelihood function and a Dirichlet prior to model the probabilities of these toxicity scores at each dose, and characterize the overall toxicity using an average toxicity score (ATS) parameter. To address the issue of heterogeneity in patients' susceptibility to toxicity, we categorize patients into different risk groups based on their susceptibility. A Bayesian isotonic transformation is applied to induce an order‐restricted posterior inference on the ATS. We demonstrate the performance of the proposed dose‐finding design using simulations based on a clinical trial in multiple myeloma.     

Cancer phase I trial design using drug combinations when a fraction of dose limiting toxicities is attributable to one or more agents

Drug combination trials are increasingly common nowadays in clinical research. However, very few methods have been developed to consider toxicity attributions in the dose escalation process. We are motivated by a trial in which the clinician is able to identify certain toxicities that can be attributed to one of the agents. We present a Bayesian adaptive design in which toxicity attributions are modeled via copula regression and the maximum tolerated dose (MTD) curve is estimated as a function of model parameters. The dose escalation algorithm uses cohorts of two patients, following the continual reassessment method (CRM) scheme, where at each stage of the trial, we search for the dose of one agent given the current dose of the other agent. The performance of the design is studied by evaluating its operating characteristics when the underlying model is either correctly specified or misspecified. We show that this method can be extended to accommodate discrete dose combinations.     

A Hierarchical Bayesian Design for Phase I Trials of Novel Combinations of Cancer Therapeutic Agents

Summary We propose a hierarchical model for the probability of dose‐limiting toxicity (DLT) for combinations of doses of two therapeutic agents. We apply this model to an adaptive Bayesian trial algorithm whose goal is to identify combinations with DLT rates close to a prespecified target rate. We describe methods for generating prior distributions for the parameters in our model from a basic set of information elicited from clinical investigators. We survey the performance of our algorithm in a series of simulations of a hypothetical trial that examines combinations of four doses of two agents. We also compare the performance of our approach to two existing methods and assess the sensitivity of our approach to the chosen prior distribution.     

Ethical Considerations for Outcome‐adaptive Trial Designs: A Clinical Researcher's Perspective

In a typical comparative clinical trial the randomization scheme is fixed at the beginning of the study, and maintained throughout the course of the trial. A number of researchers have championed a randomized trial design referred to as ‘outcome‐adaptive randomization.’ In this type of trial, the likelihood of a patient being enrolled to a particular arm of the study increases or decreases as preliminary information becomes available suggesting that treatment may be superior or inferior. While the design merits of outcome‐adaptive trials have been debated, little attention has been paid to significant ethical concerns that arise in the conduct of such studies. These include loss of equipoise, lack of processes for adequate informed consent, and inequalities inherent in the research design which could lead to perceptions of injustice that may have negative implications for patients and the research enterprise. This article examines the ethical difficulties inherent in outcome‐adaptive trials.     

Assessment of Male Rodent Fertility in General Toxicology 6‐Month Studies

An outcome and statistical review of male reproductive performance assessed by including a mating phase within 6‐month general toxicity studies in the Han Wistar rat was undertaken. The basic study design was 16–20 animals per group dosed for approximately 9 weeks before pairing the male rats with undosed females. This design provides opportunity for remating and automatically includes general toxicity parameters. The dose levels used in the 1‐ and 6‐month studies show that male reproduction was assessed at generally similar doses. The majority of males (compound‐dosed and controls) mated within 7 days. All vehicle‐dosed males mated and 98.5% of these females were pregnant. Modeling shows that a pregnancy rate of less than 14 out of 16 pregnant animals is very unlikely to occur due to biological variability. Power calculations based on vehicle control data show that group sizes of >10 males have a >80% power of detecting a decrease in median of three embryos per group compared with the control group. Even if the number of pregnancies decreased by a third, a group size of ≥12 would still detect a decrement in the median of three embryos with >80% power. Based on the statistical modeling and inherent strengths of the study design, this review indicates that decrements in male reproductive function can be successfully detected by incorporating a mating phase into a 6‐month rat study and that a group size of 12–16 is generally adequate rather than the 16–20 group size indicated as a generic default within ICHS5(R2).     

A Bootstrap Procedure for Adaptive Selection of the Test Statistic in Flexible Two‐Stage Designs

Adaptive two‐stage designs allow a data‐driven change of design characteristics during the ongoing trial. One of the available options is an adaptive choice of the test statistic for the second stage of the trial based on the results of the interim analysis. Since there is often only a vague knowledge of the distribution shape of the primary endpoint in the planning phase of a study, a change of the test statistic may then be considered if the data indicate that the assumptions underlying the initial choice of the test are not correct. Collings and Hamilton proposed a bootstrap method for the estimation of the power of the two‐sample Wilcoxon test for shift alternatives. We use this approach for the selection of the test statistic. By means of a simulation study, we show that the gain in terms of power may be considerable when the initial assumption about the underlying distribution was wrong, whereas the loss is relatively small when in the first instance the optimal test statistic was chosen. The results also hold true for comparison with a one‐stage design. Application of the method is illustrated by a clinical trial example.     

Toxicity of bryostatin‐1 on the embryo‐fetal development of Sprague‐Dawley rats

BACKGROUND: Bryostatin‐1, a highly oxygenated marine macrolide with a unique polyacetate backbone isolated from the marine animal Bugula neritina (Linnaeus), is now being developed as an anti‐cancer drug for treating malignancy. In the present study, developmental toxicity of bryostatin‐1 was evaluated in Sprague–Dawley rats. METHODS: Bryostatin‐1 was intravenously administered to rats on gestation days 6–15 at 4.0, 8.0, and 16.0 µg/kg on a daily basis. Then the reproductive parameters were determined in animals, and fetuses were examined for external, visceral, and skeletal malformations. RESULTS: The total weight gains were significantly different in animals between the control group and 8.0 and 16.0 µg/kg bryostatin‐1 groups during and after treatment. The resorption and death fetus rates were significantly different between the bryostatin‐1 group (16 µg/kg) and the control group. The fetal weight and fetal crown‐rump length in the bryostatin‐1 groups were significantly lower than that in the control group. CONCLUSIONS: Our results indicated that maternal toxicity occurred when the dose of bryostatin‐1 was at 8.0 µg/kg, embryotoxicity at 16.0 µg/kg, and fetotoxicity at 4.0 µg/kg; but bryostatin‐1 showed no teratogenic effect in rats. In light of our findings, bryostatin‐1 should be used with caution in pregnant women with cancer, if they would like to continue the pregnancy. Birth Defects Res (Part B) 89:171–174, 2010. © 2010 Wiley‐Liss, Inc.     

Multiple Comparisons of Treatments with Stable Multivariate Tests in a Two‐Stage Adaptive Design,Including a Test for Non‐Inferiority

The application of stabilized multivariate tests is demonstrated in the analysis of a two‐stage adaptive clinical trial with three treatment arms. Due to the clinical problem, the multiple comparisons include tests of superiority as well as a test for non‐inferiority, where non‐inferiority is (because of missing absolute tolerance limits) expressed as linear contrast of the three treatments. Special emphasis is paid to the combination of the three sources of multiplicity – multiple endpoints, multiple treatments, and two stages of the adaptive design. Particularly, the adaptation after the first stage comprises a change of the a‐priori order of hypotheses.     

Adaptive decision making in a lymphocyte infusion trial

We describe an adaptive Bayesian design for a clinical trial of an experimental treatment for patients with hematologic malignancies who initially received an allogeneic bone marrow transplant but subsequently suffered a disease recurrence. Treatment consists of up to two courses of targeted immunotherapy followed by allogeneic donor lymphocyte infusion. The immunotherapy is a necessary precursor to the lymphocyte infusion, but it may cause severe liver toxicity and is certain to cause a low white blood cell count and low platelets. The primary scientific goal is to determine the infusion time that has the highest probability of treatment success, defined as the event that the patient does not suffer severe toxicity and is alive with recovered white blood cell count 50 days from the start of therapy. The method is based on a parametric model accounting for toxicity, time to white blood cell recovery, and survival time. The design includes an algorithm for between-patient immunotherapy dose de-escalation based on the toxicity data and an adaptive randomization among five possible infusion times according to their most recent posterior success probabilities. A simulation study shows that the design reliably selects the best infusion time while randomizing greater proportions of patients to superior infusion times.     

Response Adaptive Designs with a Variance‐penalized Criterion

We consider a response adaptive design of clinical trials with a variance‐penalized criterion. It is shown that this criterion evaluates the performance of a response adaptive design based on both the number of patients assigned to the better treatment and the power of the statistical test. A new proportion of treatment allocation is proposed and the doubly biased coin procedure is used to target the proposed proportion. Under reasonable assumptions, the proposed design is demonstrated to generate an asymptotic variance of allocation proportions, which is smaller than that of the drop‐the‐loser design. Simulation comparisons of the proposed design with some existing designs are presented.     

Solvent selection and optimization of α‐chymotrypsin‐catalyzed synthesis of N‐Ac‐Phe‐Tyr‐NH2 using mixture design and response surface methodology

A peptide, N‐Ac‐Phe‐Tyr‐NH₂, with angiotensin I‐converting enzyme (ACE) inhibitor activity was synthesized by an α‐chymotrypsin‐catalyzed condensation reaction of N‐acetyl phenylalanine ethyl ester (N‐Ac‐Phe‐OEt) and tyrosinamide (Tyr‐NH₂). Three kinds of solvents: a Tris–HCl buffer (80 mM, pH 9.0), dimethylsulfoxide (DMSO), and acetonitrile were employed in this study. The optimum reaction solvent component was determined by simplex centroid mixture design. The synthesis efficiency was enhanced in an organic‐aqueous solvent (Tris‐HCl buffer: DMSO: acetonitrile = 2:1:1) in which 73.55% of the yield of N‐Ac‐Phe‐Tyr‐NH₂ could be achieved. Furthermore, the effect of reaction parameters on the yield was evaluated by response surface methodology (RSM) using a central composite rotatable design (CCRD). Based on a ridge max analysis, the optimum condition for this peptide synthesis included a reaction time of 7.4 min, a reaction temperature of 28.1°C, an enzyme activity of 98.9 U, and a substrate molar ratio (Phe:Tyr) of 1:2.8. The predicted and the actual (experimental) yields were 87.6 and 85.5%, respectively. The experimental design and RSM performed well in the optimization of synthesis of N‐Ac‐Phe‐Tyr‐NH₂, so it is expected to be an effective method for obtaining a good yield of enzymatic peptide. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Solar‐Light‐Driven CO2 Reduction by CH4 on Silica‐Cluster‐Modified Ni Nanocrystals with a High Solar‐to‐Fuel Efficiency and Excellent Durability

Catalytic CO₂ reforming of CH₄ (CRM) to produce syngas (H₂ and CO) provides a promising approach to reducing global CO₂ emissions and the extensive utilization of natural gas resources. However, the rapid deactivation of the reported catalysts due to severe carbon deposition at high reaction temperatures and the large energy consumption of the process hinder its industrial application. Here, a method for almost completely preventing carbon deposition is reported by modifying the surface of Ni nanocrystals with silica clusters. The obtained catalyst exhibits excellent durability for CRM with almost no carbon deposition and deactivation after reaction for 700 h. Very importantly, it is found that CRM on the catalyst can be driven by focused solar light, thus providing a promising new approach to the conversion of renewable solar energy to fuel due to the highly endothermic characteristics of CRM. The reaction yields high production rates of H₂ and CO (17.1 and 19.9 mmol min^?1 g^?1, respectively) with a very high solar‐to‐fuel efficiency (η, 12.5%). Even under focused IR irradiation with a wavelength above 830 nm, the η of the catalyst remains as high as 3.1%. The highly efficient catalytic activity arises from the efficient solar‐light‐driven thermocatalytic CRM enhanced by a novel photoactivation effect.     

A systems‐based approach to investigate dose‐ and time‐dependent methylmercury‐induced gene expression response in C57BL/6 mouse embryos undergoing neurulation

BACKGROUND: Aberrations during neurulation due to genetic and/or environmental factors underlie a variety of adverse developmental outcomes, including neural tube defects (NTDs). Methylmercury (MeHg) is a developmental neurotoxicant and teratogen that perturbs a wide range of biological processes/pathways in animal models, including those involved in early gestation (e.g., cell cycle, cell differentiation). Yet, the relationship between these MeHg‐linked effects and changes in gestational development remains unresolved. Specifically, current information lacks mechanistic comparisons across dose or time for MeHg exposure during neurulation. These detailed investigations are crucial for identifying sensitive indicators of toxicity and for risk assessment applications. METHODS: Using a systems‐based toxicogenomic approach, we examined dose‐ and time‐dependent effects of MeHg on gene expression in C57BL/6 mouse embryos during cranial neural tube closure, assessing for significantly altered genes and associated Gene Ontology (GO) biological processes. Using the GO‐based application GO‐Quant, we quantitatively assessed dose‐ and time‐dependent effects on gene expression within enriched GO biological processes impacted by MeHg. RESULTS: We observed MeHg to significantly alter expression of 883 genes, including several genes (e.g., Vangl2, Celsr1, Ptk7, Twist, Tcf7) previously characterized to be crucial for neural tube development. Significantly altered genes were associated with development cell adhesion, cell cycle, and cell differentiation–related GO biological processes. CONCLUSIONS: Our results suggest that MeHg‐induced impacts within these biological processes during gestational development may underlie MeHg‐induced teratogenic and neurodevelopmental toxicity outcomes. Birth Defects Res (Part B) 89:188–200, 2010. © 2010 Wiley‐Liss, Inc.     

Blinded and unblinded sample size reestimation procedures for stepped‐wedge cluster randomized trials

The ability to accurately estimate the sample size required by a stepped‐wedge (SW) cluster randomized trial (CRT) routinely depends upon the specification of several nuisance parameters. If these parameters are misspecified, the trial could be overpowered, leading to increased cost, or underpowered, enhancing the likelihood of a false negative. We address this issue here for cross‐sectional SW‐CRTs, analyzed with a particular linear‐mixed model, by proposing methods for blinded and unblinded sample size reestimation (SSRE). First, blinded estimators for the variance parameters of a SW‐CRT analyzed using the Hussey and Hughes model are derived. Following this, procedures for blinded and unblinded SSRE after any time period in a SW‐CRT are detailed. The performance of these procedures is then examined and contrasted using two example trial design scenarios. We find that if the two key variance parameters were underspecified by 50%, the SSRE procedures were able to increase power over the conventional SW‐CRT design by up to 41%, resulting in an empirical power above the desired level. Thus, though there are practical issues to consider, the performance of the procedures means researchers should consider incorporating SSRE in to future SW‐CRTs.     

Dose–Response Effects of Diphenylhydantoin on Pregnant Dams and Embryo‐Fetal Development in Rats

Despite the widespread use of diphenylhydantoin (DPH), there is a lack of reliable information on the teratogenic effects, correlation with maternal and developmental toxicity, and dose–response relationship of DPH. This study investigated the dose–response effects of DPH on pregnant dams and embryo‐fetal development as well as the relationship between maternal and developmental toxicity. DPHwas orally administered to pregnant rats from gestational days 6 through 15 at 0, 50, 150, and 300 mg/kg/day. At 300 mg/kg, maternal toxicity including increased clinical signs, suppressed body weight, decreased food intake, and increased weights of adrenal glands, liver, kidneys, and brain were observed in dams. Developmental toxicity, including a decrease in fetal and placental weights, increased incidence of morphological alterations, and a delay in fetal ossification delay also occurred. At 150 mg/kg, maternal toxicity manifested as an increased incidence of clinical signs, reduced body weight gain and food intake, and increased weights of adrenal glands and brain. Only minimal developmental toxicity, including decreased placental weight and an increased incidence of visceral and skeletal variations, was observed. No treatment‐related maternal or developmental effects were observed at 50 mg/kg. These results show that DPH is minimally embryotoxic at a minimal maternotoxic dose (150 mg/kg/day) but is embryotoxic and teratogenic at an overt maternotoxic dose (300 mg/kg/day). Under these experimental conditions, the no‐observed‐adverse‐effect level of DPH for pregnant dams and embryo‐fetal development is considered to be 50 mg/kg/day. These data indicate that DPH is not a selective developmental toxicant in the rat.     

Dose-finding with two agents in Phase I oncology trials

We propose an adaptive two-stage Bayesian design for finding one or more acceptable dose combinations of two cytotoxic agents used together in a Phase I clinical trial. The method requires that each of the two agents has been studied previously as a single agent, which is almost invariably the case in practice. A parametric model is assumed for the probability of toxicity as a function of the two doses. Informative priors for parameters characterizing the single-agent toxicity probability curves are either elicited from the physician(s) planning the trial or obtained from historical data, and vague priors are assumed for parameters characterizing two-agent interactions. A method for eliciting the single-agent parameter priors is described. The design is applied to a trial of gemcitabine and cyclophosphamide, and a simulation study is presented.     

High‐throughput downstream process development for cell‐based products using aqueous two‐phase systems (ATPS) – A case study

The availability of preparative‐scale downstream processing strategies for cell‐based products presents a critical juncture between fundamental research and clinical development. Aqueous two‐phase systems (ATPS) present a gentle, scalable, label‐free, and cost‐effective method for cell purification, and are thus a promising tool for downstream processing of cell‐based therapeutics. Here, the application of a previously developed robotic screening platform that enables high‐throughput cell partitioning analysis in ATPS is reported. In the present case study a purification strategy for two model cell lines based on high‐throughput screening (HTS)‐data and countercurrent distribution (CCD)‐modeling, and validated the CCD‐model experimentally is designed. The obtained data are shown an excellent congruence between CCD‐model and experimental data, indicating that CCD‐models in combination with HTS‐data are a powerful tool in downstream process development. Finally, the authors are shown that while cell cycle phase significantly influences cell partitioning, cell type specific differences in surface properties are the main driving force in charge‐dependent separation of HL‐60 and L929 cells. In order to design a highly robust purification process it is, however, advisable to maintain constant growth conditions.