Uncertainty directed factorial clinical trials.

The development and evaluation of novel treatment combinations is a key component of modern clinical research. The primary goals of factorial clinical trials of treatment combinations range from the estimation of intervention-specific effects, or the discovery of potential synergies, to the identification of combinations with the highest response probabilities. Most factorial studies use balanced or block randomization, with an equal number of patients assigned to each treatment combination, irrespective of the specific goals of the trial. Here, we introduce a class of Bayesian response-adaptive designs for factorial clinical trials with binary outcomes. The study design was developed using Bayesian decision-theoretic arguments and adapts the randomization probabilities to treatment combinations during the enrollment period based on the available data. Our approach enables the investigator to specify a utility function representative of the aims of the trial, and the Bayesian response-adaptive randomization algorithm aims to maximize this utility function. We considered several utility functions and factorial designs tailored to them. Then, we conducted a comparative simulation study to illustrate relevant differences of key operating characteristics across the resulting designs. We also investigated the asymptotic behavior of the proposed adaptive designs. We also used data summaries from three recent factorial trials in perioperative care, smoking cessation, and infectious disease prevention to define realistic simulation scenarios and illustrate advantages of the introduced trial designs compared to other study designs.

Optimum designs for clinical trials in personalized medicine when response variance depends on treatment.

We study optimal designs for clinical trials when the value of the response and its variance depend on treatment and covariates are included in the response model. Such designs are generalizations of Neyman allocation, commonly used in personalized medicine when external factors may have differing effects on the response depending on subgroups of patients. We develop theoretical results for D-, A-, E- and D A-optimal designs and construct semidefinite programming (SDP) formulations that support their numerical computation. D-, A-, and E-optimal designs are appropriate for efficient estimation of distinct properties of the parameters of the response models. Our formulation allows finding optimal allocation schemes for a general number of treatments and of covariates. Finally, we study frequentist sequential clinical trial allocation within contexts where response parameters and their respective variances remain unknown. We illustrate, with a simulated example and with a redesigned clinical trial on the treatment of neuro-degenerative disease, that both theoretical and SDP results, derived under the assumption of known variances, converge asymptotically to allocations obtained through the sequential scheme. Procedures to use static and sequential allocation are proposed.

Two-stage designs with small sample sizes.

When applying group-sequential designs in clinical trials with normally distributed outcomes, approximate critical values are often applied. Here, normally distributed test statistics are assumed which, however, are in fact t-distributed. For small sample sizes, the approximation may lead to a serious inflation of the type I error rate. Recently, a method for computing the exact critical boundaries assuring type I error rate control was proposed and the critical boundaries for Pocock- and O'Brien-Fleming-like group-sequential designs were provided. For designs with one interim analysis, we present six alternative designs, which also control the type I error rate and in addition allow flexible design modifications. We compare the characteristics of these 6 two-stage designs. It is shown that considerable sample size savings can be achieved by including futility stopping and by optimizing the designs. Therefore, for clinical trials with small sample sizes as, for example, in the area of rare diseases, optimal two-stage designs with futility stopping may be a valuable alternative to classical group-sequential designs.

An Overview of Adaptive Designs and Some of Their Challenges, Benefits, and Innovative Applications.

Adaptive designs are increasingly developed and used to improve all phases of clinical trials and in biomedical studies in various ways to address different statistical issues. We first present an overview of adaptive designs and note their numerous advantages over traditional clinical trials. In particular, we provide a concrete demonstration that shows how recent adaptive design strategies can further improve an adaptive trial implemented 13 years ago. Despite their usefulness, adaptive designs are still not widely implemented in clinical trials. We offer a few possible reasons and propose some ways to use them more broadly in practice, which include greater availability of software tools and interactive websites to generate optimal adaptive trials freely and effectively, including the use of metaheuristics to facilitate the search for an efficient trial design. To this end, we present several web-based tools for finding various adaptive and nonadaptive optimal designs and discuss nature-inspired metaheuristics. Metaheuristics are assumptions-free general purpose optimization algorithms widely used in computer science and engineering to tackle all kinds of challenging optimization problems, and their use in designing clinical trials is just emerging. We describe a few recent such applications and some of their capabilities for designing various complex trials. Particle swarm optimization is an exemplary nature-inspired algorithm, and similar to others, it has a simple definition but many moving parts, making it hard to study its properties analytically. We investigated one of its hitherto unstudied issues on how to bring back out-of-range candidates during the search for the optimum of the search domain and show that different strategies can impact the success and time of the search. We conclude with a few caveats on the use of metaheuristics for a successful search.

Optimal designs of LID based on LID experiments and SWMM for a small-scale community in Tianjin, north China.

Urban flooding and waterlogging are becoming increasingly serious due to rapid urbanization and climate change. The stormwater management philosophy of low-impact development (LID) has been applied in urban construction to alleviate these problems. The selection and placement of LID designs are the most important tasks. In this study, LID experiments were performed to calibrate the Storm Water Management Model (SWMM). Then, a multi-objective optimization model, which adopted the minimum surface runoff coefficient, surcharge time, and investment cost as objectives, was established by coupling the SWMM and non-dominated sorting genetic algorithm-II (NSGA-II). Hydrological simulations were performed with the SWMM, and optimal calculations were conducted with NSGA-II. Real-coded optimal variables containing detailed size and location information of multiple LID measures were generated, and a decision space for LID design selection was obtained. The optimization designs reduced the surface runoff coefficient from 0.7 to approximately 0.5, the conduit surcharge duration was reduced from 1.62 h to 0.04-0.47 h, and the total investment cost only ranged from 395,000-872,000 ¥. Thus, the optimization model could achieve synchronous optimization of all objectives. This study could provide valuable information for LID design with the aim of urban flooding and waterlogging control.

Optimization of sampling designs for pedigrees and association studies.

In many studies, related individuals are phenotyped in order to infer how their genotype contributes to their phenotype, through the estimation of parameters such as breeding values or locus effects. When it is not possible to phenotype all the individuals, it is important to properly sample the population to improve the precision of the statistical analysis. This article studies how to optimize such sampling designs for pedigrees and association studies. Two sampling methods are developed, stratified sampling and D optimality. It is found that it is important to take account of mutation when sampling pedigrees with many generations: as the size of mutation effects increases, optimized designs sample more individuals in late generations. Optimized designs for association studies tend to improve the joint estimation of breeding values and locus effects, all the more as sample size is low and the genetic architecture of the trait is simple. When the trait is determined by few loci, they are reminiscent of classical experimental designs for regression models and tend to select homozygous individuals. When the trait is determined by many loci, locus effects may be difficult to estimate, even if an optimized design is used.

An Effective Method to Model and Simulate the Behavior of Inductive Angle Encoders.

Many angle or position sensors rank among the inductive encoders, although their sensing principle is different. The sensor design investigated in this paper is based on coupled coils, whereas the information about the position angle is modulated on the induced voltage, measured at the receiving coils. Unfortunately, no closed solution for most of the physical quantities exists, since this principle is based on eddy currents, which are rather complex to calculate for the given geometry. Consequently, the common way is to calculate the sensor quantities by a 3D finite-element (FE) simulation. However, this leads in most cases to a high time and computational effort. To overcome the limitations with respect to computational resources, a novel method is presented to reduce simulation effort and calculate regression models, which can even replace simulations. In the following investigations, D-optimal designs are used-a subdomain in the field of statistical design of experiments-and combined with a numerical implementation of Faraday's law, in order to calculate the induced voltages afterwards from simulated magnetic field data. With this method, the sensor signals can be calculated for multiple angle positions from one simulated position by shifting the integration boundaries. Hence, simulation time is significantly reduced for a full period. The regression models obtained by this method, can predict the Tx-coil inductance, induced Rx-voltage amplitude and angular error in dependency of geometric design parameters.

Optimal designs for discrete-time survival models with random effects.

This paper considers the optimal design for the frailty model with discrete-time survival endpoints in longitudinal studies. We introduce the random effects into the discrete hazard models to account for the heterogeneity between experimental subjects, which causes the observations of the same subject at the sequential time points being correlated. We propose a general design method to collect the survival endpoints as inexpensively and efficiently as possible. A cost-based generalized D ([Formula: see text])-optimal design criterion is proposed to derive the optimal designs for estimating the fixed effects with cost constraint. Different computation strategies based on grid search or particle swarm optimization (PSO) algorithm are provided to obtain generalized D ([Formula: see text])-optimal designs. The equivalence theorem for the cost-based D ([Formula: see text])-optimal design criterion is given to verify the optimality of the designs. Our numerical results indicate that the presence of the random effects has a great influence on the optimal designs. Some useful suggestions are also put forward for future designing longitudinal studies.

Design and analysis of bridging studies with prior probabilities on the null and alternative hypotheses.

The pharmaceutical industry and regulatory agencies are increasingly interested in conducting bridging studies in order to bring an approved drug product from the original region (eg, United States or European Union) to a new region (eg, Asian-Pacific countries). In this article, we provide a new methodology for the design and analysis of bridging studies by assuming prior knowledge on how the null and alternative hypotheses in the original, foreign study are related to the null and alternative hypotheses in the bridging study and setting the type I error for the bridging study according to the strength of the foreign-study evidence. The new methodology accounts for randomness in the foreign-study evidence and controls the average type I error of the bridging study over all possibilities of the foreign-study evidence. In addition, the new methodology increases statistical power, when compared to approaches that do not use foreign-study evidence, and it allows for the possibility of not conducting the bridging study when the foreign-study evidence is unfavorable. Finally, we conducted extensive simulation studies to demonstrate the usefulness of the proposed methodology.

Two-stage optimal designs based on exact variance for a single-arm trial with survival endpoints.

Sample size calculation based on normal approximations is often associated with the loss of statistical power for a single-arm trial with a time-to-event endpoint. Recently, Wu (2015) derived the exact variance for the one-sample log-rank test under the alternative and showed that a single-arm one-stage study based on exact variance often has power above the nominal level while the type I error rate is controlled. We extend this approach to a single-arm two-stage design by using exact variances of the one-sample log-rank test for the first stage and the two stages combined. The empirical power of the proposed two-stage optimal designs is often not guaranteed under a two-stage design setting, which could be due to the asymptotic bi-variate normal distribution used to estimate the joint distribution of the test statistics. We adjust the nominal power level in the design search to guarantee the simulated power of the identified optimal design being above the nominal level. The sample size and the study time savings of the proposed two-stage designs are substantial as compared to the one-stage design.

Locally optimal designs for some binary dose-response models.

In this paper, we consider the problem of seeking locally optimal designs for nonlinear dose-response models with binary outcomes. Applying the theory of Tchebycheff Systems and other algebraic tools, we show that the locally D-, A-, and c-optimal designs for three binary dose-response models are minimally supported in finite, closed design intervals. The methods to obtain such designs are presented along with examples. The efficiencies of these designs are also discussed.

OPTIMAL DESIGNS FOR SPLINE WAVELET REGRESSION MODELS.

In this article we investigate the optimal design problem for some wavelet regression models. Wavelets are very flexible in modeling complex relations, and optimal designs are appealing as a means of increasing the experimental precision. In contrast to the designs for the Haar wavelet regression model (Herzberg and Traves 1994; Oyet and Wiens 2000), the I-optimal designs we construct are different from the D-optimal designs. We also obtain c-optimal designs. Optimal (D- and I-) quadratic spline wavelet designs are constructed, both analytically and numerically. A case study shows that a significant saving of resources may be realized by employing an optimal design. We also construct model robust designs, to address response misspecification arising from fitting an incomplete set of wavelets.

Using blocked fractional factorial designs to construct discrete choice experiments for healthcare studies.

Discrete choice experiments (DCEs) are increasingly used for studying and quantifying subjects preferences in a wide variety of healthcare applications. They provide a rich source of data to assess real-life decision-making processes, which involve trade-offs between desirable characteristics pertaining to health and healthcare and identification of key attributes affecting healthcare. The choice of the design for a DCE is critical because it determines which attributes' effects and their interactions are identifiable. We apply blocked fractional factorial designs to construct DCEs and address some identification issues by utilizing the known structure of blocked fractional factorial designs. Our design techniques can be applied to several situations including DCEs where attributes have different number of levels. We demonstrate our design methodology using two healthcare studies to evaluate (i) asthma patients' preferences for symptom-based outcome measures and (ii) patient preference for breast screening services. Copyright © 2016 John Wiley & Sons, Ltd.

Optimal designs for a multiresponse Emax model and efficient parameter estimation.

The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach, and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations, etc. In this paper, we assume fixed N and consider estimation approaches and study designs for multiresponse dose finding studies. We work with diabetes dose-response data and compare a system estimation approach that fits a multiresponse Emax model to the data to equation-by-equation estimation that fits uniresponse Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi- and uniresponse Emax model and study the efficiency of these designs.

Discrete choice experiments: An overview on constructing D-optimal and near-optimal choice sets.

Discrete choice experiments (DCEs) are frequently used to estimate and forecast the behavior of an individual's choice. DCEs are based on stated preference; therefore, underlying experimental designs are required for this type of study. According to psychologists, DCE designs consist of a small number of choice sets with a limited size in the number of alternatives within a choice set to increase the response efficiency in the questionnaire. Even though algorithmic constructions (known as efficient designs) become quite common for practitioners, optimal designs (sometimes so-called orthogonal designs) continue to be used in choice experiment studies, particularly in the case that prior information about the extent of the population preference is not available. Various approaches have been developed to construct DCE designs with fewer choice sets. However, the question in many practitioners' minds is which techniques perform better (i.e. given small designs with high efficiency) in a given circumstance. In this paper and to address these concerns, we conducted an overview of the constructions of discrete choice experiments in the literature for models with only main effects. The various ways of constructing optimal and near-optimal designs were compared in terms of their ability to minimize the number of choice sets in the survey. Our findings shed light on the optimal sample sizes needed for efficient experimentation which then can help the researchers to design more effective experiments in this area.

Holistic Design of Experiments Using an Integrated Process Model.

Statistical experimental designs such as factorial, optimal, or definitive screening designs represent the state of the art in biopharmaceutical process characterization. However, such methods alone do not leverage the fact that processes operate as a mutual interplay of multiple steps. Instead, they aim to investigate only one process step at a time. Here, we want to develop a new experimental design method that seeks to gain information about final product quality, placing the right type of run at the right unit operation. This is done by minimizing the simulated out-of-specification rate of an integrated process model comprised of a chain of regression models that map process parameters to critical quality attributes for each unit operation. Unit operation models are connected by passing their response to the next unit operation model as a load parameter, as is done in real-world manufacturing processes. The proposed holistic DoE (hDoE) method is benchmarked against standard process characterization approaches in a set of in silico simulation studies where data are generated by different ground truth processes to illustrate the validity over a range of scenarios. Results show that the hDoE approach leads to a >50% decrease in experiments, even for simple cases, and, at the same time, achieves the main goal of process development, validation, and manufacturing to consistently deliver product quality.

Optimal two-stage designs based on restricted mean survival time for a single-arm study.

Restricted mean survival time is an alternative measure of treatment effect to hazard ratio in clinical trials with time-to-event outcome. The current methods have been focused on one-stage designs. In this article, we propose optimal two-stage designs for a single-arm study with the smallest expected sample size. We compare the performance of the new optimal two-stage designs with the existing one-stage design with regards to the expected sample size and the expected total study length. The simulation results indicate that the new two-stage designs can save the expected sample size substantially as compared to the one-stage design. We use a non-small cell lung cancer trial to illustrate the application of the proposed designs. The proposed optimal two-stage designs are recommended for use when time for patient accrual is longer than the pre-specified follow-up time.

Pharmacometrics meets statistics-A synergy for modern drug development.

Modern drug development problems are very complex and require integration of various scientific fields. Traditionally, statistical methods have been the primary tool for design and analysis of clinical trials. Increasingly, pharmacometric approaches using physiology-based drug and disease models are applied in this context. In this paper, we show that statistics and pharmacometrics have more in common than what keeps them apart, and collectively, the synergy from these two quantitative disciplines can provide greater advances in clinical research and development, resulting in novel and more effective medicines to patients with medical need.

Dose optimisation with simultaneous pharmacokinetic estimation in adaptive clinical trials.

Determination of the optimal dose is a critical objective in the drug developmental process. An optimal dose prevents over- and under-exposure to the treatment drug thereby facilitating superior patient experience and reduced costs to the healthcare system. In this paper, we present a method for model-based dose optimisation with simultaneous pharmacokinetic estimation of the model parameters. Multiple doses of the drug are considered and the objective is to maintain the blood concentration of the drug around a pre-decided target concentration. We consider an adaptive setting wherein the model parameters are estimated from the blood samples collected at D-optimal time points from all subjects enrolled so far in the trial. The estimated parameters are then used to determine the optimal dose regimen for the next cohort. This procedure continues until the condition of a pre-decided stopping rule is met. Simulation studies and sensitivity analysis are undertaken to validate the methodology. We also evaluate the performance of the methodology when carried out in a non-adaptive setting. A two-stage design is then presented which combines the advantages of the adaptive as well as the non-adaptive approach. We demonstrate that our methodology enables pharmacokinetic estimation and dose regimen optimisation simultaneously in an ethical and cost-effective manner protecting the subjects from the ill-effects of suboptimal dose regimens and economising the number of subjects required in the trial.

Designing dose finding studies with an active control for exponential families.

In a recent paper Dette et al. (2014) introduced optimal design problems for dose finding studies with an active control. These authors concentrated on regression models with normal distributed errors (with known variance) and the problem of determining optimal designs for estimating the smallest dose, which achieves the same treatment effect as the active control. This paper discusses the problem of designing active-controlled dose finding studies from a broader perspective. In particular, we consider a general class of optimality criteria and models arising from an exponential family, which are frequently used analyzing count data. We investigate under which circumstances optimal designs for dose finding studies including a placebo can be used to obtain optimal designs for studies with an active control. Optimal designs are constructed for several situations and the differences arising from different distributional assumptions are investigated in detail. In particular, our results are applicable for constructing optimal experimental designs to analyze active-controlled dose finding studies with discrete data, and we illustrate the efficiency of the new optimal designs with two recent examples from our consulting projects.