An interactive tool for designing efficient toxicology experiments.

The design of dose-response experiments is an important part of toxicology research. Efficient design of these experiments requires choosing optimal doses and assigning the correct number of subjects to those doses under a given criterion. Optimal design theory provides the tools to find the most efficient experimental designs in terms of cost and statistical efficiency. However, the mathematical details can be distracting and make these designs inaccessible to many toxicologists. To facilitate use of these designs, we present an easy to use web-app for finding two types of optimal designs for models commonly used in toxicology. We include tools for checking the optimality of a given design and for assessing efficiency of any user-supplied design. Using state-of-the-art nature-inspired metaheuristic algorithms, the web-app allows the user to quickly find optimal designs for estimating model parameters or the benchmark dose.

Mathematical programming tools for randomization purposes in small two-arm clinical trials: A case study with real data.

Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods use mathematical programming to construct attractive clinical trials that balance the group features, such as their sizes and covariate distributions of their subjects. We review some of these methods and compare their performance with common covariate-adaptive randomization methods for small clinical trials. We introduce an energy distance measure that compares the discrepancy between the two groups using the joint distribution of the subjects' covariates. This metric is more appealing than evaluating the discrepancy between the groups using their marginal covariate distributions. Using numerical experiments, we demonstrate the advantages of the mathematical programming methods under the new measure. In the supplementary material, we provide R codes to reproduce our study results and facilitate comparisons of different randomization procedures.

Single-cell generalized trend model (scGTM): a flexible and interpretable model of gene expression trend along cell pseudotime.

MOTIVATION: Modeling single-cell gene expression trends along cell pseudotime is a crucial analysis for exploring biological processes. Most existing methods rely on nonparametric regression models for their flexibility; however, nonparametric models often provide trends too complex to interpret. Other existing methods use interpretable but restrictive models. Since model interpretability and flexibility are both indispensable for understanding biological processes, the single-cell field needs a model that improves the interpretability and largely maintains the flexibility of nonparametric regression models. RESULTS: Here, we propose the single-cell generalized trend model (scGTM) for capturing a gene's expression trend, which may be monotone, hill-shaped or valley-shaped, along cell pseudotime. The scGTM has three advantages: (i) it can capture non-monotonic trends that are easy to interpret, (ii) its parameters are biologically interpretable and trend informative, and (iii) it can flexibly accommodate common distributions for modeling gene expression counts. To tackle the complex optimization problems, we use the particle swarm optimization algorithm to find the constrained maximum likelihood estimates for the scGTM parameters. As an application, we analyze several single-cell gene expression datasets using the scGTM and show that scGTM can capture interpretable gene expression trends along cell pseudotime and reveal molecular insights underlying biological processes. AVAILABILITY AND IMPLEMENTATION: The Python package scGTM is open-access and available at https://github.com/ElvisCuiHan/scGTM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The Future Glioblastoma Clinical Trials Landscape: Early Phase 0, Window of Opportunity, and Adaptive Phase I-III Studies.

PURPOSE OF REVIEW: Innovative clinical trial designs for glioblastoma (GBM) are needed to expedite drug discovery. Phase 0, window of opportunity, and adaptive designs have been proposed, but their advanced methodologies and underlying biostatistics are not widely known. This review summarizes phase 0, window of opportunity, and adaptive phase I-III clinical trial designs in GBM tailored to physicians. RECENT FINDINGS: Phase 0, window of opportunity, and adaptive trials are now being implemented for GBM. These trials can remove ineffective therapies earlier during drug development and improve trial efficiency. There are two ongoing adaptive platform trials: GBM Adaptive Global Innovative Learning Environment (GBM AGILE) and the INdividualized Screening trial of Innovative GBM Therapy (INSIGhT). The future clinical trials landscape in GBM will increasingly involve phase 0, window of opportunity, and adaptive phase I-III studies. Continued collaboration between physicians and biostatisticians will be critical for implementing these trial 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.

Orthogonal array composite designs for drug combination experiments with applications for tuberculosis.

The aim of this article is to provide an overview of the orthogonal array composite design (OACD) methodology, illustrate the various advantages, and provide a real-world application. An OACD combines a two-level factorial design with a three-level orthogonal array and it can be used as an alternative to existing composite designs for building response surface models. We compare the D$$ D $$ -efficiencies of OACDs relative to the commonly used central composite design (CCD) when there are a few missing observations and demonstrate that OACDs are more robust to missing observations for two scenarios. The first scenario assumes one missing observation either from one factorial point or one additional point. The second scenario assumes two missing observations either from two factorial points or from two additional points, or from one factorial point and one additional point. Furthermore, we compare OACDs and CCDs in terms of I$$ I $$ -optimality for precise predictions. Lastly, a real-world application of an OACD for a tuberculosis drug combination study is provided.

A model-based approach to designing developmental toxicology experiments using sea urchin embryos.

The key aim of this paper is to suggest a more quantitative approach to designing a dose-response experiment, and more specifically, a concentration-response experiment. The work proposes a departure from the traditional experimental design to determine a dose-response relationship in a developmental toxicology study. It is proposed that a model-based approach to determine a dose-response relationship can provide the most accurate statistical inference for the underlying parameters of interest, which may be estimating one or more model parameters or pre-specified functions of the model parameters, such as lethal dose, at maximal efficiency. When the design criterion or criteria can be determined at the onset, there are demonstrated efficiency gains using a more carefully selected model-based optimal design as opposed to an ad-hoc empirical design. As an illustration, a model-based approach was theoretically used to construct efficient designs for inference in a developmental toxicity study of sea urchin embryos exposed to trimethoprim. This study compares and contrasts the results obtained using model-based optimal designs versus an ad-hoc empirical design.

Spatial Two-stage Designs for Phase II Clinical Trials.

A common endpoint in a single-arm phase II study is tumor response as a binary variable. Two widely used designs for such a study are Simon's two-stage minimax and optimal designs. The minimax design minimizes the maximal sample size and the optimal design minimizes the expected sample size under the null hypothesis. The optimal design generally has the larger total sample size than the minimax design, but its first stage's sample size is smaller than that of the minimax design. The difference in the total sample size between two types of designs can be large and so both designs can be unappealing to investigators. We develop novel designs that compromise on the two optimality criteria and avoid such occurrences using the spatial information on the first stage's required sample size and the total required sample size. We study properties of these spatial designs and show our proposed designs have advantages over Simon's designs and one of its extensions by Lin and Shih. As applications, we construct spatial designs for real-life studies on patients with Hodgkin disease and another study on effect of head and neck cancer on apnea.

Using Differential Evolution to Design Optimal Experiments.

Differential Evolution (DE) has become one of the leading metaheuristics in the class of Evolutionary Algorithms, which consists of methods that operate off of survival-of-the-fittest principles. This general purpose optimization algorithm is viewed as an improvement over Genetic Algorithms, which are widely used to find solutions to chemometric problems. Using straightforward vector operations and random draws, DE can provide fast, efficient optimization of any real, vector-valued function. This article reviews the basic algorithm and a few of its modifications with various enhancements. We provide guidance for practitioners, discuss implementation issues and give illustrative applications of DE with the corresponding R codes to find different types of optimal designs for various statistical models in chemometrics that involve the Arrhenius equation, reaction rates, concentration measures and chemical mixtures.

Optimal design of multiple-objective Lot Quality Assurance Sampling (LQAS) plans.

Lot Quality Assurance Sampling (LQAS) plans are widely used for health monitoring purposes. We propose a systematic approach to design multiple-objective LQAS plans that meet user-specified type 1 and 2 error rates and targets for selected diagnostic accuracy metrics. These metrics may include sensitivity, specificity, positive predictive value, and negative predictive value in high or low anticipated prevalence rate populations. We use Mixed Integer Nonlinear Programming (MINLP) tools to implement our design methodology. Our approach is flexible in that it can directly generate classic LQAS plans that control error rates only and find optimal LQAS plans that meet multiple objectives in terms of diagnostic metrics. We give examples, compare results with the classic LQAS and provide an application using a malaria outcome indicator survey in Mozambique.

A model-based multithreshold method for subgroup identification.

Thresholding variable plays a crucial role in subgroup identification for personalized medicine. Most existing partitioning methods split the sample based on one predictor variable. In this paper, we consider setting the splitting rule from a combination of multivariate predictors, such as the latent factors, principle components, and weighted sum of predictors. Such a subgrouping method may lead to more meaningful partitioning of the population than using a single variable. In addition, our method is based on a change point regression model and thus yields straight forward model-based prediction results. After choosing a particular thresholding variable form, we apply a two-stage multiple change point detection method to determine the subgroups and estimate the regression parameters. We show that our approach can produce two or more subgroups from the multiple change points and identify the true grouping with high probability. In addition, our estimation results enjoy oracle properties. We design a simulation study to compare performances of our proposed and existing methods and apply them to analyze data sets from a Scleroderma trial and a breast cancer study.

Using SeDuMi to find various optimal designs for regression models.

We introduce a powerful and yet seldom used numerical approach in statistics for solving a broad class of optimization problems where the search space is discretized. This optimization tool is widely used in engineering for solving semidefinite programming (SDP) problems and is called SeDuMi (self-dual minimization). We focus on optimal design problems and demonstrate how to formulate A-, A s -, c-, I-, and L-optimal design problems as SDP problems and show how they can be effectively solved by SeDuMi in MATLAB. We also show the numerical approach is flexible by applying it to further find optimal designs based on the weighted least squares estimator or when there are constraints on the weight distribution of the sought optimal design. For approximate designs, the optimality of the SDP-generated designs can be verified using the Kiefer-Wolfowitz equivalence theorem. SDP also finds optimal designs for nonlinear regression models commonly used in social and biomedical research. Several examples are presented for linear and nonlinear models.

Varying-coefficient semiparametric model averaging prediction.

Forecasting and predictive inference are fundamental data analysis tasks. Most studies employ parametric approaches making strong assumptions about the data generating process. On the other hand, while nonparametric models are applied, it is sometimes found in situations involving low signal to noise ratios or large numbers of covariates that their performance is unsatisfactory. We propose a new varying-coefficient semiparametric model averaging prediction (VC-SMAP) approach to analyze large data sets with abundant covariates. Performance of the procedure is investigated with numerical examples. Even though model averaging has been extensively investigated in the literature, very few authors have considered averaging a set of semiparametric models. Our proposed model averaging approach provides more flexibility than parametric methods, while being more stable and easily implemented than fully multivariate nonparametric varying-coefficient models. We supply numerical evidence to justify the effectiveness of our methodology.

Maximin optimal designs for cluster randomized trials.

We consider design issues for cluster randomized trials (CRTs) with a binary outcome where both unit costs and intraclass correlation coefficients (ICCs) in the two arms may be unequal. We first propose a design that maximizes cost efficiency (CE), defined as the ratio of the precision of the efficacy measure to the study cost. Because such designs can be highly sensitive to the unknown ICCs and the anticipated success rates in the two arms, a local strategy based on a single set of best guesses for the ICCs and success rates can be risky. To mitigate this issue, we propose a maximin optimal design that permits ranges of values to be specified for the success rate and the ICC in each arm. We derive maximin optimal designs for three common measures of the efficacy of the intervention, risk difference, relative risk and odds ratio, and study their properties. Using a real cancer control and prevention trial example, we ascertain the efficiency of the widely used balanced design relative to the maximin optimal design and show that the former can be quite inefficient and less robust to mis-specifications of the ICCs and the success rates in the two arms.

Standardized maximim D-optimal designs for enzyme kinetic inhibition models.

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters. An alternative is the maximin approach that allows the user to specify a range of values for each parameter of interest. However, the maximin approach is difficult because we first have to determine the locally optimal design for each set of nominal values before maximin types of optimal designs can be found via a nested optimization process. We show that particle swarm optimization (PSO) techniques can solve such complex optimization problems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae for standardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact and nonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibition models are not necessarily supported at a minimum number of points. To facilitate use of such designs, we create a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs.

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.

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D-, A- and E-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

Optimal designs based on the maximum quasi-likelihood estimator.

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses.

Optimal treatment allocation for placebo-treatment comparisons in trials with discrete-time survival endpoints.

In many randomized controlled trials, treatment groups are of equal size, but this is not necessarily the best choice. This paper provides a methodology to calculate optimal treatment allocations for longitudinal trials when we wish to compare multiple treatment groups with a placebo group, and the comparisons may have unequal importance. The focus is on trials with a survival endpoint measured in discrete time. We assume the underlying survival process is Weibull and show that values for the parameters in the Weibull distribution have an impact on the optimal treatment allocation scheme in an interesting way. Additionally, we incorporate different cost considerations at the subject and measurement levels and determine the optimal number of time periods. We also show that when many events occur at the beginning of the trial, fewer time periods are more efficient. As an application, we revisit a risperidone maintenance treatment trial in schizophrenia and use our proposed methodology to redesign it and compare merits of our optimal design.

Inference for reclassification statistics under nested and non-nested models for biomarker evaluation.

The Net Reclassification Improvement (NRI) and the Integrated Discrimination Improvement (IDI) are used to evaluate the diagnostic accuracy improvement for biomarkers in a wide range of applications. Most applications for these reclassification metrics are confined to nested model comparison. We emphasize the important extensions of these metrics to the non-nested comparison. Non-nested models are important in practice, in particular, in high-dimensional data analysis and in sophisticated semiparametric modeling. We demonstrate that the assessment of accuracy improvement may follow the familiar NRI and IDI evaluation. While the statistical properties of the estimators for NRI and IDI have been well studied in the nested setting, one cannot always rely on these asymptotic results to implement the inference procedure for practical data, especially for testing the null hypothesis of no improvement, and these properties have not been established for the non-nested setting. We propose a generic bootstrap re-sampling procedure for the construction of confidence intervals and hypothesis tests. Extensive simulations and real biomedical data examples illustrate the applicability of the proposed inference methods for both nested and non-nested models.