Optimal spending functions for asymmetric group sequential designs

We present optimized group sequential designs where testing of a single parameter theta is of interest. We require specification of a loss function and of a prior distribution for theta. For the examples presented, we pre-specify Type I and II error rates and minimize the expected sample size over the prior distribution for theta. Minimizing the square of sample size rather than the sample size is found to produce designs with slightly less aggressive interim stopping rules and smaller maximum sample sizes with essentially identical expected sample size. We compare optimal designs using Hwang-Shih-DeCani and Kim-DeMets spending functions to fully optimized designs not restricted by a spending function family. In the examples selected, we also examine when there might be substantial benefit gained by adding an interim analysis. Finally, we provide specific optimal asymmetric spending function designs that should be generally useful and simply applied when a design with minimal expected sample size is desired.     

Statistical inference and power analysis for direct and spillover effects in two-stage randomized experiments

Two-stage randomized experiments become an increasingly popular experimental design for causal inference when the outcome of one unit may be affected by the treatment assignments of other units in the same cluster. In this paper, we provide a methodological framework for general tools of statistical inference and power analysis for two-stage randomized experiments. Under the randomization-based framework, we consider the estimation of a new direct effect of interest as well as the average direct and spillover effects studied in the literature. We provide unbiased estimators of these causal quantities and their conservative variance estimators in a general setting. Using these results, we then develop hypothesis testing procedures and derive sample size formulas. We theoretically compare the two-stage randomized design with the completely randomized and cluster randomized designs, which represent two limiting designs. Finally, we conduct simulation studies to evaluate the empirical performance of our sample size formulas. For empirical illustration, the proposed methodology is applied to the randomized evaluation of the Indian National Health Insurance Program. An open-source software package is available for implementing the proposed methodology.     

Optimal nested row-column designs with specified components

We consider nested row-column designs where each of the rowand column component designs is specified. For the case thateach of the component designs has second-order balance, we definesuch a nested row-column design to be special if it is generallybalanced, with the smallest possible number of canonical treatmentcontrasts having the lower canonical efficiency factor in bothcomponents. We show that if any special row-column design existsthen it is A-optimal over all nested row-column designs withthe given components.     

Detecting anthropogenic disturbance in an environment with multiple gradients of physical disturbance,Manukau Harbour,New Zealand

Demonstrating spatial or temporal gradients of effects on macrobenthic communities can be a useful way of providing strong empirical evidence of natural or anthropogenic disturbance. Gradient designs for environmental assessment are sensitive to change for point source data, enabling the scale of the effects of a disturbance to be readily identified. If the spatial scale that is sampled from the point source is adequate, problems of selecting control sites can be avoided. However, sources of spatial variation in macrobenthic communities, which are not related to the impact, can confound the use of gradient designs. This can occur if the natural spatial structure overlaps that of the gradient and cannot be identified either as a location or environmental covariable. The ability to detect point source impacts using a gradient design against natural spatial variability was tested using benthic macrofaunal data collected from Manukau Harbour, New Zealand. Treated sewage wastewater is discharged into the north-west area of the Manukau Harbour. Sandflats in the vicinity of the outfall are also subject to physical disturbance from wind-waves and strong tides. Ordination techniques and the testing of a priori predictions were used to try and separate the relative effects of organic and physical disturbance on the benthic communities. While the occurrence of other environmental disturbances along a gradient of anthropogenic disturbance makes interpretation of community pattern more difficult, the use of a gradient sampling layout, ordination analysis and the testing of a priori predictions enabled impacts of the anthropogenic and natural environmental disturbances to be interpreted. Gradient designs, therefore, provide a method of assessing complex impacts that operate over broad spatial and temporal scales.     

Adaptive seamless clinical trials using early outcomes for treatment or subgroup selection: Methods,simulation model and their implementation in R

Adaptive seamless designs combine confirmatory testing, a domain of phase III trials, with features such as treatment or subgroup selection, typically associated with phase II trials. They promise to increase the efficiency of development programmes of new drugs, for example, in terms of sample size and/or development time. It is well acknowledged that adaptive designs are more involved from a logistical perspective and require more upfront planning, often in the form of extensive simulation studies, than conventional approaches. Here, we present a framework for adaptive treatment and subgroup selection using the same notation, which links the somewhat disparate literature on treatment selection on one side and on subgroup selection on the other. Furthermore, we introduce a flexible and efficient simulation model that serves both designs. As primary endpoints often take a long time to observe, interim analyses are frequently informed by early outcomes. Therefore, all methods presented accommodate interim analyses informed by either the primary outcome or an early outcome. The R package asd , previously developed to simulate designs with treatment selection, was extended to include subgroup selection (so-called adaptive enrichment designs). Here, we describe the functionality of the R package asd and use it to present some worked-up examples motivated by clinical trials in chronic obstructive pulmonary disease and oncology. The examples both illustrate various features of the R package and provide insights into the operating characteristics of adaptive seamless studies.     

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.     

Optimal designs for evaluating a series of treatments

Several articles in this journal have studied optimal designs for testing a series of treatments to identify promising ones for further study. These designs formulate testing as an ongoing process until a promising treatment is identified. This formulation is considered to be more realistic but substantially increases the computational complexity. In this article, we show that these new designs, which control the error rates for a series of treatments, can be reformulated as conventional designs that control the error rates for each individual treatment. This reformulation leads to a more meaningful interpretation of the error rates and hence easier specification of the error rates in practice. The reformulation also allows us to use conventional designs from published tables or standard computer programs to design trials for a series of treatments. We illustrate these using a study in soft tissue sarcoma.     

OpenSim as a preliminary kinematic testing platform for the development of total knee arthroplasty implants

The design of a total knee replacement implant needs to take account the complex surfaces of the knee which it is replacing. Ensuring design performance of the implant requires in vitro testing of the implant. A considerable amount of time is required to produce components and evaluate them inside an experimental setting. Numerous adjustments in the design of an implant and testing each individual design can be time consuming and expensive.Our solution is to use the OpenSim simulation software to rapidly test multiple design configurations of implants. This study modeled a testing rig which characterized the motion and laxity of knee implants. Three different knee implant designs were used to test and validate the accuracy of the simulation: symmetrical, asymmetric, and anatomic. Kinematics were described as distances measured from the center of each femoral condyle to a plane intersecting the most posterior points of the tibial condyles between 0 and 135° of flexion with 15° increments. Excluding the initial flexion measurement (∼0°) results, the absolute differences between all experimental and simulation results (neutral path, anterior-posterior shear, internal-external torque) for the symmetric, asymmetric, and anatomical designs were 1.98 mm ± 1.15, 1.17 mm ± 0.89, and 1.24 mm ± 0.97, respectively. Considering all designs, the accuracy of the simulation across all tests was 1.46 mm ± 1.07. It was concluded that the results of the simulation were an acceptable representation of the testing rig and hence applicable as a design tool for new total knees.     

Compliance subsampling designs for comparative research: estimation and optimal planning

For studies with treatment noncompliance, analyses have been developed recently to better estimate treatment efficacy. However, the advantage and cost of measuring compliance data have implications on the study design that have not been as systematically explored. In order to estimate better treatment efficacy with lower cost, we propose a new class of compliance subsampling (CSS) designs where, after subjects are assigned treatment, compliance behavior is measured for only subgroups of subjects. The sizes of the subsamples are allowed to relate to the treatment assignment, the assignment probability, the total sample size, the anticipated distributions of outcome and compliance, and the cost parameters of the study. The CSS design methods relate to prior work (i) on two-phase designs in which a covariate is subsampled and (ii) on causal inference because the subsampled postrandomization compliance behavior is not the true covariate of interest. For each CSS design, we develop efficient estimation of treatment efficacy under binary outcome and all-or-none observed compliance. Then we derive a minimal cost CSS design that achieves a required precision for estimating treatment efficacy. We compare the properties of the CSS design to those of conventional protocols in a study of patient choices for medical care at the end of life.     

Screening designs for drug development

We propose drug screening designs based on a Bayesian decision-theoretic approach. The discussion is motivated by screening designs for phase II studies. The proposed screening designs allow consideration of multiple treatments simultaneously. In each period, new treatments can arise and currently considered treatments can be dropped. Once a treatment is removed from the phase II screening trial, a terminal decision is made about abandoning the treatment or recommending it for a future confirmatory phase III study. The decision about dropping treatments from the active set is a sequential stopping decision. We propose a solution based on decision boundaries in the space of marginal posterior moments for the unknown parameter of interest that relates to each treatment. We present a Monte Carlo simulation algorithm to implement the proposed approach. We provide an implementation of the proposed method as an easy to use R library available for public domain download (http://www.stat.rice.edu/~rusi/ or http://odin.mdacc.tmc.edu/~pm/).     

Computational design of a specific heavy chain/κ light chain interface for expressing fully IgG bispecific antibodies

The use of bispecific antibodies (BsAbs) to treat human diseases is on the rise. Increasingly complex and powerful therapeutic mechanisms made possible by BsAbs are spurring innovation of novel BsAb formats and methods for their production. The long‐lived in vivo pharmacokinetics, optimal biophysical properties and potential effector functions of natural IgG monoclonal (and monospecific) antibodies has resulted in a push to generate fully IgG BsAb formats with the same quaternary structure as monoclonal IgGs. The production of fully IgG BsAbs is challenging because of the highly heterogeneous pairing of heavy chains (HCs) and light chains (LCs) when produced in mammalian cells with two IgG HCs and two LCs. A solution to the HC heterodimerization aspect of IgG BsAb production was first discovered two decades ago; however, addressing the LC mispairing issue has remained intractable until recently. Here, we use computational and rational engineering to develop novel designs to the HC/LC pairing issue, and particularly for κ LCs. Crystal structures of these designs highlight the interactions that provide HC/LC specificity. We produce and characterize multiple fully IgG BsAbs using these novel designs. We demonstrate the importance of specificity engineering in both the variable and constant domains to achieve robust HC/LC specificity within all the BsAbs. These solutions facilitate the production of fully IgG BsAbs for clinical use.     

Highly efficient stepped wedge designs for clusters of unequal size

The stepped wedge design (SWD) is a form of cluster randomized trial, usually comparing two treatments, which is divided into time periods and sequences, with clusters allocated to sequences. Typically all sequences start with the standard treatment and end with the new treatment, with the change happening at different times in the different sequences. The clusters will usually differ in size but this is overlooked in much of the existing literature. This paper considers the case when clusters have different sizes and determines how efficient designs can be found. The approach uses an approximation to the variance of the treatment effect, which is expressed in terms of the proportions of clusters and of individuals allocated to each sequence of the design. The roles of these sets of proportions in determining an efficient design are discussed and illustrated using two SWDs, one in the treatment of sexually transmitted diseases and one in renal replacement therapy. Cluster-balanced designs, which allocate equal numbers of clusters to each sequence, are shown to have excellent statistical and practical properties; suggestions are made about the practical application of the results for these designs. The paper concentrates on the cross-sectional case, where subjects are measured once, but it is briefly indicated how the methods can be extended to the closed-cohort design.     

Extension of the rank sum test for clustered data: two-group comparisons with group membership defined at the subunit level

The Wilcoxon rank sum test is widely used for two-group comparisons for nonnormal data. An assumption of this test is independence of sampling units both between and within groups. In ophthalmology, data are often collected on two eyes of an individual, which are highly correlated. In ophthalmological clinical trials, randomization is usually performed at the subject level, but the unit of analysis is the eye. If the eye is used as the unit of analysis, then a modification to the usual Wilcoxon rank sum variance formula must be made to account for the within-cluster dependence. For some clustered data designs, where the unit of analysis is the subunit, group membership may be defined at the subunit level. For example, in some randomized ophthalmologic clinical trials, different treatments may be applied to fellow eyes of some patients, while the same treatment may be applied to fellow eyes of other patients. In general, binary eye-specific covariates may be present (scored as exposed or unexposed) and one wishes to compare nonnormally distributed outcomes between exposed and unexposed eyes using the Wilcoxon rank sum test while accounting for the clustering. In this article, we present a corrected variance formula for the Wilcoxon rank sum statistic in the setting of eye (subunit)-specific covariates. We apply it to compare ocular itching scores in ocular allergy patients between eyes treated with active versus placebo eye drops, where some patients receive the same eye drop in both eyes, while other patients receive different eye drops in fellow eyes. We also present comparisons between the clustered Wilcoxon test and each of the signed rank tests and mixed model approaches and show dramatic differences in power in favor of the clustered Wilcoxon test for some designs.     

False discovery rate control in two-stage designs

ABSTRACT: BACKGROUND: For gene expression or gene association studies with a large number of hypotheses the number of measurements per marker in a conventional single-stage design is often low due to limited resources. Two-stage designs have been proposed where in a first stage promising hypotheses are identified and further investigated in the second stage with larger sample sizes. For two types of two-stage designs proposed in the literature we derive multiple testing procedures controlling the False Discovery Rate (FDR) demonstrating FDR control by simulations: designs where a fixed number of top-ranked hypotheses are selected and designs where the selection in the interim analysis is based on an FDR threshold. In contrast to earlier approaches which use only the second-stage data in the hypothesis tests (pilot approach), the proposed testing procedures are based on the pooled data from both stages (integrated approach). Results: For both selection rules the multiple testing procedures control the FDR in the considered simulation scenarios. This holds for the case of independent observations across hypotheses as well as for certain correlation structures. Additionally, we show that in scenarios with small effect sizes the testing procedures based on the pooled data from both stages can give a considerable improvement in power compared to tests based on the second-stage data only. Conclusion: The proposed hypothesis tests provide a tool for FDR control for the considered two-stage designs. Comparing the integrated approaches for both selection rules with the corresponding pilot approaches showed an advantage of the integrated approach in many simulation scenarios.     

Optimal design of genetic studies of gene expression with two-color microarrays in outbred crosses

Combining global gene-expression profiling and genetic analysis of natural allelic variation (genetical genomics) has great potential in dissecting the genetic pathways underlying complex phenotypes. Efficient use of microarrays is paramount in experimental design as the cost of conducting this type of study is high. For those organisms where recombinant inbred lines are available for mapping, the “distant pair design” maximizes the number of informative contrasts over all marker loci. Here, we describe an extension of this design, named the “optimal pair design,” for use with F₂ crosses between outbred lines. The performance of this design is investigated by simulation and compared to several other two-color microarray designs. We show that, for a given number of microarrays, the optimal pair design outperforms all other designs considered for detection of expression quantitative trait loci (eQTL) with additive effects by linkage analysis. We also discuss the suitability of this design for outbred crosses in organisms with large genomes and for detection of dominance.     

Bayesian adaptive biased-coin designs for clinical trials with normal responses

Adaptive designs are used in phase III clinical trials for skewing the allocation pattern toward the better treatments. We use optimum design theory to derive a skewed Bayesian biased-coin procedure for sequential designs with continuous responses. The skewed designs are used to provide adaptive designs, the performance of which is studied numerically and theoretically. Important properties are loss and the proportion of allocation to the better treatment.     

Flexible Designs for Genomewide Association Studies

Summary .  Genomewide association studies attempting to unravel the genetic etiology of complex traits have recently gained attention. Frequently, these studies employ a sequential genotyping strategy: A large panel of markers is examined in a subsample of subjects, and the most promising markers are genotyped in the remaining subjects. In this article, we introduce a novel method for such designs enabling investigators to, for example, modify marker densities and sample proportions while strongly controlling the family-wise type I error rate. Loss of efficiency is avoided by redistributing conditional type I error rates of discarded markers. Our approach can be combined with cost optimal designs and entails a greater flexibility than all previously suggested designs. Among other features, it allows for marker selections based upon biological criteria instead of statistical criteria alone, or the option to modify the sample size at any time during the course of the project. For practical applicability, we develop a new algorithm, subsequently evaluate it by simulations, and illustrate it using a real data set.     

De novo design and Rosetta-based assessment of high-affinity antibody variable regions (Fv) against the SARS-CoV-2 spike receptor binding domain (RBD)

The continued emergence of new SARS-CoV-2 variants has accentuated the growing need for fast and reliable methods for the design of potentially neutralizing antibodies (Abs) to counter immune evasion by the virus. Here, we report on the de novo computational design of high-affinity Ab variable regions (Fv) through the recombination of VDJ genes targeting the most solvent-exposed hACE2-binding residues of the SARS-CoV-2 spike receptor binding domain (RBD) protein using the software tool OptMAVEn-2.0. Subsequently, we carried out computational affinity maturation of the designed variable regions through amino acid substitutions for improved binding with the target epitope. Immunogenicity of designs was restricted by preferring designs that match sequences from a 9-mer library of “human Abs” based on a human string content score. We generated 106 different antibody designs and reported in detail on the top five that trade-off the greatest computational binding affinity for the RBD with human string content scores. We further describe computational evaluation of the top five designs produced by OptMAVEn-2.0 using a Rosetta-based approach. We used Rosetta SnugDock for local docking of the designs to evaluate their potential to bind the spike RBD and performed “forward folding” with DeepAb to assess their potential to fold into the designed structures. Ultimately, our results identified one designed Ab variable region, P1.D1, as a particularly promising candidate for experimental testing. This effort puts forth a computational workflow for the de novo design and evaluation of Abs that can quickly be adapted to target spike epitopes of emerging SARS-CoV-2 variants or other antigenic targets.     

Decision theoretic designs for phase II clinical trials with multiple outcomes

In many phase II clinical trials, it is essential to assess both efficacy and safety. Although several phase II designs that accommodate multiple outcomes have been proposed recently, none are derived using decision theory. This paper describes a Bayesian decision theoretic strategy for constructing phase II designs based on both efficacy and adverse events. The gain function includes utilities assigned to patient outcomes, a reward for declaring the new treatment promising, and costs associated with the conduct of the phase II trial and future phase III testing. A method for eliciting gain function parameters from medical collaborators and for evaluating the design's frequentist operating characteristics is described. The strategy is illustrated by application to a clinical trial of peripheral blood stem cell transplantation for multiple myeloma.     

3D finite element analysis of porous Ti-based alloy prostheses

In this paper, novel designs of porous acetabular cups are created and tested with 3D finite element analysis (FEA). The aim is to develop a porous acetabular cup with low effective radial stiffness of the structure, which will be near to the architectural and mechanical behavior of the natural bone. For the realization of this research, a 3D-scanner technology was used for obtaining a 3D-CAD model of the pelvis bone, a 3D-CAD software for creating a porous acetabular cup, and a 3D-FEA software for virtual testing of a novel design of the porous acetabular cup. The results obtained from this research reveal that a porous acetabular cup from Ti-based alloys with 60 ± 5% porosity has the mechanical behavior and effective radial stiffness (Young’s modulus in radial direction) that meet and exceed the required properties of the natural bone. The virtual testing with 3D-FEA of a novel design with porous structure during the very early stage of the design and the development of orthopedic implants, enables obtaining a new or improved biomedical implant for a relatively short time and reduced price.