A simulation study using the hybrid statistic and the meta-analysis t-test for data with matched and unmatched subjects in the interim analysis of clinical trials

An interim analysis is usually applied in later phase II or phase III trials to find convincing evidence of a significant treatment difference that may lead to trial termination at an earlier point than planned at the beginning. This can result in the saving of patient resources and shortening of drug development and approval time. In addition, ethics and economics are also the reasons to stop a trial earlier. In clinical trials of eyes, ears, knees, arms, kidneys, lungs, and other clustered treatments, data may include distribution-free random variables with matched and unmatched subjects in one study. It is important to properly include both subjects in the interim and the final analyses so that the maximum efficiency of statistical and clinical inferences can be obtained at different stages of the trials. So far, no publication has applied a statistical method for distribution-free data with matched and unmatched subjects in the interim analysis of clinical trials. In this simulation study, the hybrid statistic was used to estimate the empirical powers and the empirical type I errors among the simulated datasets with different sample sizes, different effect sizes, different correlation coefficients for matched pairs, and different data distributions, respectively, in the interim and final analysis with 4 different group sequential methods. Empirical powers and empirical type I errors were also compared to those estimated by using the meta-analysis t-test among the same simulated datasets. Results from this simulation study show that, compared to the meta-analysis t-test commonly used for data with normally distributed observations, the hybrid statistic has a greater power for data observed from normally, log-normally, and multinomially distributed random variables with matched and unmatched subjects and with outliers. Powers rose with the increase in sample size, effect size, and correlation coefficient for the matched pairs. In addition, lower type I errors were observed estimated by using the hybrid statistic, which indicates that this test is also conservative for data with outliers in the interim analysis of clinical trials.^

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

A simulation study of the effects of small center enrollment in multi -center clinical trials

Multi-center clinical trials are very common in the development of new drugs and devices. One concern in such trials, is the effect of individual investigational sites enrolling small numbers of patients on the overall result. Can the presence of small centers cause an ineffective treatment to appear effective when treatment-by-center interaction is not statistically significant?^ In this research, simulations are used to study the effect that centers enrolling few patients may have on the analysis of clinical trial data. A multi-center clinical trial with 20 sites is simulated to investigate the effect of a new treatment in comparison to a placebo treatment. Twelve of these 20 investigational sites are considered small, each enrolling less than four patients per treatment group. Three clinical trials are simulated with sample sizes of 100, 170 and 300. The simulated data is generated with various characteristics, one in which treatment should be considered effective and another where treatment is not effective. Qualitative interactions are also produced within the small sites to further investigate the effect of small centers under various conditions.^ Standard analysis of variance methods and the "sometimes-pool" testing procedure are applied to the simulated data. One model investigates treatment and center effect and treatment-by-center interaction. Another model investigates treatment effect alone. These analyses are used to determine the power to detect treatment-by-center interactions, and the probability of type I error.^ We find it is difficult to detect treatment-by-center interactions when only a few investigational sites enrolling a limited number of patients participate in the interaction. However, we find no increased risk of type I error in these situations. In a pooled analysis, when the treatment is not effective, the probability of finding a significant treatment effect in the absence of significant treatment-by-center interaction is well within standard limits of type I error. ^

Comparative analysis of meta-analysis methods: when to use which?

Background: Several meta-analysis methods can be used to quantitatively combine the results of a group of experiments, including the weighted mean difference, statistical vote counting, the parametric response ratio and the non-parametric response ratio. The software engineering community has focused on the weighted mean difference method. However, other meta-analysis methods have distinct strengths, such as being able to be used when variances are not reported. There are as yet no guidelines to indicate which method is best for use in each case. Aim: Compile a set of rules that SE researchers can use to ascertain which aggregation method is best for use in the synthesis phase of a systematic review. Method: Monte Carlo simulation varying the number of experiments in the meta analyses, the number of subjects that they include, their variance and effect size. We empirically calculated the reliability and statistical power in each case Results: WMD is generally reliable if the variance is low, whereas its power depends on the effect size and number of subjects per meta-analysis; the reliability of RR is generally unaffected by changes in variance, but it does require more subjects than WMD to be powerful; NPRR is the most reliable method, but it is not very powerful; SVC behaves well when the effect size is moderate, but is less reliable with other effect sizes. Detailed tables of results are annexed. Conclusions: Before undertaking statistical aggregation in software engineering, it is worthwhile checking whether there is any appreciable difference in the reliability and power of the methods. If there is, software engineers should select the method that optimizes both parameters.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

Simulation Model for Sea Clutter in Airborne Radars

This paper presents the architecture and the methods used to dynamically simulate the sea backscatter of an airborne radar operating in a medium repetition frequency mode (MPRF). It offers a method of generating a sea backscatter signal which fulfills the intensity statistics of real clutter in time domain, spatial correlation and local Doppler spectrum of real data. Three antenna channels (sum, guard and difference) and their cross-correlation properties are simulated. The objective of this clutter generator is to serve as the signal source for the simulation of complex airborne pulsed radar signal processors

Analysis and design of a thrombectomy device by using simulation techniques

Purpose: In this work, we present the analysis, design and optimization of one experimental device recently developed in the UK, called the 'GP' Thrombus Aspiration Device (GPTAD). This device has been designed to remove blood clots without the need to make contact with the clot itself thereby potentially reducing the risk of problems such as downstream embolisation. Method: To obtain the minimum pressure necessary to extract the clot and to optimize the device, we have simulated the performance of the GPTAD analysing the resistances, compliances and inertances effects. We model a range of diameters for the GPTAD considering different forces of adhesion of the blood clot to the artery wall, and different lengths of blood clot. In each case we determine the optimum pressure required to extract the blood clot from the artery using the GPTAD, which is attached at its proximal end to a suction pump. Result: We then compare the results of our mathematical modelling to measurements made in laboratory using plastic tube models of arteries of comparable diameter. We use abattoir porcine blood clots that are extracted using the GPTAD. The suction pressures required for such clot extraction in the plastic tube models compare favourably with those predicted by the mathematical modelling. Discussion & Conclusion: We conclude therefore that the mathematical modelling is a useful technique in predicting the performance of the GPTAD and may potentially be used in optimising the design of the device.

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

FPGA Acceleration of Monte Carlo-based Financial Simulation: Design Challenges and Lessons Learnt

The simulation of interest rate derivatives is a powerful tool to face the current market fluctuations. However, the complexity of the financial models and the way they are processed require exorbitant computation times, what is in clear conflict with the need of a processing time as short as possible to operate in the financial market. To shorten the computation time of financial derivatives the use of hardware accelerators becomes a must.

Provisos for classic linear oscillator design methods. New linear oscillator design based on the NDF/RRT

In this paper, the classic oscillator design methods are reviewed, and their strengths and weaknesses are shown. Provisos for avoiding the misuse of classic methods are also proposed. If the required provisos are satisfied, the solutions provided by the classic methods (oscillator start-up linear approximation) will be correct. The provisos verification needs to use the NDF (Network Determinant Function). The use of the NDF or the most suitable RRT (Return Relation Transponse), which is directly related to the NDF, as a tool to analyze oscillators leads to a new oscillator design method. The RRT is the "true" loop-gain of oscillators. The use of the new method is demonstrated with examples. Finally, a comparison of NDF/RRT results with the HB (Harmonic Balance) simulation and practical implementation measurements prove the universal use of the new methods.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

A novel method for radio propagation simulation based on automatic 3D environment reconstruction

In this paper, a novel method to simulate radio propagation is presented. The method consists of two steps: automatic 3D scenario reconstruction and propagation modeling. For 3D reconstruction, a machine learning algorithm is adopted and improved to automatically recognize objects in pictures taken from target region, and 3D models are generated based on the recognized objects. The propagation model employs a ray tracing algorithm to compute signal strength for each point on the constructed 3D map. By comparing with other methods, the work presented in this paper makes contributions on reducing human efforts and cost in constructing 3D scene; moreover, the developed propagation model proves its potential in both accuracy and efficiency.

Simulation of wind farms in flat and complex terrain using CFD

Use of computational fluid dynamic (CFD) methods to predict the power production from wind entire wind farms in flat and complex terrain is presented in this paper. Two full 3D Navier–Stokes solvers for incompressible flow are employed that incorporate the k–ε and k–ω turbulence models respectively. The wind turbines (W/Ts) are modelled as momentum absorbers by means of their thrust coefficient using the actuator disk approach. The WT thrust is estimated using the wind speed one diameter upstream of the rotor at hub height. An alternative method that employs an induction-factor based concept is also tested. This method features the advantage of not utilizing the wind speed at a specific distance from the rotor disk, which is a doubtful approximation when a W/T is located in the wake of another and/or the terrain is complex. To account for the underestimation of the near wake deficit, a correction is introduced to the turbulence model. The turbulence time scale is bounded using the general “realizability” constraint for the turbulent velocities. Application is made on two wind farms, a five-machine one located in flat terrain and another 43-machine one located in complex terrain. In the flat terrain case, the combination of the induction factor method along with the turbulence correction provides satisfactory results. In the complex terrain case, there are some significant discrepancies with the measurements, which are discussed. In this case, the induction factor method does not provide satisfactory results.

Numerical methods for option pricing.

This thesis aims to introduce some fundamental concepts underlying option valuation theory including implementation of computational tools. In many cases analytical solution for option pricing does not exist, thus the following numerical methods are used: binomial trees, Monte Carlo simulations and finite difference methods. First, an algorithm based on Hull and Wilmott is written for every method. Then these algorithms are improved in different ways. For the binomial tree both speed and memory usage is significantly improved by using only one vector instead of a whole price storing matrix. Computational time in Monte Carlo simulations is reduced by implementing a parallel algorithm (in C) which is capable of improving speed by a factor which equals the number of processors used. Furthermore, MatLab code for Monte Carlo was made faster by vectorizing simulation process. Finally, obtained option values are compared to those obtained with popular finite difference methods, and it is discussed which of the algorithms is more appropriate for which purpose.

The european project NURISP for nuclear reactor simulation

The NURISP project aims at developing the European NURESIM reference simulation platform [1] for nuclear reactor. A first version of NURESIM was delivered in 2008. 22 organizations from 14 European countries contribute to the further development of this platform. NURISP also includes a User’s Group (UG) whose members are not NURISP partners and come from the industrial nuclear sector or European and non-European R&D labs. Users can benefit from the use of the NURESIM platform, methods, results and modules and they provide concrete input and feedback on the use of these elements.