Fence methods for backcross experiments

Model search strategies play an important role in finding simultaneous susceptibility genes that are associated with a trait. More particularly, model selection via the information criteria, such as the BIC with modifications, have received considerable attention in quantitative trait loci mapping. However, such modifications often depend upon several factors, such as sample size, prior distribution, and the type of experiment, for example, backcross, intercross. These changes make it difficult to generalize the methods to all cases. The fence method avoids such limitations with a unified approach, and hence can be used more broadly. In this article, this method is studied in the case of backcross experiments throughout a series of simulation studies. The results are compared with those of the modified BIC method as well as some of the most popular shrinkage methods for model selection.     

On design and inference for two-stage adaptive clinical trials with dependent data

We consider two-stage adaptive designs for clinical trials where data from the two stages are dependent. This occurs when additional data are obtained from patients during their second stage follow-up. While the proposed flexible approach allows modifications of trial design, sample size, or statistical analysis using the first stage data, there is no need for a complete prespecification of the adaptation rule. Methods are provided for an adaptive closed testing procedure, for calculating overall adjusted p-values, and for obtaining unbiased estimators and confidence bounds for parameters that are invariant to modifications. A motivating example is used to illustrate these methods.     

Computer experiments: a review

In this paper we provide a broad introduction to the topic of computer experiments. We begin by briefly presenting a number of applications with different types of output or different goals. We then review modelling strategies, including the popular Gaussian process approach, as well as variations and modifications. Other strategies that are reviewed are based on polynomial regression, non-parametric regression and smoothing spline ANOVA. The issue of multi-level models, which combine simulators of different resolution in the same experiment, is also addressed. Special attention is given to modelling techniques that are suitable for functional data. To conclude the modelling section, we discuss calibration, validation and verification. We then review design strategies including Latin hypercube designs and space-filling designs and their adaptation to computer experiments. We comment on a number of special issues, such as designs for multi-level simulators, nested factors and determination of experiment size.     

Applying the rescaling bootstrap under imputation: a simulation study

Resampling methods are a common measure to estimate the variance of a statistic of interest when data consist of nonresponse and imputation is used as compensation. Applying resampling methods usually means that subsamples are drawn from the original sample and that variance estimates are computed based on point estimators of several subsamples. However, newer resampling methods such as the rescaling bootstrap of Chipperfield and Preston [Efficient bootstrap for business surveys. Surv Methodol. 2007;33:167–172] include all elements of the original sample in the computation of its point estimator. Thus, procedures to consider imputation in resampling methods cannot be applied in the ordinary way. For such methods, modifications are necessary. This paper presents an approach applying newer resampling methods for imputed data. The Monte Carlo simulation study conducted in the paper shows that the proposed approach leads to reliable variance estimates in contrast to other modifications.     

A Test for the Equality of Parameters for Separate Regression Models in the Presence of Heteroskedasticity

Testing for the equality of regression coefficients across two regressions is a problem considered by analysts in a variety of fields. If the variances of the errors of the two regressions are not equal, then it is known that the standard large sample F-test used to test the equality of the coefficients is compromised by the fact that its actual size can differ substantially from the stated level of significance in small samples. This article addresses this problem and borrows from the literature on the Behrens-Fisher problem to provide some simple modifications of the large sample test which allows one to better control the probability of committing a Type I error. Empirical evidence is presented which indicates that the suggested modifications provide tests which are superior to well-known alternative tests over a wide range of the parameter space.     

Improved log‐linear model estimators of abundance in capture‐recapture experiments

The authors review log‐linear models for estimating the size of a closed population and propose a new log‐linear estimator for experiments having between animal heterogeneity and a behavioral response. They give a general formula for evaluating the asymptotic biases of estimators of abundance derived from log‐linear models. They propose simple frequency modifications for reducing these asymptotic biases and investigate the modifications in a Monte Carlo experiment which reveals that they reduce both the bias and the mean squared error of abundance estimators.     

Modified probability proportional to size sampling

Probability proportional to size (PPS) sampling is one of the most widely used designs for finite populations. We propose modifications to PPS designs with replacement and Rao–Hartley–Cochran design without replacement. These modifications consist of division of the population into two groups. Units in the first group are included in the sample with probability one. Under certain conditions, in both with and without replacement designs, the estimator of the population total based on the modified PPS sampling design is shown to be better than the corresponding estimator based on a PPS design. We illustrate our modification by an example and an application.     

Methods for estimating relative risk in studies of common binary outcomes

Studying the effect of exposure or intervention on a dichotomous outcome is very common in medical research. Logistic regression (LR) is often used to determine such association which provides odds ratio (OR). OR often overestimates the effect size for prevalent outcome data. In such situations, use of relative risk (RR) has been suggested. We propose modifications in Zhang and Yu and Diaz-Quijano methods. These methods were compared with stratified Mantel Haenszel method, LR, log binomial regression (LBR), Zhang and Yu method, Poisson/Cox regression, modified Poisson/Cox regression, marginal probability method, COPY method, inverse probability of treatment weighted LBR, and Diaz-Quijano method. Our proposed modified Diaz-Quijano (MDQ) method provides RR and its confidence interval similar to those estimated by modified Poisson/Cox and LBRs. The proposed modifications in Zhang and Yu method provides better estimate of RR and its standard error as compared to Zhang and Yu method in a variety of situations with prevalent outcome. The MDQ method can be used easily to estimate the RR and its confidence interval in the studies which require reporting of RRs. Regression models which directly provide the estimate of RR without convergence problems such as the MDQ method and modified Poisson/Cox regression should be preferred.     

New Lilliefors and Srinivasan tables with applications

Two approaches to the problem of goodness-of-fit with nuisance parameters are presented in this paper, both based on modifications of the Kolmogorov-Smirnov statistics. Improved tables of critical values originally computed by Lilliefors and Srinivasan are presented in the normal and exponential cases. Also given are tables for the uniform case, normal with known mean and normal with known variance. All tables were computed using Monte Carlo simulation with sample size n = 20000.     

Accurate probabilities for the sign test

Limitations in currently available methods for producing significance probabilities for the sign test are discussed. Two simple modifications to the continuity corrected normal approximation are derived and presented in a simple form. These modifications are shown to markedly reduce the relative error in approximating exact probabilities. The relative simplicity of these modifications and the importance of accurate p values suggest that one or both modifications could be useful improvements.     

Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative hypothesis requires complex analytic approximations, and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say p≤20. On the other hand, assuming that the data dimension p as well as the number q of regression variables are fixed while the sample size n grows, several asymptotic approximations are proposed in the literature for Wilk's Λ including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension p and a large sample size n. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null hypothesis and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large p and large n context, but also for moderately large data dimensions such as p=30 or p=50. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in multivariate analysis of variance which is valid for high-dimensional data.     

Two Non-Negative Estimators for the Model With a Common Mean

Recently C. R. Rao (1984) suggested two modifications to the MINQUE, called MINQUE(S.D.) and MINQUE(C.P.), for estimating the variance components in a linear model. These modifications provide non-negative estimates unlike the MINQUE. In this article we shall compare the performance of these two estimators with some of the other existing modifications of MINQUE in terms of standard criteria such as the mean squared error and total squared bias.     

Notes on Kolassa’s Method for Estimating the Power of Wilcoxon–Mann–Whitney Test

The Kolassa method implemented in the nQuery Advisor software has been widely used for approximating the power of the Wilcoxon–Mann–Whitney (WMW) test for ordered categorical data, in which Edgeworth approximation is used to estimate the power of an unconditional test based on the WMW U statistic. When the sample size is small or when the sizes in the two groups are unequal, Kolassa’s method may yield quite poor approximation to the power of the conditional WMW test that is commonly implemented in statistical packages. Two modifications of Kolassa’s formula are proposed and assessed by simulation studies.     

A likelihood ratio test and its modifications for the homogeneity of the covariance matrices of dependent multivariate normals

For the problem of testing the homogeneity of the covariance matrices of several dependent multivariate normals, a likelihood ratio test is derived in this paper. The software SAS can be used to perform the test and the code is given and explained. Several modifications of the test that allow their distributions to be better approximated by the chi-square distribution are also considered. Formulae for calculating approximate sample size and power are derived. Small sample performances of these tests in the case of two dependent bivariate normals are compared to each other and to the competing tests by simulating levels of significance and powers, and recommendation is made of the ones that have good performance. The recommended tests are then applied to real data from a crossover bioequivalence trial.     

Power Maps in Goodness-of-fit Testing Based on Censored Samples

In goodness-of-fit testing based on Type-II right censored samples, mainly either classical tests are applied to transformed samples, which can be considered as full samples under the null hypothesis, or modifications of the tests are applied to the original samples. Results of an extensive simulation study are presented and discussed in order to compare the different approaches and tests by means of powers against beta alternatives. Depending on the beta parameters, illustrative plots lead to recommended tests in given situations, where there is some prior belief about the size of these parameters in the alternative. Moreover, the effects of adding artificial realizations via random dilation are examined.     

Inference of Seasonal Long‐memory Time Series with Measurement Error

We consider the Whittle likelihood estimation of seasonal autoregressive fractionally integrated moving‐average models in the presence of an additional measurement error and show that the spectral maximum Whittle likelihood estimator is asymptotically normal. We illustrate by simulation that ignoring measurement errors may result in incorrect inference. Hence, it is pertinent to test for the presence of measurement errors, which we do by developing a likelihood ratio (LR) test within the framework of Whittle likelihood. We derive the non‐standard asymptotic null distribution of this LR test and the limiting distribution of LR test under a sequence of local alternatives. Because in practice, we do not know the order of the seasonal autoregressive fractionally integrated moving‐average model, we consider three modifications of the LR test that takes model uncertainty into account. We study the finite sample properties of the size and the power of the LR test and its modifications. The efficacy of the proposed approach is illustrated by a real‐life example.     

Potential impact of COVID-19 on ongoing clinical trials: a simulation study with the neurological Yale Global Tic Severity Scale based on the CANNA-TICS study

The COVID-19 pandemic has manifold impacts on clinical trials. In response, drug regulatory agencies and public health bodies have issued guidance on how to assess potential impacts on ongoing clinical trials and stress the importance of a risk-assessment as a pre-requisite for modifications to the clinical trial conduct. This article presents a simulation study to assess the impact on the power of an ongoing clinical trial without the need to unblind trial data and compromise trial integrity. In the context of the CANNA-TICS trial, investigating the effect of nabiximols on reducing the total tic score of the Yale Global Tic Severity Scale (YGTSS-TTS) in patients with chronic tic disorders and Tourette syndrome, the impact of the two COVID-19 related intercurrent events handled by a treatment policy strategy is investigated using a multiplicative and additive data generating model. The empirical power is examined for the analysis of the YGTSS-TTS as a continuous and dichotomized endpoint using analysis techniques adjusted and unadjusted for the occurrence of the intercurrent event. In the investigated scenarios, the simulation studies showed that substantial power losses are possible, potentially making sample size increases necessary to retain sufficient power. However, we were also able to identify scenarios with only limited loss of power. By adjusting for the occurrence of the intercurrent event, the power loss could be diminished to different degrees in most scenarios. In summary, the presented risk assessment approach may support decisions on trial modifications like sample size increases, while maintaining trial integrity.     

非线性GARCH模型在中国股市波动预测中的应用研究

股票价格频繁的波动是股票市场最明显的特征之一。股票价格的时间序列经常表现出一个时期的波动明显地大于另一时期的特征。尽管有大量证据表明,短期的金融资产价格及收益率是不可预测的[1];但目前人们普遍认为,使用特定的时间序列技术可成功地预测金融资产收益率的方差。国外学者的研究结果表明,Ｂｏｌｌｅｒｓｌｅｖ提出的广义自回归条件异方差(ＧＡＲＣＨ)模型[2]和Ｅｎｇｌｅ的自回归条件异方差(ＡＲＣＨ)模型[3],在预测金融资产收益率方差方面是最为成功的。文献[4]较全面地综述了ＧＡＲＣＨ模型的应用。简单地讲,ＧＡＲＣＨ模型的建模…     

Adaptive graph‐based multiple testing procedures

Multiple testing procedures defined by directed, weighted graphs have recently been proposed as an intuitive visual tool for constructing multiple testing strategies that reflect the often complex contextual relations between hypotheses in clinical trials. Many well‐known sequentially rejective tests, such as (parallel) gatekeeping tests or hierarchical testing procedures are special cases of the graph based tests. We generalize these graph‐based multiple testing procedures to adaptive trial designs with an interim analysis. These designs permit mid‐trial design modifications based on unblinded interim data as well as external information, while providing strong family wise error rate control. To maintain the familywise error rate, it is not required to prespecify the adaption rule in detail. Because the adaptive test does not require knowledge of the multivariate distribution of test statistics, it is applicable in a wide range of scenarios including trials with multiple treatment comparisons, endpoints or subgroups, or combinations thereof. Examples of adaptations are dropping of treatment arms, selection of subpopulations, and sample size reassessment. If, in the interim analysis, it is decided to continue the trial as planned, the adaptive test reduces to the originally planned multiple testing procedure. Only if adaptations are actually implemented, an adjusted test needs to be applied. The procedure is illustrated with a case study and its operating characteristics are investigated by simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Linear predictors of future order statistics

In this paper we establish an optimal asymptotic linear predictor which does not involve the finite-sample variance-covariance structure. Extensions to the problem of finding the best linear unbiased and simple linear unbiased predictors for k samples are given. Moreover, we obtain alternative linear predictors by modifying the covariance matrix by either an identity matrix or a diagonal matrix. For normal, logistic and Rayleigh samples of size 10, the alternative linear predictors with these modifications have high efficiency when compared with the best linear unbiased predictor.