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Direct, indirect and synthetic estimators have a long history in official statistics. While model-based or model-assisted approaches have become very popular, direct and indirect estimators remain the predominant standard and are therefore important tools in practice. This is mainly due to their simplicity, including low data requirements, assumptions and straightforward inference. With the increasing use of domain estimates in policy, the demands on these tools have also increased. Today, they are frequently used for comparative statistics. This requires appropriate tools for simultaneous inference. We study devices for constructing simultaneous confidence intervals and show that simple tools like the Bonferroni correction can easily fail. In contrast, uniform inference based on max-type statistics in combination with bootstrap methods, appropriate for finite populations, work reasonably well. We illustrate our methods with frequently applied estimators of totals and means.

Given k (≥2) independent and normally distributed populations with unknown means and unknown (and possibly unequal) variances, we used the single-stage sampling procedure for multiple comparison with a control to the problem of unequal sample sizes. A simulation of the family-wise error type I was conducted to validate the quality of the procedure and a numerical example was provided for illustrating this procedure. We provided a user-friendly interface by R shiny to obtain the critical values for the practitioners. [ABSTRACT FROM AUTHOR]

Direct, indirect and synthetic estimators have a long history in official statistics. While model-based or model-assisted approaches have become very popular, direct and indirect estimators remain the predominant standard and are therefore important tools in practice. This is mainly due to their simplicity, including low data requirements, assumptions and straightforward inference. With the increasing use of domain estimates in policy, the demands on these tools have also increased. Today, they are frequently used for comparative statistics. This requires appropriate tools for simultaneous inference. We study devices for constructing simultaneous confidence intervals and show that simple tools like the Bonferroni correction can easily fail. In contrast, uniform inference based on max-type statistics in combination with bootstrap methods, appropriate for finite populations, work reasonably well. We illustrate our methods with frequently applied estimators of totals and means. [ABSTRACT FROM AUTHOR]

Introduction In practice, inferences on a quantile or several quantiles of a normal population may be more informative than inferences on the mean or variance of the population. Some researchers discussed the problem of making inferences on several quantiles when the underlying population has a normal distribution. They described that constructing a set of simultaneous confidence intervals (SCI) for several normal quantiles may be of interest in medicine or engineering studies (e.g. in the body weight or blood pressure or drug-drug interaction studies or in measuring the reliability of systems). We consider the problem of constructing SCI for all quantiles of a normal population. We propose an exact set of SCI for all normal quantiles. We also propose two algorithms for calculating the required critical values. Then, we illustrate and discuss the performance of the methods with two real examples and a simulation study. Material and Methods Suppose that X1, ... ,Xn1is a random sample of size ݊n ≥ 2 from a normal population with mean μ and variance σ2. Let ܼZp denote the p-th quantile of the standard normal distribution and let qp = μ+Zpσ denote the p-th quantile of a normal population. If ܺx̄ and ܵS2 are the sample mean and variance, q̂p = x̄+aSzp is the uniformly minimum variance unbiased estimator (UMVUE) of qpwhere ܽa = √(n-1)/2Γ((n-1)/2)/Γ(n/2). The UMVUE of vp = var(q̂p) = bpσ2 is ...p = bpS2where bp1/݊ n+Zp2(a2-1). We propose T = maxp∈(0,1) |Tp| where Tp = (q̂p-qp)/...p1/2 as a pivotal quantity for constructing SCI for qp for all p ∈ (0,1). We derived the maximum value of ܶ in a closed form and consequently, we could provide two numerical algorithms to calculate the required critical values of T. Results and discussion Rosenkrantz [3] proposed a conservative set of SCI for qp for all p ∈ (0,1). Rosenkrantz proposed to draw the graph of the empirical quantile along with the corresponding simultaneous upper and lower bounds for these quantiles. He mentioned that “the more the parent distribution of the data departs from the normal, the more likely the empirical quantile plot will have points that lie outside these bounds.” Although the proposed bands by Rosenkrantz are easily computable, they are not optimal (they are conservative). Our proposed SCI are exact and thus these bands are narrower than those of Rosenkrantz. Therefore, our proposed set of SCI performs better than the one proposed by Rosenkrantz in terms of the volume of the SCI. Liu et al. [4] also proposed SCI for several normal quantiles. Although the proposed SCI by Liu et al. is exact, they are not for all normal quantiles. Our proposed SCI is also applicable for several normal quantiles and in this case, our SCI will be conservative. However, the performance of our SCI is comparable with that of Liu et al. when the number of considered quantiles and sample sizes are increased. Our findings are valid when the underlying population is normally distributed; however, these results can be extended to the log-normal populations. When the population distribution is not known, constructing a set of non-parametric SCI for all quantiles is a complicated task. One can refer to [4] for more discussion. Conclusion We proposed an exact set of SCI for all normal quantiles. We could derive a closed form of the pivotal quantity and its distribution function. Therefore, we could calculate the required critical values. Our proposed SCI performs better than or comparable with the existing methods in terms of the volume of SCI. Therefore, our proposed SCI can be recommended in practice for making simultaneous inferences on several normal quantiles. [ABSTRACT FROM AUTHOR]

We propose a method to construct simultaneous confidence intervals for a parameter vector from inverting a series of randomization tests (RT). The randomization tests are facilitated by an efficient multivariate Robbins–Monro procedure that takes the correlation information of all components into account. The estimation method does not require any distributional assumption of the population other than the existence of the second moments. The resulting simultaneous confidence intervals are not necessarily symmetric about the point estimate of the parameter vector but possess the property of equal tails in all dimensions. In particular, we present the constructing the mean vector of one population and the difference between two mean vectors of two populations. Extensive simulation is conducted to show numerical comparison with four methods. We illustrate the application of the proposed method to test bioequivalence with multiple endpoints on some real data. [ABSTRACT FROM AUTHOR]

Three-arm 'gold-standard' non-inferiority trials are recommended for indications where only unstable reference treatments are available and the use of a placebo group can be justified ethically. For such trials, several study designs have been suggested that use the placebo group for testing 'assay sensitivity', that is, the ability of the trial to replicate efficacy. Should the reference fail in the given trial, then non-inferiority could also be shown with an ineffective experimental treatment and hence becomes useless. In this article, we extend the so-called Koch-Röhmel design where a proof of efficacy for the experimental treatment is required in order to qualify for the non-inferiority test. While the efficacy of the experimental treatment is an indication of assay sensitivity, it does not guarantee that the reference is sufficiently efficient to let the non-inferiority claim be meaningful. It has, therefore, been suggested to adaptively test the non-inferiority only if the reference demonstrates superiority to placebo and otherwise to test δ -superiority of the experimental treatment over placebo, where δ is chosen in such a way that it provides proof of non-inferiority with regard to the reference's historical effect. In this article, we extend the previous work by complementing its adaptive test with compatible simultaneous confidence intervals. Confidence intervals are commonly used and suggested by regulatory guidelines for non-inferiority trials. We show how to adopt different approaches to simultaneous confidence intervals from the literature to the setting of three-arm non-inferiority trials and compare these methods in a simulation study. Finally, we apply these methods to a real clinical trial example. [ABSTRACT FROM AUTHOR]

In this article, we consider a parallelism test and confidence interval of level difference with uniform covariance structure wherein each dataset has a monotone missing data. A likelihood ratio test statistic is derived using the maximum likelihood estimators of the parameters for the transformed dataset of a contrast matrix. Furthermore, its exact null distribution is presented using a contrast transformation matrix. Moreover, an approximate confidence interval of level difference in two sample problem is presented under parallelism using the upper percentiles of Student's t-distribution. Finally, a Monte Carlo simulation and a numerical example are given. [ABSTRACT FROM AUTHOR]

In otolaryngologic studies, subjects may contribute either unilateral observations from only one ear or bilateral observations from a pair of ears. For bilateral subjects, each person contributes information from two ears, the values of which are generally highly correlated. To avoid the confounding effect in stratified otolaryngologic studies, stratified data analysis is an important research topic. Based on the dependence model in stratified designs, this article presents five simultaneous confidence intervals (CIs) and two bootstrap simultaneous CIs for proportion differences with combined unilateral and bilateral data. Six approximate CIs and two bootstrap CIs for the common proportion difference are also developed. The proposed CIs are evaluated by empirical coverage probability, empirical coverage width and the ratio of mesial non-coverage probability to the non-coverage probability. Simulation results show that the simultaneous CIs based on Wilson method, the inverse hyperbolic tangent transformation, score statistic and the bootstrap percentile simultaneous CIs perform well and hence be recommended for applications, score CI and the CI based on Cochran statistic for the common proportion difference behave well even under small sample sizes, other CIs produce good performance when sample size is not small. A real otolaryngology study data is used to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test. We demonstrate the proposed approach with ANOVA problems for functional data and sparse count data. The proposed methodology is shown to work well in simulations and several real data applications. [ABSTRACT FROM AUTHOR]

Abstract Background To detect changes in biological processes, samples are often studied at several time points. We examined expression data measured at different developmental stages, or more broadly, historical data. Hence, the main assumption of our proposed methodology was the independence between the examined samples over time. In addition, however, the examinations were clustered at each time point by measuring littermates from relatively few mother mice at each developmental stage. As each examination was lethal, we had an independent data structure over the entire history, but a dependent data structure at a particular time point. Over the course of these historical data, we wanted to identify abrupt changes in the parameter of interest - change points. Results In this study, we demonstrated the application of generalized hypothesis testing using a linear mixed effects model as a possible method to detect change points. The coefficients from the linear mixed model were used in multiple contrast tests and the effect estimates were visualized with their respective simultaneous confidence intervals. The latter were used to determine the change point(s). In small simulation studies, we modelled different courses with abrupt changes and compared the influence of different contrast matrices. We found two contrasts, both capable of answering different research questions in change point detection: The Sequen contrast to detect individual change points and the McDermott contrast to find change points due to overall progression. We provide the R code for direct use with provided examples. The applicability of those tests for real experimental data was shown with in-vivo data from a preclinical study. Conclusion Simultaneous confidence intervals estimated by multiple contrast tests using the model fit from a linear mixed model were capable to determine change points in clustered expression data. The confidence intervals directly delivered interpretable effect estimates representing the strength of the potential change point. Hence, scientists can define biologically relevant threshold of effect strength depending on their research question. We found two rarely used contrasts best fitted for detection of a possible change point: the Sequen and McDermott contrasts.

Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, which combines the binomial and gamma distributions. Precipitation in various areas of a country can be estimated by using simultaneous confidence intervals (CIs) for the ratios of the means of multiple zero-inflated gamma populations. Herein, we propose six simultaneous CIs constructed using the fiducial generalized CI method, Bayesian and highest posterior density (HPD) interval methods based on the Jeffreys'rule or uniform prior, and method of variance estimates recovery (MOVER). The performances of the proposed simultaneous CI methods were evaluated using a Monte Carlo simulation in terms of the coverage probabilities and expected lengths. The results from a comparative simulation study show that the HPD interval based on the Jeffreys'rule prior performed the best in most cases, while in some situations, the fiducial generalized CI performed well. All of the methods were applied to estimate the simultaneous CIs for the ratios of the means of natural rainfall data from six regions in Thailand. [ABSTRACT FROM AUTHOR]

In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μ m (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Background: To detect changes in biological processes, samples are often studied at several time points. We examined expression data measured at different developmental stages, or more broadly, historical data. Hence, the main assumption of our proposed methodology was the independence between the examined samples over time. In addition, however, the examinations were clustered at each time point by measuring littermates from relatively few mother mice at each developmental stage. As each examination was lethal, we had an independent data structure over the entire history, but a dependent data structure at a particular time point. Over the course of these historical data, we wanted to identify abrupt changes in the parameter of interest - change points. Results: In this study, we demonstrated the application of generalized hypothesis testing using a linear mixed effects model as a possible method to detect change points. The coefficients from the linear mixed model were used in multiple contrast tests and the effect estimates were visualized with their respective simultaneous confidence intervals. The latter were used to determine the change point(s). In small simulation studies, we modelled different courses with abrupt changes and compared the influence of different contrast matrices. We found two contrasts, both capable of answering different research questions in change point detection: The Sequen contrast to detect individual change points and the McDermott contrast to find change points due to overall progression. We provide the R code for direct use with provided examples. The applicability of those tests for real experimental data was shown with in-vivo data from a preclinical study. Conclusion: Simultaneous confidence intervals estimated by multiple contrast tests using the model fit from a linear mixed model were capable to determine change points in clustered expression data. The confidence intervals directly delivered interpretable effect estimates representing the strength of the potential change point. Hence, scientists can define biologically relevant threshold of effect strength depending on their research question. We found two rarely used contrasts best fitted for detection of a possible change point: the Sequen and McDermott contrasts. [ABSTRACT FROM AUTHOR]

In modern drug development, genotype information becomes more frequently collected in randomized controlled trials (RCTs) for individualized risk prediction and personalized medicine development. Finding single nucleotide polymorphisms (SNPs) that are predictive of differential treatment efficacy, measured by a clinical outcome, is fundamentally different and more challenging than the traditional association test for a quantitative trait. With the objective to confidently identify and infer genetic subgroups with enhanced treatment efficacy from a large RCT for an eye disease, age‐related macular degeneration (AMD), where the clinical endpoint is binary (progressed or not), we propose a novel SNP‐testing procedure for binary clinical outcomes. Specifically, we formulate four contrasts to simultaneously assess all possible genetic effects on a logic‐respecting efficacy measure, the relative risk (between treatment and control). Our method controls both within‐ and across‐SNP multiplicity rigorously. We then use real genotype data to perform chromosome‐wide simulations to evaluate our method performance and to provide practical recommendations. Finally, we apply the proposed method to perform a genome‐wide SNP testing for the AMD trial and successfully identify multiple gene regions with genetic subgroups exhibiting enhanced efficacy in terms of decreasing the AMD progression rate. [ABSTRACT FROM AUTHOR]

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the parameters and Kolmogorov–Smirnov type statistics. Simple explicit representations for the boundaries and for the coverage probabilities of the confidence bands are analytically derived, and the performance of the bands is compared in terms of band width and area by means of a data example. As a by-product, a novel confidence region for the location-scale parameter is obtained. Extensions of the results to related models for ordered data, such as sequential order statistics, as well as to other underlying location-scale families of distributions are discussed. [ABSTRACT FROM AUTHOR]

The welding process in aluminum is a complex process that commonly presents several issues such as weld bead discontinuity, cracks, and lack of penetration. Thus, an accurate specification of the parameters in order to achieve optimal values for the investigated responses is aimed by the industry. The present paper proposes the application of a multiobjective optimization approach considering multivariate constraints based on the simultaneous confidence intervals and the elliptical region of the correlated data. Structured experiments for the welding process of aluminum alloy (AA) 6063 TA tubes used in corona rings were performed according to a face-centered composite design with 4 factors, wire feed rate (Wf), arc voltage (V), contact tip to the workpiece distance (Ct), and motor frequency (Fr), resulting in 31 experiments. Poisson regression was applied to model the values of yield (Y), dilution (D), reinforcement index (RI), and penetration index (PI), allowing to estimate the optimal individual values with regard to the multivariate constraints. Rotated factor scores were obtained in order to replace the original data, and therefore, the factor multivariate square error was used as objective functions to be minimized through normal boundary intersection method. A satisfactory weld bead with large values of PI, D, and Y and a small value of RI was reached as prespecified by the manager of the process. [ABSTRACT FROM AUTHOR]

Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, which combines the binomial and gamma distributions. Precipitation in various areas of a country can be estimated by using simultaneous confidence intervals (CIs) for the ratios of the means of multiple zero-inflated gamma populations. Herein, we propose six simultaneous CIs constructed using the fiducial generalized CI method, Bayesian and highest posterior density (HPD) interval methods based on the Jeffreys’rule or uniform prior, and method of variance estimates recovery (MOVER). The performances of the proposed simultaneous CI methods were evaluated using a Monte Carlo simulation in terms of the coverage probabilities and expected lengths. The results from a comparative simulation study show that the HPD interval based on the Jeffreys’rule prior performed the best in most cases, while in some situations, the fiducial generalized CI performed well. All of the methods were applied to estimate the simultaneous CIs for the ratios of the means of natural rainfall data from six regions in Thailand.

In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μm (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods.

Background and Purpose: Multi-arm non-inferiority (MANI) trials, here defined as non-inferiority trials with multiple experimental treatment arms, can be useful in situations where several viable treatments exist for a disease area or for testing different dose schedules. To maintain the statistical integrity of such trials, issues regarding both design and analysis must be considered, from both the multi-arm and the non-inferiority perspectives. Little guidance currently exists on exactly how these aspects should be addressed and it is the aim of this paper to provide recommendations to aid the design of future MANI trials.Methods: A comprehensive literature review covering four databases was conducted to identify publications associated with MANI trials. Literature was split into methodological and trial publications in order to investigate the required design and analysis considerations for MANI trials and whether they were being addressed in practice.Results: A number of issues were identified that if not properly addressed, could lead to issues with the FWER, power or bias. These ranged from the structuring of trial hypotheses at the design stage to the consideration of potential heterogeneous treatment variances at the analysis stage. One key issue of interest was adjustment for multiple testing at the analysis stage. There was little consensus concerning whether more powerful p value adjustment methods were preferred to approximate adjusted CIs when presenting and interpreting the results of MANI trials. We found 65 examples of previous MANI trials, of which 31 adjusted for multiple testing out of the 39 that were adjudged to require it. Trials generally preferred to utilise simple, well-known methods for study design and analysis and while some awareness was shown concerning FWER inflation and choice of power, many trials seemed not to consider the issues and did not provide sufficient definition of their chosen design and analysis approaches.Conclusions: While MANI trials to date have shown some awareness of the issues raised within this paper, very few have satisfied the criteria of the outlined recommendations. Going forward, trials should consider the recommendations in this paper and ensure they clearly define and reason their choices of trial design and analysis techniques. [ABSTRACT FROM AUTHOR]

This paper proposes a new multiobjective optimization with elliptical constraints approach for nonlinear models implemented in a cladding process of ABNT 1020 carbon steel plate using austenitic ABNT 316L stainless steel cored wire. Stainless steel stands out among the cladding materials as it allows obtaining surfaces with determined desirable characteristics from lower cost materials. This kind of process may be controlled by a relatively small number of input variables, i.e., the wire feed rate (WF), voltage (V), welding speed (WS), and the distance from the contact tip to the workpiece (N). Besides that, many outputs can be evaluated and simultaneously optimized. In the present paper, dilution (D), yield (Y), convexity index (CI), and penetration index (PI) were investigated. In order to consider the problem's multivariate nature, techniques such as factor analysis and Bonferroni's multivariate intervals were applied combined with elliptical constraints. The response variables were mathematically modeled using Poisson regression, and the obtained results were satisfactory since accurate models were achieved. The normal boundary intersection (NBI) method produced a set of viable configurations for the input variables that allows the experimenter to encounter the best system setup regarding the importance level of each response. Feasible and non-dominated solutions were found which means that the best possible scenario considering all the constraints was reached. [ABSTRACT FROM AUTHOR]

This paper considers screening of adaptive interventions or adaptive treatment strategies embedded in a sequential multiple assignment randomized trial (SMART). As a SMART typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in efficiency after accounting for multiplicity. We propose simultaneous confidence intervals that compare the values of interventions of interest to that of the unknown best intervention by generalizing the method in Edwards and Hsu (1983). The multiple comparison with the best (MCB) intervals are applied as screening tool: an intervention with MCB interval excluding zero will be declared as inferior to the true best at a pre-specified confidence level, and hence excluded from further exploration. Simulation studies show that the proposed method outperforms the multiple comparison procedures based on Bonferroni's correction in terms of width of confidence intervals for estimation. The method is applied to analyze data from the CODIACS trial in patients with depression. • A sequential multiple assignment randomized trial (SMART) typically consists of numerous adaptive interventions, inferential procedures based on pairwise comparisons of all interventions may suffer substantial loss in efficiency after accounting for multiplicity. • We propose simultaneous confidence intervals that compare the values of interventions of interest to that of the unknown best intervention by generalizing the method in Edwards and Hsu (1983). • The multiple comparison with the best (MCB) intervals are applied as screening tool: An intervention with MCB interval excluding zero will be declared as inferior to the true best at a pre-specified confidence level, and hence excluded from further exploration. • Simulation studies show that the proposed method outperforms the multiple comparison procedures based on Bonferroni's correction in terms of width of confidence intervals for estimation. • The method is applied to analyze data from the CODIACS trial in patients with depression. [ABSTRACT FROM AUTHOR]

In many experiments and especially in translational and preclinical research, sample sizes are (very) small. In addition, data designs are often high dimensional, i.e. more dependent than independent replications of the trial are observed. The present paper discusses the applicability of max t -test-type statistics (multiple contrast tests) in high-dimensional designs (repeated measures or multivariate) with small sample sizes. A randomization-based approach is developed to approximate the distribution of the maximum statistic. Extensive simulation studies confirm that the new method is particularly suitable for analyzing data sets with small sample sizes. A real data set illustrates the application of the methods. [ABSTRACT FROM AUTHOR]

Two major problems besetting count data analysis in multiple comparisons are over-dispersion and violation of distributional assumptions of real data. In this article, we describe the simultaneous confidence interval method to inference a collection of estimable functions in generalized linear models based on quasi-likelihood estimation. We assume that the independent observations have the variance proportional to a given function of the mean. We define the pivotal quantities in an asymptotic sense. We derive the joint limiting distribution of the pivotal quantities and the asymptotic distribution of the maximum modulus statistic. In the presence of over-dispersion, large-sample approximation method is shown to be liberal in multiple comparisons. We propose a percentile-t bootstrap method based on Pearson residuals as a robust alternative. It shows that the proposed method outperforms large-sample approximation method in the spirit of attaining the overall coverage probability, even when the working variance-mean structure moderately deviates from the real structure of the underlying distribution. [ABSTRACT FROM AUTHOR]

In many experiments, several observations are taken over time or with several treatments applied to each subject. These observations tend to be highly correlated, particularly those observed adjacent to each other with respect to time. In this paper, we investigate the effect of the correlations among observations in one‐way and two‐way ANOVA. A modification of the standard tests suitable for AR(1) correlation structure is proposed and its properties are investigated. We also apply the approximations to the distribution of F tests as suggested by some authors in the past and carry out the analysis. The modified procedure allows us to have a better control of the nominal significance level α. Consequently, the multiple comparisons and multiple tests based on this modified procedure will lead to conclusions with better accuracy. [ABSTRACT FROM AUTHOR]

Considering a study design with two experimental treatments, a reference treatment and a placebo, we extend a previous approach considering the ratios of effects to a procedure for analyzing multiple ratios. The technical framework for constructing tests and compatible simultaneous confidence intervals is set in a general manner. Besides a single step procedure and its extension to a stepdown procedure, also, an informative stepwise procedure in the spirit of our previous work is developed. The latter is especially interesting, because noninferiority studies require informative confidence intervals to infer more information than just noninferiority at the prespecified margin. Results from a simulation study for the three methods are shown. We also argue that an extension to more than two experimental treatments is straightforward. [ABSTRACT FROM AUTHOR]

Summary: Analysing subgroups defined by biomarkers is of increasing importance in clinical research. In many situations the biomarker is subject to misclassification error, meaning that the subgroups are identified with imperfect sensitivity and specificity. In these cases, it is improper to assume the Cox proportional hazards model for the subgroup‐specific treatment effects for time‐to‐event data with respect to the true subgroups, since the survival distributions with respect to the diagnosed subgroups will not adhere to the proportional hazards assumption. This precludes the possibility of using simple adjustment procedures. Two approaches to modelling are considered; the corrected score approach and a method based on formally modelling the data as a mixture of Cox models using an expectation–maximization algorithm for estimation. The methods are comparable for moderate‐to‐large sample sizes, but the expectation–maximization algorithm performs better when there are 100 patients per group. An estimate of the overall population treatment effect is obtained through the interpretation of the hazard ratio as a concordance odds. The methods are illustrated on data from a renal cell cancer trial. [ABSTRACT FROM AUTHOR]

In the competitive global business environment of the 21st century, enterprises must respond effectively to customer demands. The selection of suppliers and the evaluation of their performance are becoming major challenges that face manufacturing managers. Assessing a group of suppliers and selecting one or more of them is a complex task because various criteria must be considered in the decision making process. Quality is an essential factor in qualifying a corporation to enter the marketplace. In fact, the quality of parts obtained from suppliers determines the quality of the finished product. Hence, quality is the fundamental factor for supplier evaluation among various criteria. This study applies the process incapability index C pp to develop an evaluation model that assesses the quality performance of suppliers. The model simplifies the evaluation of suppliers, facilitates their effective selection, and provides insights into the process situation of suppliers who may enter into a long-term partnership with a company. [ABSTRACT FROM AUTHOR]

We develop purely nonparametric multiple inference methods for general multivariate data that neither assume any specific data distribution nor identical covariance matrices across the treatment groups. Continuous, discrete, and even ordered categorical (ordinal) data can be analyzed with these procedures in a unified way. To test hypotheses formulated in terms of purely nonparametric treatment effects, we derive pseudo-rank based multiple contrast tests and simultaneous confidence intervals. Hereby, the simultaneous confidence intervals are compatible with the multiple comparisons. The small-sample performance of the procedures is examined in a simulation study which indicates that the proposed procedures (i) control the family-wise error rate quite accurately and (ii) have a substantially higher power under non-normality than mean-based parametric competing methods. Application of the proposed tests is demonstrated by analyzing a real data set. [ABSTRACT FROM AUTHOR]

The article constructs simultaneous (simultaneous) confidence intervals for the mean of repeated observations in a multiple linear normal regression. A numerical method is described and applied for the adjustment of point confidence intervals of the mean of repeated observations. A more accurate result is obtained by a numerical method that computes the critical value that determines the simultaneous confidence interval of a given level. We conduct numerical simulation and carry out a comparative analysis of the simultaneous confidence interval with the point confidence interval for the mean of repeated observations and for an individual observation. [ABSTRACT FROM AUTHOR]

Abstract Repeated measures designs are frequently used for planning experiments in the life or social sciences. Typical examples include the comparison of different treatments over time, where both factor levels may possess an additional structure. For such designs, the statistical analysis typically consists of several steps. If the global null is rejected, multiple comparisons are performed. Usually, general factorial repeated measures designs are inferred by classical linear mixed models. Common underlying assumptions, such as normality or variance homogeneity are, however, often not met in practice. Furthermore, when dealing with, e.g., ordinal or ordered categorical data, means are no longer meaningful to describe an effect and other effect sizes should be used. To this end, we developmultiple contrast tests for nonparametric treatment effects in general factorial repeated measures designs within this paper and equip them with a novel, asymptotically correct wild bootstrap approach. Because regulatory authorities require the calculation of confidence intervals, this work also provides simultaneous confidence intervals for linear contrasts and for the ratio of different contrasts in meaningful effects. Extensive simulations are conducted to foster the theoretical findings. Finally, the analysis of two datasets exemplify the applicability of the novel procedures. [ABSTRACT FROM AUTHOR]

This paper discusses a number of methods for adjusting treatment effect estimates in clinical trials where differential effects in several subpopulations are suspected. In such situations, the estimates from the most extreme subpopulation are often overinterpreted. The paper focusses on the construction of simultaneous confidence intervals intended to provide a more realistic assessment regarding the uncertainty around these extreme results. The methods from simultaneous inference are compared with shrinkage estimates arising from Bayesian hierarchical models by discussing salient features of both approaches in a typical application. [ABSTRACT FROM AUTHOR]

The problem is considered of modeling simultaneous confidence intervals for the mean values of multiple responses in a linear multivariate normal regression model with predictor variables defined in intervals. To solve it, a numerical way of calculating the critical value that determines the simultaneous confidence interval of a given level is used. Simultaneous confidence intervals are numerically modelled and analyzed by comparison for regression, the mean value of multiple responses, and individual observation. [ABSTRACT FROM AUTHOR]

Considerkindependent random samples such thatithsample is drawn from a two-parameter exponential population with location parameter μiand scale parameter θi, i= 1, …,k. For simultaneously testing differences between location parameters of successive exponential populations, closed testing procedures are proposed separately for the following cases (i) when scale parameters are unknown and equal and (ii) when scale parameters are unknown and unequal. Critical constants required for the proposed procedures are obtained numerically and the selected values of the critical constants are tabulated. Simulation study revealed that the proposed procedures has better ability to detect the significant differences and has more power in comparison to exiting procedures. The illustration of the proposed procedures is given using real data. [ABSTRACT FROM PUBLISHER]

In this article we review recent advances in -value-based multiple test procedures (MTPs). We begin with a brief review of the basic tests of Bonferroni and Simes. Standard stepwise MTPs derived from them using the closure method of Marcus et al. (1976) are discussed next. They include the well-known MTPs of Holm (1979), Hochberg (1988) and Hommel (1988), and their extensions and improvements. This is followed by stepwise MTPs for a priori ordered hypotheses. Next we present gatekeeping MTPs (Dmitrienko and Tamhane, 2007) for hierarchically ordered families of hypotheses with logical relations among them. Finally, we give a brief review of the graphical approach (Bretz et al., 2009) to constructing and visualizing gatekeeping and other MTPs. Simple numerical examples are given to illustrate the various procedures. [ABSTRACT FROM AUTHOR]

When multiple treatments are analyzed together with a covariate, a treatment-covariate interaction complicates the interpretation of the treatment effects. The construction of simultaneous confidence bands for differences of the treatment specific regression lines is one option to proceed. The application of these methods is difficult because they are described as a collection of special cases and the implementation requires additional programming or relies on non-standard or proprietary software. If inferential interest can be restricted to a pre-specified set of covariate values, a flexible alternative is to compute simultaneous confidence intervals for multiple contrasts of the treatment effects over this grid. This approach is available in the R software: next to treatment differences in the linear model, approximate simultaneous confidence intervals for ratios of expected values and asymptotic extensions to generalized linear models are straightforward. The paper summarizes the available methodology and presents three case studies to illustrate the application to different models, differences and ratios, as well as different types of between treatment comparisons. Simulation studies in the general linear model, for different parameters and different types of comparisons are provided. The R code to reproduce the case studies and a hint to a related R package is provided. [ABSTRACT FROM AUTHOR]

Most interval estimates are derived from computable conditional distributions conditional on the data. In this article, we call the random variables having such conditional distributions confidence distribution variables and define their finite-sample breakdown values. Based on this, the definition of breakdown value of confidence intervals is introduced, which covers the breakdowns in both the coverage probability and interval length. High-breakdown confidence intervals are constructed by the structural method in location-scale families. Simulation results are presented to compare the traditional confidence intervals and their robust analogues. [ABSTRACT FROM AUTHOR]

In parametric statistics, confidence bands for continuous distribution (quantile) functions may be constructed by unifying the graphs of all distribution (quantile) functions corresponding to parameters lying in some confidence region. It is then desirable that the coverage probabilities of both, band and region, coincide, e.g., to prevent from wide and less informative bands or to transfer the property of unbiasedness; this is ensured if the confidence region is exhaustive. Properties and representations of exhaustive confidence regions are presented. In location-scale families, the property of some confidence region to be exhaustive depends on the boundedness of the supports of the distributions in the family. For unbounded, one-sided bounded and bounded supports, characterizations of exhaustive confidence regions are derived. The results are useful to decide whether the trapezoidal confidence regions based on the standard pivotal quantities are exhaustive and may serve to construct exhaustive confidence regions in (log-)location-scale models. [ABSTRACT FROM AUTHOR]

Composite endpoints are widely used as primary endpoints of randomized controlled trials across clinical disciplines. A common critique of the conventional analysis of composite endpoints is that all disease events are weighted equally, whereas their clinical relevance may differ substantially. We address this by introducing a framework for the weighted analysis of composite endpoints and interpretable test statistics, which are applicable to both binary and time-to-event data. To cope with the difficulty of selecting an exact set of weights, we propose a method for constructing simultaneous confidence intervals and tests that asymptotically preserve the family-wise type I error in the strong sense across families of weights satisfying flexible inequality or order constraints based on the theory of χ¯2-distributions. We show that the method achieves the nominal simultaneous coverage rate with substantial efficiency gains over Scheffé's procedure in a simulation study and apply it to trials in cardiovascular disease and enteric fever. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. [ABSTRACT FROM AUTHOR]

When a moderate number of potential predictors are available and a survival model is fit with regularization to achieve variable selection, providing accurate inference on the predicted survival can be challenging. We investigate inference on the predicted survival estimated after fitting a Cox model under regularization guaranteeing the oracle property. We demonstrate that existing asymptotic formulas for the standard errors of the coefficients tend to underestimate the variability for some coefficients, while typical resampling such as the bootstrap tends to overestimate it; these approaches can both lead to inaccurate variance estimation for predicted survival functions. We propose a two-stage adaptation of a resampling approach that brings the estimated error in line with the truth. In stage 1, we estimate the coefficients in the observed data set and in [Formula: see text] resampled data sets, and allow the resampled coefficient estimates to vote on whether each coefficient should be 0. For those coefficients voted as zero, we set both the point and interval estimates to [Formula: see text] In stage 2, to make inference about coefficients not voted as zero in stage 1, we refit the penalized model in the observed data and in the [Formula: see text] resampled data sets with only variables corresponding to those coefficients. We demonstrate that ensemble voting-based point and interval estimators of the coefficients perform well in finite samples, and prove that the point estimator maintains the oracle property. We extend this approach to derive inference procedures for survival functions and demonstrate that our proposed interval estimation procedures substantially outperform estimators based on asymptotic inference or standard bootstrap. We further illustrate our proposed procedures to predict breast cancer survival in a gene expression study. [ABSTRACT FROM AUTHOR]

A method is proposed to construct simultaneous confidence intervals for multiple linear combinations of generalized linear model parameters, that uses a multivariate normal- ort-distribution together with the signed likelihood root statistic. In an application to a case study simultaneous confidence bands for logistic regression are calculated. A simulation study based on the example evaluation suggests superior performance compared to the common Wald-type approaches. The proposed methods are readily implemented in the R extension package mcprofile. [ABSTRACT FROM PUBLISHER]

This article deals with simultaneous comparisons of k(k ⩾ 1) populations with a control population with respect to variance in direction-mixed families of hypotheses. Computation of critical constants required for the implementation of the proposed procedures is discussed and selected values of the critical constants are tabulated. Power comparison of the proposed procedures with their existing competitors is carried out using Monte Carlo simulation. An example is given to illustrate the implementation of proposed procedures. [ABSTRACT FROM AUTHOR]

We consider the problem of simultaneously estimating Poisson rate differences via applications of the Hsu and Berger stepwise confidence interval method (termed HBM), where comparisons to a common reference group are performed. We discuss continuity-corrected confidence intervals (CIs) and investigate the HBM performance with a moment-based CI, and uncorrected and corrected for continuity Wald and Pooled confidence intervals (CIs). Using simulations, we compare nine individual CIs in terms of coverage probability and the HBM with nine intervals in terms of family-wise error rate (FWER) and overall and local power. The simulations show that these statistical properties depend highly on parameter settings. [ABSTRACT FROM AUTHOR]