Asymptotic equivalence of the harrell-davis median estimator and the sample median

This paper presents an asymptotic equivalence result with a sharp rate of convergence forthe sample median and the Harrell-Davis median estimator. The consequences of this result are discussed.     

Practical guide to sample size calculations: non‐inferiority and equivalence trials

A sample size justification is a vital part of any trial design. However, estimating the number of participants required to give a meaningful result is not always straightforward. A number of components are required to facilitate a suitable sample size calculation. In this paper, the steps for conducting sample size calculations for non‐inferiority and equivalence trials are summarised. Practical advice and examples are provided that illustrate how to carry out the calculations by hand and using the app SampSize. Copyright © 2015 John Wiley & Sons, Ltd.     

Confidence intervals for the difference between independent binomial proportions: comparison using a graphical approach and moving averages

This paper uses graphical methods to illustrate and compare the coverage properties of a number of methods for calculating confidence intervals for the difference between two independent binomial proportions. We investigate both small‐sample and large‐sample properties of both two‐sided and one‐sided coverage, with an emphasis on asymptotic methods. In terms of aligning the smoothed coverage probability surface with the nominal confidence level, we find that the score‐based methods on the whole have the best two‐sided coverage, although they have slight deficiencies for confidence levels of 90% or lower. For an easily taught, hand‐calculated method, the Brown‐Li ‘Jeffreys’ method appears to perform reasonably well, and in most situations, it has better one‐sided coverage than the widely recommended alternatives. In general, we find that the one‐sided properties of many of the available methods are surprisingly poor. In fact, almost none of the existing asymptotic methods achieve equal coverage on both sides of the interval, even with large sample sizes, and consequently if used as a non‐inferiority test, the type I error rate (which is equal to the one‐sided non‐coverage probability) can be inflated. The only exception is the Gart‐Nam ‘skewness‐corrected’ method, which we express using modified notation in order to include a bias correction for improved small‐sample performance, and an optional continuity correction for those seeking more conservative coverage. Using a weighted average of two complementary methods, we also define a new hybrid method that almost matches the performance of the Gart‐Nam interval. Copyright © 2014 John Wiley & Sons, Ltd.     

Methods for one-sided testing of the difference between proportions and sample size considerations related to non-inferiority clinical trials

Assessment of non-inferiority is often performed using a one-sided statistical test through an analogous one-sided confidence limit. When the focus of attention is the difference in success rates between test and active control proportions, the lower confidence limit is computed, and many methods exist in the literature to address this objective. This paper considers methods which have been shown to be popular in the literature and have surfaced in this research as having good performance with respect to controlling type I error at the specified level. Performance of these methods is assessed with respect to power and type I error through simulations. Sample size considerations are also included to aid in the planning stages of non-inferiority trials focusing on the difference in proportions. Results suggest that the appropriate method to use depends on the sample size allocation of subjects in the test and active control groups.     

Multiple comparisons to both a negative and a positive control

This paper addresses multiple comparisons in the presence of both a negative and a positive control. The methodology of the three-arm trial is extended to the case of many experimental treatment arms or different doses of a compound. In contrast to the classic three-arm trial, the focus is on the family-wise error type I. Normally distributed data with either homogeneous or heterogeneous group variances are considered. Explicit criteria for an optimal allocation are proposed. Depending on the pattern of heterogeneity, remarkably unbalanced designs are power-optimal. As an example, the method will be applied to a toxicological experiment.     

Simultaneous confidence interval for assessing non‐inferiority with assay sensitivity in a three‐arm trial with binary endpoints

A three‐arm trial including an experimental treatment, an active reference treatment and a placebo is often used to assess the non‐inferiority (NI) with assay sensitivity of an experimental treatment. Various hypothesis‐test‐based approaches via a fraction or pre‐specified margin have been proposed to assess the NI with assay sensitivity in a three‐arm trial. There is little work done on confidence interval in a three‐arm trial. This paper develops a hybrid approach to construct simultaneous confidence interval for assessing NI and assay sensitivity in a three‐arm trial. For comparison, we present normal‐approximation‐based and bootstrap‐resampling‐based simultaneous confidence intervals. Simulation studies evidence that the hybrid approach with the Wilson score statistic performs better than other approaches in terms of empirical coverage probability and mesial‐non‐coverage probability. An example is used to illustrate the proposed approaches.     

Exact sample-size determination in testing non-inferiority under a simple crossover trial

For testing the non-inferiority (or equivalence) of an experimental treatment to a standard treatment, the odds ratio (OR) of patient response rates has been recommended to measure the relative treatment efficacy. On the basis of an exact test procedure proposed elsewhere for a simple crossover design, we develop an exact sample-size calculation procedure with respect to the OR of patient response rates for a desired power of detecting non-inferiority at a given nominal type I error. We note that the sample size calculated for a desired power based on an asymptotic test procedure can be much smaller than that based on the exact test procedure under a given situation. We further discuss the advantage and disadvantage of sample-size calculation using the exact test and the asymptotic test procedures. We employ an example by studying two inhalation devices for asthmatics to illustrate the use of sample-size calculation procedure developed here.     

Nonparametric estimation of the limiting availability

The point availability of a repairable system is the probability that the system is operating at a specified time. As time increases, the point availability converges to a positive constant called the limiting availability. Baxter and Li (1994a) developed a technique for constructing nonparametric confidence intervals for the point availability. However, nonparametric estimators of the limiting availability have not previously been studied in the literature. In this paper, we consider two separate cases: (1) the data are complete and (2) the data are subject to right censorship. For each case, a nonparametric confidence interval for the limiting availability is derived. Applications and simulation studies are presented.deceased after the paper was accepted     

Some inequalities in elementary special functions with applications to nonparametric statistical inference

Some inequalities are established in P₁(r, s) and P₁(r+1, s), where P₁(r, s) is the confidence coefficient of Wilks’ (1962) outer confidence interval (X_(r) X_(s)) for the quantile interval (ξ_p1, ξ_p2). An inequality concerning incomplete beta functions is also presented and it is shown to be an improved version of one of Koti's (1989) inequalities.     

Confidence intervals for the difference of marginal probabilities in clustered matched-pair binary data

Although there are several available test statistics to assess the difference of marginal probabilities in clustered matched‐pair binary data, associated confidence intervals (CIs) are not readily available. Herein, the construction of corresponding CIs is proposed, and the performance of each CI is investigated. The results from Monte Carlo simulation study indicate that the proposed CIs perform well in maintaining the nominal coverage probability: for small to medium numbers of clusters, the intracluster correlation coefficient‐adjusted McNemar statistic and its associated Wald or Score CIs are preferred; however, this statistic becomes conservative when the number of clusters is larger so that alternative statistics and their associated CIs are preferred. In practice, a combination of the intracluster correlation coefficient‐adjusted McNemar statistic with an alternative statistic is recommended. To illustrate the practical application, a real clustered matched‐pair collection of data is used to illustrate testing the difference of marginal probabilities and constructing the associated CIs. Copyright © 2012 John Wiley & Sons, Ltd.     

An extension of the median test to analysis of variance

In a k-way analysis of variance model, the major concern is testing for main effects and for the presence of interaction between the factors. When the assumptions of normality and equal variances are satisfied, the appropriate test to use is the usual F-test for ANOVA. However, when the normality assumption is not satisfied then a robust or nonparametric test is needed to conduct the analysis. In this paper a nonparametric method based on cell counts is proposed. Each cell is divided into L subcells based on predetermined outpoints and the resulting frequencies are laid out in a contingency table. Then the Pearson x² and tne likelihood ratio tests are performed. A comparison with the classical ANOVA F-test indicates that the proposed method is preferable when the data comes from a thick-tailed highly skewed distribution.     

Comparison of conditional and unconditional confidence intervals for the double exponential distribution

Conditional confidence intervals for the location parameter of the double exponential distribution based on maximum likelihood estimators conditioned on a set of ancillary statistics and the corresponding unconditional confidence intervals based on the maximum likelihood estimators alone are compared in two ways. Monte Carlo techniques are used and the conditional approach appears to give slightly better results although agreement as n becomes larger is noted     

Multiple comparisons in two-factor testing of psychophysical thresholds by the delta test method

We propose an algorithm of multiple comparisons in two-factor testing of psychophysical thresholds. We use logistic regression combined with guessing rate and adopt the step-down procedure with Ryan–Einot–Gabriel–Welsch (REGW) significance levels for multiple test. We test hypotheses of main effects and interaction in two-factor problem by using the delta test statistics.     

Issues in applying recent CPMP ‘Points to Consider’ and FDA guidance documents with biostatistical implications

The International Conference on Harmonisation guideline ‘Statistical Principles for Clinical Trials’ was adopted by the Committee for Proprietary Medicinal Products (CPMP) in March 1998, and consequently is operational in Europe. Since then more detailed guidance on selected topics has been issued by the CPMP in the form of ‘Points to Consider’ documents. The intent of these was to give guidance particularly to non‐statistical reviewers within regulatory authorities, although of course they also provide a good source of information for pharmaceutical industry statisticians. In addition, the Food and Drug Administration has recently issued a draft guideline on data monitoring committees. In November 2002 a one‐day discussion forum was held in London by Statisticians in the Pharmaceutical Industry (PSI). The aim of the meeting was to discuss how statisticians were responding to some of the issues covered in these new guidelines, and to document consensus views where they existed. The forum was attended by industry, academic and regulatory statisticians. This paper outlines the questions raised, resulting discussions and consensus views reached. It is clear from the guidelines and discussions at the workshop that the statistical analysis strategy must be planned during the design phase of a clinical trial and carefully documented. Once the study is complete the analysis strategy should be thoughtfully executed and the findings reported. Copyright © 2003 John Wiley & Sons, Ltd.     

Inference in the presence of ranking error in ranked set sampling

The author proposes inference techniques for ranked set sample data in the presence of judgment ranking errors. He bases his analysis on the models of Bohn & Wolfe (1994) and Frey (2007a, b), of which parameters are estimated by minimizing a distance measure. He then uses the fitted models to calibrate confidence intervals and tests. He shows the validity of his approach through simulation and illustrates its application through the construction of distribution‐free confidence intervals for the median area of apple tree leaves covered by a spray.