An update on ‘a comparative study of tests for homogeneity of variance’

Tests for equality of variances using independent samples are widely used in data analysis. Conover et al. [A comparative study of tests for homogeneity of variance, with applications to the outer continental shelf bidding data. Technometrics. 1981;23:351–361], won the Youden Prize by comparing 56 variations of popular tests for variance on the basis of robustness and power in 60 different scenarios. None of the tests they compared were robust and powerful for the skewed distributions they considered. This study looks at 12 variations they did not consider, and shows that 10 are robust for the skewed distributions they considered plus the lognormal distribution, which they did not study. Three of these 12 have clearly superior power for skewed distributions, and are competitive in terms of robustness and power for all of the distributions considered. They are recommended for general use based on robustness, power, and ease of application.     

Statistical considerations in clinical trial design with event-free survival as the primary efficacy endpoint

In late-phase confirmatory clinical trials in the oncology field, time-to-event (TTE) endpoints are commonly used as primary endpoints for establishing the efficacy of investigational therapies. Among these TTE endpoints, overall survival (OS) is always considered as the gold standard. However, OS data can take years to mature, and its use for measurement of efficacy can be confounded by the use of post-treatment rescue therapies or supportive care. Therefore, to accelerate the development process and better characterize the treatment effect of new investigational therapies, other TTE endpoints such as progression-free survival and event-free survival (EFS) are applied as primary efficacy endpoints in some confirmatory trials, either as a surrogate for OS or as a direct measure of clinical benefits. For evaluating novel treatments for acute myeloid leukemia, EFS has been gradually recognized as a direct measure of clinical benefits. However, the application of an EFS endpoint is still controversial mainly due to the debate surrounding definition of treatment failure (TF) events. In this article, we investigate the EFS endpoint with the most conservative definition for the timing of TF, which is Day 1 since randomization. Specifically, the corresponding non-proportional hazard pattern of the EFS endpoint is investigated with both analytical and numerical approaches.     

Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects

Focusing on the model selection problems in the family of Poisson mixture models (including the Poisson mixture regression model with random effects and zero‐inflated Poisson regression model with random effects), the current paper derives two conditional Akaike information criteria. The criteria are the unbiased estimators of the conditional Akaike information based on the conditional log‐likelihood and the conditional Akaike information based on the joint log‐likelihood, respectively. The derivation is free from the specific parametric assumptions about the conditional mean of the true data‐generating model and applies to different types of estimation methods. Additionally, the derivation is not based on the asymptotic argument. Simulations show that the proposed criteria have promising estimation accuracy. In addition, it is found that the criterion based on the conditional log‐likelihood demonstrates good model selection performance under different scenarios. Two sets of real data are used to illustrate the proposed method.     

Multivariate Approach for Comparative Evaluations of Customer Satisfaction with Application to Transport Services

In problems related to evaluations of products or services (e.g. in customer satisfaction analysis) the main difficulties concern the synthesis of the information, which is necessary for the presence of several evaluators and many response variables (aspects under evaluation). In this article, the problem of determining and comparing the satisfaction of different groups of customers, in the presence of multivariate response variables and using the results of pairwise comparisons is addressed. Within the framework of group ranking methods and multi criteria decision making theory, a new approach, based on nonparametric techniques, for evaluating group satisfaction in a multivariate framework is proposed and the concept of Multivariate Relative Satisfaction is defined. An application to the evaluation of public transport services, like the railway service and the urban bus service, by students of the University of Ferrara (Italy) is also discussed.     

Dynamic Forecasting Conditional Probability of Bombing Attacks Based on Time‐Series and Intervention Analysis

In recent years, various types of terrorist attacks occurred, causing worldwide catastrophes. According to the Global Terrorism Database (GTD), among all attack tactics, bombing attacks happened most frequently, followed by armed assaults. In this article, a model for analyzing and forecasting the conditional probability of bombing attacks (CPBAs) based on time‐series methods is developed. In addition, intervention analysis is used to analyze the sudden increase in the time‐series process. The results show that the CPBA increased dramatically at the end of 2011. During that time, the CPBA increased by 16.0% in a two‐month period to reach the peak value, but still stays 9.0% greater than the predicted level after the temporary effect gradually decays. By contrast, no significant fluctuation can be found in the conditional probability process of armed assault. It can be inferred that some social unrest, such as America's troop withdrawal from Afghanistan and Iraq, could have led to the increase of the CPBA in Afghanistan, Iraq, and Pakistan. The integrated time‐series and intervention model is used to forecast the monthly CPBA in 2014 and through 2064. The average relative error compared with the real data in 2014 is 3.5%. The model is also applied to the total number of attacks recorded by the GTD between 2004 and 2014.     

Estimation of error probabilities in stochastic dominance

The process of using data to infer the existence of stochastic dominance is subject to sampling error. Kroll and Levy (1980), among others, have presented simulation results for several normal and lognormal distributions which show high error probabilities for a wide range of parameter values. This paper continues this line of research and uses simulation to estimate error probabilities. Distributions considered are a pair of normals and a pair of lognormals. Analysis of these distributions is made computationally feasible through theoretical results which reduce the number of parameters of the pair of distributions from four to two.     

A robust test for autocorrelation in the presence of a structural break in variance

It has been known that when there is a break in the variance (unconditional heteroskedasticity) of the error term in linear regression models, a routine application of the Lagrange multiplier (LM) test for autocorrelation can cause potentially significant size distortions. We propose a new test for autocorrelation that is robust in the presence of a break in variance. The proposed test is a modified LM test based on a generalized least squares regression. Monte Carlo simulations show that the new test performs well in finite samples and it is especially comparable to other existing heteroskedasticity-robust tests in terms of size, and much better in terms of power.     

The generalized odd half-Cauchy family of distributions: Properties and applications

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.     

A comparative study of confidence intervals for negative binomial proportion

In this paper, we investigate four existing and three new confidence interval estimators for the negative binomial proportion (i.e., proportion under inverse/negative binomial sampling). An extensive and systematic comparative study among these confidence interval estimators through Monte Carlo simulations is presented. The performance of these confidence intervals are evaluated in terms of their coverage probabilities and expected interval widths. Our simulation studies suggest that the confidence interval estimator based on saddlepoint approximation is more appealing for large coverage levels (e.g., nominal level≤1% ) whereas the score confidence interval estimator is more desirable for those commonly used coverage levels (e.g., nominal level>1% ). We illustrate these confidence interval construction methods with a real data set from a maternal congenital heart disease study.     

Numerical evaluation of tests based on different heteroskedasticity-consistent covariance matrix estimators

This article considers the issue of performing tests in linear heteroskedastic models when the test statistic employs a consistent variance estimator. Several different estimators are considered, namely: HC0, HC1, HC2, HC3, and their bias-adjusted versions. The numerical evaluation is performed using numerical integration methods; the Imhof algorithm is used to that end. The results show that bias-adjustment of variance estimators used to construct test statistics delivers more reliable tests when they are performed for the HC0 and HC1 estimators, but the same does not hold for the HC3 estimator. Overall, the most reliable test is the HC3-based one.