Influence analysis on crossover design experiment in bioequivalence studies

Crossover designs are commonly used in bioequivalence studies. However, the results can be affected by some outlying observations, which may lead to the wrong decision on bioequivalence. Therefore, it is essential to investigate the influence of aberrant observations. Chow and Tse in 1990 discussed this issue by considering the methods based on the likelihood distance and estimates distance. Perturbation theory provides a useful tool for the sensitivity analysis on statistical models. Hence, in this paper, we develop the influence functions via the perturbation scheme proposed by Hampel as an alternative approach on the influence analysis for a crossover design experiment. Moreover, the comparisons between the proposed approach and the method proposed by Chow and Tse are investigated. Two real data examples are provided to illustrate the results of these approaches. Our proposed influence functions show excellent performance on the identification of outlier/influential observations and are suitable for use with small sample size crossover designs commonly used in bioequivalence studies. Copyright © 2013 John Wiley & Sons, Ltd.     

The plan of enrichment designs for dealing with high placebo response

To deal with high placebo response in clinical trials for psychiatric and other diseases, different enrichment designs, such as the sequential parallel design, two‐way enriched design, and sequential enriched design, have been proposed and implemented recently. Depending on the historical trial information and the trial sponsors' resources, detailed design elements are needed for determining which design to adopt. To assist in making more suitable decisions, we perform evaluations for selecting required design elements in terms of power optimization and sample size planning. We also discuss the implementation of the interim analysis related to its applicability.     

Global kernel estimator and test of varying‐coefficient autoregressive model

We propose a varying‐coefficient autoregressive model that contains additive models, varying‐ coefficient models, partially linear models and low‐dimensional interaction models as special cases. A global kernel backfitting method is proposed for the estimation and inference of parameters and unknown functions in this model. Key large‐sample results are established, including estimation consistency, asymptotic normality and the generalized likelihood ratio test for parameters and non‐parametric functions. The proposed methodology is examined by simulation studies and applied to examine the relationship between suicide news reports in the three leading newspapers and the daily number of suicides in Taiwan. The relationship between the media reporting and suicide incidence has been established and explored. The Canadian Journal of Statistics 47: 487–519; 2019 © 2019 Statistical Society of Canada     

On the use of priors in goodness‐of‐fit tests

Priors are introduced into goodness‐of‐fit tests, both for unknown parameters in the tested distribution and on the alternative density. Neyman–Pearson theory leads to the test with the highest expected power. To make the test practical, we seek priors that make it likely a priori that the power will be larger than the level of the test but not too close to one. As a result, priors are sample size dependent. We explore this procedure in particular for priors that are defined via a Gaussian process approximation for the logarithm of the alternative density. In the case of testing for the uniform distribution, we show that the optimal test is of the U‐statistic type and establish limiting distributions for the optimal test statistic, both under the null hypothesis and averaged over the alternative hypotheses. The optimal test statistic is shown to be of the Cramér–von Mises type for specific choices of the Gaussian process involved. The methodology when parameters in the tested distribution are unknown is discussed and illustrated in the case of testing for the von Mises distribution. The Canadian Journal of Statistics 47: 560–579; 2019 © 2019 Statistical Society of Canada     

Regression‐type models for extremal dependence

We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log‐likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate‐adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season.     

On the accuracy in high‐dimensional linear models and its application to genomic selection

Genomic selection is today a hot topic in genetics. It consists in predicting breeding values of selection candidates, using the large number of genetic markers now available owing to the recent progress in molecular biology. One of the most popular methods chosen by geneticists is ridge regression. We focus on some predictive aspects of ridge regression and present theoretical results regarding the accuracy criteria, that is, the correlation between predicted value and true value. We show the influence of singular values, the regularization parameter, and the projection of the signal on the space spanned by the rows of the design matrix. Asymptotic results in a high‐dimensional framework are given; in particular, we prove that the convergence to optimal accuracy highly depends on a weighted projection of the signal on each subspace. We discuss on how to improve the prediction. Last, illustrations on simulated and real data are proposed.     

Non‐parametric interval estimation for the partial area under the ROC curve

Accurate diagnosis of disease is a critical part of health care. New diagnostic and screening tests must be evaluated based on their abilities to discriminate diseased conditions from non‐diseased conditions. For a continuous‐scale diagnostic test, a popular summary index of the receiver operating characteristic (ROC) curve is the area under the curve (AUC). However, when our focus is on a certain region of false positive rates, we often use the partial AUC instead. In this paper we have derived the asymptotic normal distribution for the non‐parametric estimator of the partial AUC with an explicit variance formula. The empirical likelihood (EL) ratio for the partial AUC is defined and it is shown that its limiting distribution is a scaled chi‐square distribution. Hybrid bootstrap and EL confidence intervals for the partial AUC are proposed by using the newly developed EL theory. We also conduct extensive simulation studies to compare the relative performance of the proposed intervals and existing intervals for the partial AUC. A real example is used to illustrate the application of the recommended intervals. The Canadian Journal of Statistics 39: 17–33; 2011 © 2011 Statistical Society of Canada     

Label‐ and Level‐Invariant Graphical Log‐Linear Models

We introduce two types of graphical log‐linear models: label‐ and level‐invariant models for triangle‐free graphs. These models generalise symmetry concepts in graphical log‐linear models and provide a tool with which to model symmetry in the discrete case. A label‐invariant model is category‐invariant and is preserved after permuting some of the vertices according to transformations that maintain the graph, whereas a level‐invariant model equates expected frequencies according to a given set of permutations. These new models can both be seen as instances of a new type of graphical log‐linear model termed the restricted graphical log‐linear model, or RGLL, in which equality restrictions on subsets of main effects and first‐order interactions are imposed. Their likelihood equations and graphical representation can be obtained from those derived for the RGLL models.