Recurrence relations for moments of progressively censored order statistics from logistic distribution with applications to inference

In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a logistic distribution. The use of these relations in a systematic manner allows us to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R₁,…,R_m). The results established here generalize the corresponding results for the usual order statistics due to [Shah, 1966] and [Shah, 1970]. These moments are then utilized to derive best linear unbiased estimators of the location and scale parameters of the logistic distribution. A comparison of these estimators with the maximum likelihood estimations is then made. The best linear unbiased predictors of censored failure times are briefly discussed. Finally, an illustrative example is presented.     

Reliability analysis of consecutive k-out-of-n systems with non-identical components lifetimes

In recent years, the study of reliability properties of consecutive k-out-of-n systems has attracted a great deal of attention from both theoretical and practical perspectives. In this paper we consider linear and circular consecutive k-out-of-n systems. It is assumed that lifetimes of components of the systems are independent but their probability distributions are non-identical. We study the reliability properties of the residual lifetimes of such systems under the condition that at least (n−r+1), r≤n, components of the system are operating. We also investigate the probability that a specific number of components of the above-mentioned system operate at time t, t>0, under the condition that the system is alive at time t.     

Why a Bayesian approach to safety analysis in pharmacovigilance is important

Large databases of routinely collected data are a valuable source of information for detecting potential associations between drugs and adverse events (AE). A pharmacovigilance system starts with a scan of these databases for potential signals of drug-AE associations that will subsequently be examined by experts to aid in regulatory decision-making. The signal generation process faces some key challenges: (1) an enormous volume of drug-AE combinations need to be tested (i.e. the problem of multiple testing); (2) the results are not in a format that allows the incorporation of accumulated experience and knowledge for future signal generation; and (3) the signal generation process ignores information captured from other processes in the pharmacovigilance system and does not allow feedback. Bayesian methods have been developed for signal generation in pharmacovigilance, although the full potential of these methods has not been realised. For instance, Bayesian hierarchical models will allow the incorporation of established medical and epidemiological knowledge into the priors for each drug-AE combination. Moreover, the outputs from this analysis can be incorporated into decision-making tools to help in signal validation and posterior actions to be taken by the regulators and companies. We discuss in this paper the apparent advantage of the Bayesian methods used in safety signal generation and the similarities and differences between the two widely used Bayesian methods. We will also propose the use of Bayesian hierarchical models to address the three key challenges and discuss the reasons why Bayesian methodology still have not been fully utilised in pharmacovigilance activities.     

A course for clinical trial personnel in clinical study designs, randomization, allocation schedules, and interactive response systems

This continuing education course for professionals involved in all areas of clinical trials integrates concepts related to the role of randomization in the scientific process. The course includes two interactive lecture and discussion sections and a workshop practicum. The first interactive lecture introduces basic clinical trial issues and statistical principles such as bias, blinding, randomization, control groups, and the importance of formulating clear and discriminating clinical and statistical hypotheses. It then focuses on the most commonly used clinical study designs and the corresponding patient randomization schemes. The second interactive lecture focuses on the implementation of randomization of patients and drug supply through allocation and component ID schedules. The workshop practicum, conducted in small groups, enables students to apply the lecture concepts to real clinical studies. Flexibility was built into the workshop practicum materials to allow the course content to be customized to specific audiences, and the interactive lecture sessions can be stretched to cover more advanced topics according to class interest and time availability.     

Robust variable selection with application to quality of life research

A large database containing socioeconomic data from 60 communities in Austria and Germany has been built, stemming from 18,000 citizens’ responses to a survey, together with data from official statistical institutes about these communities. This paper describes a procedure for extracting a small set of explanatory variables to explain response variables such as the cognition of quality of life. For better interpretability, the set of explanatory variables needs to be very small and the dependencies among the selected variables need to be low. Due to possible inhomogeneities within the data set, it is further required that the solution is robust to outliers and deviating points. In order to achieve these goals, a robust model selection method, combined with a strategy to reduce the number of selected predictor variables to a necessary minimum, is developed. In addition, this context-sensitive method is applied to obtain responsible factors describing quality of life in communities.     

A linear model-based test for the heterogeneity of conditional correlations

Current methods of testing the equality of conditional correlations of bivariate data on a third variable of interest (covariate) are limited due to discretizing of the covariate when it is continuous. In this study, we propose a linear model approach for estimation and hypothesis testing of the Pearson correlation coefficient, where the correlation itself can be modeled as a function of continuous covariates. The restricted maximum likelihood method is applied for parameter estimation, and the corrected likelihood ratio test is performed for hypothesis testing. This approach allows for flexible and robust inference and prediction of the conditional correlations based on the linear model. Simulation studies show that the proposed method is statistically more powerful and more flexible in accommodating complex covariate patterns than the existing methods. In addition, we illustrate the approach by analyzing the correlation between the physical component summary and the mental component summary of the MOS SF-36 form across a fair number of covariates in the national survey data.     

ESTIMATION OF MULTIVARIATE SHANNON ENTROPY USING MOMENTS

Three new entropy estimators of multivariate distributions are introduced. The two cases considered here concern when the distribution is supported by a unit sphere and by a unit cube. In the former case, the consistency and the upper bound of the absolute error for the proposed entropy estimator are established. In the latter one, under the assumption that only the moments of the underlying distribution are available, a non‐traditional estimator of the entropy is suggested. We also study the practical performances of the constructed estimators through simulation studies and compare the estimators based on the moment‐recovered approaches with their counterparts derived by using the histogram and k th nearest neighbour constructions. In addition, one worked example is briefly discussed.     

A quasi-Newton acceleration for high-dimensional optimization algorithms

In many statistical problems, maximum likelihood estimation by an EM or MM algorithm suffers from excruciatingly slow convergence. This tendency limits the application of these algorithms to modern high-dimensional problems in data mining, genomics, and imaging. Unfortunately, most existing acceleration techniques are ill-suited to complicated models involving large numbers of parameters. The squared iterative methods (SQUAREM) recently proposed by Varadhan and Roland constitute one notable exception. This paper presents a new quasi-Newton acceleration scheme that requires only modest increments in computation per iteration and overall storage and rivals or surpasses the performance of SQUAREM on several representative test problems.