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Objective To examine a robust relative risk (RR) estimation for survey data analysis with ideal inferential properties under various model assumptions. Data sources We employed secondary data from the Household Component of the 2000-2016 U.S. Medical Expenditure Panel Survey (MEPS). Study design We investigate a broad range of data-balancing techniques by implementing influence function (IF) methods, which allows us to easily estimate the variability for the RR estimates in the complex survey setting. We conduct a simulation study of seasonal influenza vaccine effectiveness to evaluate these approaches and discuss techniques that show robust inferential performance across model assumptions. Data collection/extraction methods Demographic information, vaccine status, and self-administered questionnaire surveys were obtained from the longitudinal data files. We linked this information with medical condition files and medical event to extract the disease type and associated expenditures for each medical visit. We excluded individuals who were 18 years or younger at the beginning of each panel. Principal findings Under various model assumptions, the IF methods show robust inferential performance when the data-balancing procedures are incorporated. Once IF methods and data-balancing techniques are implemented, contingency table-based RR estimation yields a comparable result to the generalized linear model approach. We demonstrate the applicability of the proposed methods for complex survey data using 2000-2016 MEPS data. When employing these methods, we find a significant, negative association between vaccine effectiveness (VE) estimates and influenza-incurred expenditures. Conclusions We describe and demonstrate a robust method for RR estimation and relevant inferences for influenza vaccine effectiveness using MEPS data. The proposed method is flexible and can be extended to weighted data for survey data analysis. Hence, these methods have great potential for health services research, especially when data is non-experimental and imbalanced. This article is protected by copyright. All rights reserved.

Publicly available national survey data are useful for the evidence-based research to advance our understanding of important questions in the health and biomedical sciences. Appropriate variance estimation is a crucial step to evaluate the strength of evidence in the data analysis. In survey data analysis, the conventional linearization method for estimating the variance of a statistic of interest uses the variance estimator of the total based on linearized variables. We warn that this common practice may result in undesirable consequences such as susceptibility to data shift and severely inflated variance estimates, when unequal weights are incorporated into variance estimation. We propose to use the variance estimator of the mean (mean-approach) instead of the variance estimator of the total (total-approach). We show a superiority of the mean-approach through analytical investigations. A real data example (the National Comorbidity Survey Replication) and simulation-based studies strongly support our conclusion.

Sample entropy based tests, methods of sieves and Grenander estimation type procedures are known to be very efficient tools for assessing normality of underlying data distributions, in one-dimensional nonparametric settings. Recently, it has been shown that the density based empirical likelihood (EL) concept extends and standardizes these methods, presenting a powerful approach for approximating optimal parametric likelihood ratio test statistics, in a distribution-free manner. In this paper, we discuss difficulties related to constructing density based EL ratio techniques for testing bivariate normality and propose a solution regarding this problem. Toward this end, a novel bivariate sample entropy expression is derived and shown to satisfy the known concept related to bivariate histogram density estimations. Monte Carlo results show that the new density based EL ratio tests for bivariate normality behave very well for finite sample sizes. In order to exemplify the excellent applicability of the proposed approach, we demonstrate a real data example related to a study of biomarkers associated with myocardial infarction.

Bayes factors, practical tools of applied statistics, have been dealt with extensively in the literature in the context of hypothesis testing. The Bayes factor based on parametric likelihoods can be considered both as a pure Bayesian approach as well as a standard technique to compute p-values for hypothesis testing. We employ empirical likelihood methodology to modify Bayes factor type procedures for the nonparametric setting. The paper establishes asymptotic approximations to the proposed procedures. These approximations are shown to be similar to those of the classical parametric Bayes factor approach. The proposed approach is applied towards developing testing methods involving quantiles, which are commonly used to characterize distributions. We present and evaluate one and two sample distribution free Bayes factor type methods for testing quantiles based on indicators and smooth kernel functions. An extensive Monte Carlo study and real data examples show that the developed procedures have excellent operating characteristics for one-sample and two-sample data analysis.

A storm of favorable or critical publications regarding p-values-based procedures has been observed in both the theoretical and applied literature. We focus on valid definitions of p-values in the scenarios when composite null models are in effect. A valid p-value (VpV) statistic can be used to make a prefixed level-decision. In this context, Kolmogorov Smirnov goodness-of-fit tests and the normal two sample problem are considered. In particular, we examine an issue regarding the goodness-of-fit testability based on a single observation. This article exemplifies constructions of new test procedures, advocating practical reasons to implement VpV-based mechanisms. The VpV framework induces an extension of the conventional expected p-value (EPV) tool for measuring the performance of a test. Associating the EPV concept with the receiver operating characteristic (ROC) curve methodology, a well-established biostatistical approach, we propose a Youden index based optimality principle to derive critical values of decision making procedures. In these terms, the significance level alpha=0.05 can be suggested, in many situations. In light of an ROC curve analysis, we introduce partial EPVs to characterize properties of tests including their unbiasedness. We also provide the intrinsic relationship between the Bayes Factor (BF) test statistic and the BF of test statistics. Keywords: AUC; Bayes Factor; Expected p-value; Kolmogorov Smirnov tests; Likelihood ratio; Nuisance parameters; P-value; ROC curve; Pooled data; Single observation; Type I error rate; Youden index, Annals of the Institute of Statistical Mathematics. (2020)

In this note we examine the four parameter beta family of distributions in the context of the beta-normal and beta-logistic distributions. In the process we highlight the concept of numerical and limiting alias distributions, which in turn relate to numerical instabilities in the numerical maximum likelihood fitting routines for these families of distributions. We conjecture that the numerical issues pertaining to fitting these multiparameter distributions may be more widespread than has originally been reported across several families of distributions.

The scientific literature has addressed widely the theoretical and applied framework based on probability weighted moments (PWMs). PWMs generalize the concept of conventional moments of a probability function. These methods are commonly applied for modeling extremes of natural phenomena. We propose and examine empirical likelihood (EL) inference methods for PWMs. This approach extends the classical EL technique for evaluating usual moments, including the population mean. We provide an asymptotic proposition, extending a well-known nonparametric version of Wilks theorem used to evaluate the Type I error rates of EL ratio tests. This result is applied in order to develop a powerful nonparametric EL ratio test and the corresponding distribution-free confidence interval (CI) estimation of the PWMs. We show that the proposed method can be easily employed towards inference of the Gini index, a widely used measure for assessing distributional inequality. An extensive Monte Carlo (MC) study shows that the proposed technique provides a well-controlled Type I error rate, as well as very accurate CI estimation, that outperforms the CI estimation based on the classical schemes to analyze the PWMs. These results are clearly observed in the cases when underlying data are skewed and/or consist of a relatively small number of data points. A real data example of myocardial infarction disease is used to illustrate the applicability of the proposed method.

Bayesian credible interval (CI) estimation is a statistical procedure that has been well addressed in both the theoretical and applied literature. Parametric assumptions regarding baseline data distributions are critical for the implementation of this method. We provide a nonparametric technique for incorporating prior information into the equal-tailed (ET) and highest posterior density (HPD) CI estimators in the Bayesian manner. We propose to use a data-driven likelihood function, replacing the parametric likelihood function to create a distribution-free posterior. Higher order asymptotic propositions are derived to show the efficiency and consistency of the proposed method. We demonstrate that the proposed approach may correct confidence regions with respect to skewness of the data distribution. An extensive Monte Carlo (MC) study confirms the proposed method significantly outperforms the classical CI estimation in a frequentist context. A real data example related to a study of myocardial infar...

The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. We rigorously derive the EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest. The focus of our approach is on an integrated Kullback-Leibler distance between the EL-based posterior and prior density functions. The EL prior density is the density function for which the corresponding posterior form is asymptotically negligibly different from the EL. We show that the proposed result can be used to develop a methodology for reducing the asymptotic bias of solutions of general estimating equations and M-estimation schemes by removing the first-order term. This technique is developed in a similar manner to methods employed to reduce the asymptotic bias of maximum likelihood estimates via penalizing the underlying parametric likelihoods by their Jeffreys invariant priors. A real data example related to a study of myocardial infarction illustrates the attractiveness of the proposed technique in practical aspects. Keywords: Asymptotic bias, Biased estimating equations, Empirical likelihood, Expected Kullback-Leibler distance, Penalized likelihood, Reference prior.

The inverse Gaussian (IG) distribution is widely used to model positively skewed data. An important issue is to develop a powerful goodness-of-fit test for the IG distribution. We propose and examine novel test statistics for testing the IG goodness of fit based on the density-based empirical likelihood (EL) ratio concept. To construct the test statistics, we use a new approach that employs a method of the minimization of the discrimination information loss estimator to minimize Kullback–Leibler type information. The proposed tests are shown to be consistent against wide classes of alternatives. We show that the density-based EL ratio tests are more powerful than the corresponding classical goodness-of-fit tests. The practical efficiency of the tests is illustrated by using real data examples.

The receiver operating characteristic (ROC) curve is a popular technique with applications, for example, investigating an accuracy of a biomarker to delineate between disease and non-disease groups. A common measure of accuracy of a given diagnostic marker is the area under the ROC curve (AUC). In contrast with the AUC, the partial area under the ROC curve (pAUC) looks into the area with certain specificities (i.e., true negative rate) only, and it can be often clinically more relevant than examining the entire ROC curve. The pAUC is commonly estimated based on a U-statistic with the plug-in sample quantile, making the estimator a non-traditional U-statistic. In this article, we propose an accurate and easy method to obtain the variance of the nonparametric pAUC estimator. The proposed method is easy to implement for both one biomarker test and the comparison of two correlated biomarkers because it simply adapts the existing variance estimator of U-statistics. In this article, we show accuracy and other advantages of the proposed variance estimation method by broadly comparing it with previously existing methods. Further, we develop an empirical likelihood inference method based on the proposed variance estimator through a simple implementation. In an application, we demonstrate that, depending on the inferences by either the AUC or pAUC, we can make a different decision on a prognostic ability of a same set of biomarkers. Copyright © 2016 John Wiley & Sons, Ltd.

Evaluations of relationships between pairs of variables, including testing for independence, are increasingly important. Erich Leo Lehmann noted that “the study of the power and efficiency of tests of independence is complicated by the difficulty of defining natural classes of alternatives to the hypothesis of independence.” This paper presents a general review, discussion and comparison of classical and novel tests of independence. We investigate a broad spectrum of dependence structures with/without random effects, including those that are well addressed in both the applied and the theoretical scientific literatures as well as scenarios when the classical tests of independence may break down completely. Motivated by practical considerations, the impact of random effects in dependence structures are studied in the additive and multiplicative forms. A novel index of dependence is proposed based on the area under the Kendall plot. In conjunction with the scatterplot and the Kendall plot, the proposed method provides a comprehensive presentation of the data in terms of graphing and conceptualizing the dependence. We also present a graphical methodology based on heat maps to effectively compare the powers of various tests. Practical examples illustrate the use of various tests of independence and the graphical representations of dependence structures.