Analyzing dependence in incidence of diabetes and heart problem using generalized bivariate geometric models with covariates

For analyzing incidence data on diabetes and health problems, the bivariate geometric probability distribution is a natural choice but remained unexplored largely due to lack of models linking covariates with the probabilities of bivariate incidence of correlated outcomes. In this paper, bivariate geometric models are proposed for two correlated incidence outcomes. The extended generalized linear models are developed to take into account covariate dependence of the bivariate probabilities of correlated incidence outcomes for diabetes and heart diseases for the elderly population. The estimation and test procedures are illustrated using the Health and Retirement Study data. Two models are shown in this paper, one based on conditional-marginal approach and the other one based on the joint probability distribution with an association parameter. The joint model with association parameter appears to be a very good choice for analyzing the covariate dependence of the joint incidence of diabetes and heart diseases. Bootstrapping is performed to measure the accuracy of estimates and the results indicate very small bias.     

Permuiation tesis for k-sample binomial data with comparisons of exact and approximate P-levels

Exact ksample permutation tests for binary data for three commonly encountered hypotheses tests are presented,, The tests are derived both under the population and randomization models . The generating function for the number of cases in the null distribution is obtained, The asymptotic distributions of the test statistics are derived . Actual significance levels are computed for the asymptotic test versions , Random sampling of the null distribution is suggested as a superior alternative to the asymptotics and an efficient computer technique for implementing the random sampling is described., finally, some numerical examples are presented and sample size guidelines given for computer implementation of the exact tests.     

Assessing the fit of finite mixture distributions

Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets.     

面板数据双因素误差回归模型序列相关和随机效应的联合LM检验

对面板数据双因素误差回归模型构造了检验序列相关和随机效应的一种联合LM检验,发现该LM统计量也是检验联合假设H0：σμ^2=λ=0的Baltagi-Li LM统计量和检验假设H0：σv^2=λ=0的Breusch-Pagan-LM统计量之和。当面板数据的个体数N充分大时,该联合LM统计量的渐近分布是χ^2（3）分布;无论双因素误差面板数据回归模型的剩余误差项是AR（1）过程还是MA（1）过程,联合LM检验是相同的,即对随机效应和一阶序列相关的联合LM检验是独立于序列相关的形式。     

A Distribution Free Test for the Equality of Scales

Situations where scale parameters are not nuisance factors to be controlled but outcomes to be explained arise in many contexts such as quality control, agricultural production systems, experimental education, the pharmaceutical industry and biology. Tests for homogeneity of variances are often of interest also as a preliminary to analysis of variance, dose-response modelling or discriminant analysis. The literature on tests for the equality of scales is vast. A test which usually stands out in terms of power and robustness against non normality is the modified Levene W50 test, however in the literature no test is found to be the most powerful one for every distribution. The goal of the article is to propose an effective method for comparing scales. More precisely, we propose a test for the equality of scales that, even though was not the most powerful one for every distribution, it has good overall performance under every type of distribution. This test has the form of a combined resampling test. It is important to note that non combined tests show good performance only in particular contexts. Size and power of the proposed test are studied via simulation and compared with many other robust tests for scale. A practical application to industrial quality control is discussed.     

ASYMPTOTIC NORMALITY OF GOODNESS-OF-FIT STATISTICS FOR SPARSE POISSON DATA

Goodness-of-fit tests for discrete data and models with parameters to be estimated are usually based on Pearson's χ2 or the Likelihood Ratio Statistic. Both are included in the family of Power-Divergence Statistics SDλ which are asymptotically χ2 distributed for the usual sampling schemes. We derive a limiting standard normal distribution for a standardization Tλ of SDλ under Poisson sampling by considering an approach with an increasing number of cells. In contrast to the χ2 asymptotics we do not require an increase of all expected values and thus meet the situation when data are sparse. Our limit result is useful even if a bootstrap test is used, because it implies that the statistic Tλ should be bootstrapped and not the sum SDλ. The peculiarity of our approach is that the models under test only specify associations. Hence we have to deal with an infinite number of nuisance parameters. We illustrate our approach with an application.     

A joint-modeling approach to assess the impact of biomarker variability on the risk of developing clinical outcome

In some clinical trials and epidemiologic studies, investigators are interested in knowing whether the variability of a biomarker is independently predictive of clinical outcomes. This question is often addressed via a naïve approach where a sample-based estimate (e.g., standard deviation) is calculated as a surrogate for the “true” variability and then used in regression models as a covariate assumed to be free of measurement error. However, it is well known that the measurement error in covariates causes underestimation of the true association. The issue of underestimation can be substantial when the precision is low because of limited number of measures per subject. The joint analysis of survival data and longitudinal data enables one to account for the measurement error in longitudinal data and has received substantial attention in recent years. In this paper we propose a joint model to assess the predictive effect of biomarker variability. The joint model consists of two linked sub-models, a linear mixed model with patient-specific variance for longitudinal data and a full parametric Weibull distribution for survival data, and the association between two models is induced by a latent Gaussian process. Parameters in the joint model are estimated under Bayesian framework and implemented using Markov chain Monte Carlo (MCMC) methods with WinBUGS software. The method is illustrated in the Ocular Hypertension Treatment Study to assess whether the variability of intraocular pressure is an independent risk of primary open-angle glaucoma. The performance of the method is also assessed by simulation studies.     

A Permutation and Combination-Based Solution on the Ranking of Multivariate Populations in the Case of Ordered Categorical Responses with Application to the Evaluation of the Indoor Environment

This article deals with the problem of classifying and ranking several multivariate populations of interests using the permutation and combination approach providing also an inferential validity of the procedure. The need to define an appropriate classification of populations, i.e., products, services, teaching courses, degree programs, and so on, is very common within many areas of applied research. Many times the populations of interest are multivariate in nature meaning that many aspects of that populations can be simultaneously observed on the same unit/subject. From a statistical point of view, when the response variable of interest is multivariate in nature, the problem may become quite difficult to cope with especially in case of ordered categorical responses, due to the large dimensionality of the parametric space. Nonparametric inference based on the NPC methodology however, allows us to overcome these limitations, without the need of referring to assume any specified random distribution.     

A method for combining p-values in meta-analysis by gamma distributions

Combining p-values from statistical tests across different studies is the most commonly used approach in meta-analysis for evolutionary biology. The most commonly used p-value combination methods mainly incorporate the z-transform tests (e.g., the un-weighted z-test and the weighted z-test) and the gamma-transform tests (e.g., the CZ method [Z. Chen, W. Yang, Q. Liu, J.Y. Yang, J. Li, and M.Q. Yang, A new statistical approach to combining p-values using gamma distribution and its application to genomewide association study, Bioinformatics 15 (2014), p. S3]). However, among these existing p-value combination methods, no method is uniformly most powerful in all situations [Chen et al. 2014]. In this paper, we propose a meta-analysis method based on the gamma distribution, MAGD, by pooling the p-values from independent studies. The newly proposed test, MAGD, allows for flexible accommodating of the different levels of heterogeneity of effect sizes across individual studies. The MAGD simultaneously retains all the characters of the z-transform tests and the gamma-transform tests. We also propose an easy-to-implement resampling approach for estimating the empirical p-values of MAGD for the finite sample size. Simulation studies and two data applications show that the proposed method MAGD is essentially as powerful as the z-transform tests (the gamma-transform tests) under the circumstance with the homogeneous (heterogeneous) effect sizes across studies.     

Variance Components Testing in ANOVA‐Type Mixed Models

The purpose of this article is threefold. First, variance components testing for ANOVA ‐type mixed models is considered, in which response may not be divided into independent sub‐vectors, whereas most of existing methods are for models where response can be divided into independent sub‐vectors. Second, testing that a certain subset of variance components is zero. Third, as normality is often violated in practice, it is desirable to construct tests under very mild assumptions. To achieve these goals, an adaptive difference‐based test and an adaptive trace‐based test are constructed. The test statistics are asymptotically normal under the null hypothesis, are consistent against all global alternatives and can detect local alternatives distinct from the null at a rate as close to n ^{? 1 ∕ 2} as possible with n being the sample size. Moreover, when the dimensions of variance components in different sets are bounded, we develop a test with chi‐square as its limiting null distribution. The finite sample performance of the tests is examined via simulations, and a real data set is analysed for illustration.     

A Discussion on Nonlinear Models for Price Decisions in Rating-Based Product Preference Models

The purpose of this article is to discuss the application of nonlinear models to price decisions in the framework of rating-based product preference models. As revealed by a comparative simulation study, when a nonlinear model is the true model, the traditional linear model fails to properly describe the true pattern. It appears to be unsatisfactory in comparison with nonlinear models, such as logistic and natural spline, which offer some advantages, the most important being the ability to take into account more than just linear and/or monotonic effects. Consequently, when we model the product preference with a nonlinear model, we are potentially able to detect its ‘best’ price level, i.e., the price at which consumer preference towards a given attribute is at its maximum. From an application point of view, this approach is very flexible in price decisions and may produce original managerial suggestions which might not be revealed by traditional methods.     

Accounting for uncertainty in extremal dependence modeling using Bayesian model averaging techniques

Modeling the joint tail of an unknown multivariate distribution can be characterized as modeling the tail of each marginal distribution and modeling the dependence structure between the margins. Classical methods for modeling multivariate extremes are based on the class of multivariate extreme value distributions. However, such distributions do not allow for the possibility of dependence at finite levels that vanishes in the limit. Alternative models have been developed that account for this asymptotic independence, but inferential statistical procedures seeking to combine the classes of asymptotically dependent and asymptotically independent models have been of limited use. We overcome these difficulties by employing Bayesian model averaging to account for both types of asymptotic behavior, and for subclasses within the asymptotically independent framework. Our approach also allows for the calculation of posterior probabilities of different classes of models, allowing for direct comparison between them. We demonstrate the use of joint tail models based on our broader methodology using two oceanographic datasets and a brief simulation study.     

Testing hypotheses about medical test accuracy: considerations for design and inference

Developing new medical tests and identifying single biomarkers or panels of biomarkers with superior accuracy over existing classifiers promotes lifelong health of individuals and populations. Before a medical test can be routinely used in clinical practice, its accuracy within diseased and non-diseased populations must be rigorously evaluated. We introduce a method for sample size determination for studies designed to test hypotheses about medical test or biomarker sensitivity and specificity. We show how a sample size can be determined to guard against making type I and/or type II errors by calculating Bayes factors from multiple data sets simulated under null and/or alternative models. The approach can be implemented across a variety of study designs, including investigations into one test or two conditionally independent or dependent tests. We focus on a general setting that involves non-identifiable models for data when true disease status is unavailable due to the nonexistence of or undesirable side effects from a perfectly accurate (i.e. ‘gold standard’) test; special cases of the general method apply to identifiable models with or without gold-standard data. Calculation of Bayes factors is performed by incorporating prior information for model parameters (e.g. sensitivity, specificity, and disease prevalence) and augmenting the observed test-outcome data with unobserved latent data on disease status to facilitate Gibbs sampling from posterior distributions. We illustrate our methods using a thorough simulation study and an application to toxoplasmosis.     

Adaptive choice of scale tests in flexible two-stage designs with applications in experimental ecology and clinical trials

In this paper, the two-sample scale problem is addressed within the rank framework which does not require to specify the underlying continuous distribution. However, since the power of a rank test depends on the underlying distribution, it would be very useful for the researcher to have some information on it in order to use the possibly most suitable test. A two-stage adaptive design is used with adaptive tests where the data from the first stage are used to compute a selector statistic to select the test statistic for stage 2. More precisely, an adaptive scale test due to Hall and Padmanabhan and its components are considered in one-stage and several adaptive and non-adaptive two-stage procedures. A simulation study shows that the two-stage test with the adaptive choice in the second stage and with Liptak combination, when it is not more powerful than the corresponding one-stage test, shows, however, a quite similar power behavior. The test procedures are illustrated using two ecological applications and a clinical trial.     

Quasi-binomial zero-inflated regression model suitable for variables with bounded support

In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros.     

Deriving a lower bound for the proportion of perceivers in replicated difference tests by means of multiple test theory

Analyzing repeated difference tests aims in significance testing for differences as well as in estimating the mean discrimination ability of the consumers. In addition to the average success probability, the proportion of consumers that may detect the difference between two products and therefore account for any increase of this probability is of interest. While some authors address the first two goals, for the latter one only an estimator directly linked to the average probability seems to be used. However, this may lead to unreasonable results. Therefore we propose a new approach based on multiple test theory. We define a suitable set of hypotheses that is closed under intersection. From this, we derive a series of hypotheses that may be sequentially tested while the overall significance level will not be violated. By means of this procedure we may determine a minimal number of assessors that must have perceived the difference between the products at least once in a while. From this, we can find a conservative lower bound for the proportion of perceivers within the consumers. In several examples, we give some insight into the properties of this new method and show that the knowledge about this lower bound might indeed be valuable for the investigator. Finally, an adaption of this approach for similarity tests will be proposed.     

A minimum variance adaptive technique for parameter estimation and hypothesis testing

This report presents numerical results of an approach for parameter estimation and hypothesis testing that does not rely on specific assumptions about the underlying distribution of errors in the measured data. This approach combines robust estimation procedures, the bootstrap method for estimation of parameter uncertainties, permutation techniques for hypothesis testing, and adaptive approaches to estimation in order to obtain the minimum variance estimator or test statistic (within a predefined class) for the data under consideration. The technique produces efficient estimators of central tendency and powerful test statistics, even for small sample sizes. (Portions of this work have been presented in preliminary form (Turkheimer et al., 1996)).     

A statistical software procedure for exact parametric and nonparametric likelihood-ratio tests for two-sample comparisons

Two-sample comparisons belonging to basic class of statistical inference are extensively applied in practice. There is a rich statistical literature regarding different parametric methods to address these problems. In this context, most of the powerful techniques are assumed to be based on normally distributed populations. In practice, the alternative distributions of compared samples are commonly unknown. In this case, one can propose a combined test based on the following decision rules: (a) the likelihood-ratio test (LRT) for equality of two normal populations and (b) the Shapiro–Wilk (S-W) test for normality. The rules (a) and (b) can be merged by, e.g., using the Bonferroni correction technique to offer the correct comparison of the samples distribution. Alternatively, we propose the exact density-based empirical likelihood (DBEL) ratio test. We develop the tsc package as the first R package available to perform the two-sample comparisons using the exact test procedures: the LRT; the LRT combined with the S-W test; as well as the newly developed DBEL ratio test. We demonstrate Monte Carlo (MC) results and a real data example to show an efficiency and excellent applicability of the developed procedure.     

Profile likelihood approaches for semiparametric copula and frailty models for clustered survival data

ABSTRACT

In clustered survival data, the dependence among individual survival times within a cluster has usually been described using copula models and frailty models. In this paper we propose a profile likelihood approach for semiparametric copula models with different cluster sizes. We also propose a likelihood ratio method based on profile likelihood for testing the absence of association parameter (i.e. test of independence) under the copula models, leading to the boundary problem of the parameter space. For this purpose, we show via simulation study that the proposed likelihood ratio method using an asymptotic chi-square mixture distribution performs well as sample size increases. We compare the behaviors of the two models using the profile likelihood approach under a semiparametric setting. The proposed method is demonstrated using two well-known data sets.     

Dynamic latent trait models with mixed hidden Markov structure for mixed longitudinal outcomes

We propose a general Bayesian joint modeling approach to model mixed longitudinal outcomes from the exponential family for taking into account any differential misclassification that may exist among categorical outcomes. Under this framework, outcomes observed without measurement error are related to latent trait variables through generalized linear mixed effect models. The misclassified outcomes are related to the latent class variables, which represent unobserved real states, using mixed hidden Markov models (MHMMs). In addition to enabling the estimation of parameters in prevalence, transition and misclassification probabilities, MHMMs capture cluster level heterogeneity. A transition modeling structure allows the latent trait and latent class variables to depend on observed predictors at the same time period and also on latent trait and latent class variables at previous time periods for each individual. Simulation studies are conducted to make comparisons with traditional models in order to illustrate the gains from the proposed approach. The new approach is applied to data from the Southern California Children Health Study to jointly model questionnaire-based asthma state and multiple lung function measurements in order to gain better insight about the underlying biological mechanism that governs the inter-relationship between asthma state and lung function development.