Bayesian analysis for zero-or-one inflated proportion data using quantile regression

In this paper, we propose the use of Bayesian quantile regression for the analysis of proportion data. We also consider the case when the data present a zero-or-one inflation using a two-part model approach. For the latter scheme, we assume that the response variable is generated by a mixed discrete–continuous distribution with a point mass at zero or one. Quantile regression is then used to explain the conditional distribution of the continuous part between zero and one, while the mixture probability is also modelled as a function of the covariates. We check the performance of these models with two simulation studies. We illustrate the method with data about the proportion of households with access to electricity in Brazil.     

Analysis of overdispersed paired count data

This article is about the statistical analysis of overdispersed paired count data for comparing two treatments. The data consist of the number of events obtained in a stratum during the fixed observation period. Three types of model are discussed: the Poisson, a mixed, and a semiparametric model. Overdispersion is represented in the last two models but not in the Poisson model. Of particular interests are to examine whether there is any loss of efficiency in using the estimate of the treatment effect obtained under other two models if the mixed model is true, and also whether overdispersion leads to a larger variance of the estimate than that expected from the Poisson model. It is shown that all three models provide the same estimate of the treatment effect (i.e., there is no loss of efficiency) and that the variance of the estimate of the treatment effect obtained under the Poisson model is the same as that based on the mixed model. However, the semiparametric model provides the variance of the estimate larger than those obtained under the other two models.     

Optimal weighted two-sample t-test with partially paired data in a unified framework

In this paper, we provide a unified framework for two-sample t-test with partially paired data. We show that many existing two-sample t-tests with partially paired data can be viewed as special members in our unified framework. Some shortcomings of these t-tests are discussed. We also propose the asymptotically optimal weighted linear combination of the test statistics comparing all four paired and unpaired data sets. Simulation studies are used to illustrate the performance of our proposed asymptotically optimal weighted combinations of test statistics and compare with some existing methods. It is found that our proposed test statistic is generally more powerful. Three real data sets about CD4 count, DNA extraction concentrations, and the quality of sleep are also analyzed by using our newly introduced test statistic.     

A Bayesian semiparametric model for non negative semicontinuous data

When the target variable exhibits a semicontinuous behavior (a point mass in a single value and a continuous distribution elsewhere), parametric “two-part models” have been extensively used and investigated. The applications have mainly been related to non negative variables with a point mass in zero (zero-inflated data). In this article, a semiparametric Bayesian two-part model for dealing with such variables is proposed. The model allows a semiparametric expression for the two parts of the model by using Dirichlet processes. A motivating example, based on grape wine production in Tuscany (an Italian region), is used to show the capabilities of the model. Finally, two simulation experiments evaluate the model. Results show a satisfactory performance of the suggested approach for modeling and predicting semicontinuous data when parametric assumptions are not reasonable.     

Asymptotocally nonparametric tests with censored paired data

A class of asymptotically nonparametric test with contains a test proposed by Wei(1980), is considered for testing the equality of two continuous distribution funcitons when paired observations are subject to arbitrary right censorship. It is shown that under the null hypothesis each test statistic converges in distribution to the standard normal random variable. Furthermore. the Monte Carlo simulation results indicate that some tests in this class are more powerful than Wei's test. A generalization to incomplete censored paired data is also included.     

Dynamic paired comparison models with stochastic variances

In paired comparison experiments, the worth or merit of a unit is measured through comparisons against other units. When paired comparison outcomes are collected over time and the merits of the units may be changing, it is often convenient to assume the data follow a non-linear state-space model. Typical paired comparison state-space models that assume a fixed (unknown) autoregressive variance do not account for the possibility of sudden changes in the merits. This is a particular concern, for example, in modeling cognitive ability in human development; cognitive ability not only changes over time, but also can change abruptly. We explore a particular extension of conventional state-space models for paired comparison data that allows the state variance to vary stochastically. Models of this type have recently been developed and applied to modeling financial data, but can be seen to have applicability in modeling paired comparison data. A filtering algorithm is also derived that can be used in place of likelihood-based computations when the number of objects being compared is large. Applications to National Football League game outcomes and chess game outcomes are presented.     

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.     

Confidence intervals for the difference in paired Youden indices

Comparison of accuracy between two diagnostic tests can be implemented by investigating the difference in paired Youden indices. However, few literature articles have discussed the inferences for the difference in paired Youden indices. In this paper, we propose an exact confidence interval for the difference in paired Youden indices based on the generalized pivotal quantities. For comparison, the maximum likelihood estimate‐based interval and a bootstrap‐based interval are also included in the study for the difference in paired Youden indices. Abundant simulation studies are conducted to compare the relative performance of these intervals by evaluating the coverage probability and average interval length. Our simulation results demonstrate that the exact confidence interval outperforms the other two intervals even with small sample size when the underlying distributions are normal. A real application is also used to illustrate the proposed intervals. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive paired comparison design

An important aspect of paired comparison experiments is the decision of how to form pairs in advance of collecting data. A weakness of typical paired comparison experimental designs is the difficulty in incorporating prior information, which can be particularly relevant for the design of tournament schedules for players of games and sports. Pairing methods that make use of prior information are often ad hoc algorithms with little or no formal basis. The problem of pairing objects can be formalized as a Bayesian optimal design. Assuming a linear paired comparison model for outcomes, we develop a pairing method that maximizes the expected gain in Kullback–Leibler information from the prior to the posterior distribution. The optimal pairing is determined using a combinatorial optimization method commonly used in graph-theoretic contexts. We discuss the properties of our optimal pairing criterion, and demonstrate our method as an adaptive procedure for pairing objects multiple times. We compare the performance of our method on simulated data against random pairings, and against a system that is currently in use in tournament chess.     

An exact density-based empirical likelihood ratio test for paired data

The Wilcoxon rank-sum test and its variants are historically well-known to be very powerful nonparametric decision rules for testing no location difference between two groups given paired data versus a shift alternative. In this title, we propose a new alternative empirical likelihood (EL) ratio approach for testing the equality of marginal distributions given that sampling is from a continuous bivariate population. We show that in various shift alternative scenarios the proposed exact test is superior to the classic nonparametric procedures, which may break down completely or are frequently inferior to the density-based EL ratio test. This is particularly true in the cases where there is a nonconstant shift under the alternative or the data distributions are skewed. An extensive Monte Carlo study shows that the proposed test has excellent operating characteristics. We apply the density-based EL ratio test to analyze real data from two medical studies.     

Tests for equality of variances with paired data

The normal theory test for equality of variances with paired data is shown to be nonrobust to violation of the assumption of normality. Nonparametric tests are shown to provide a much safer alternative with little loss of efficiency.     

Exploring gillnet catch efficiency of sardines in the coastal waters of Sri Lanka by means of three statistical techniques: a comparison of linear and nonlinear modelling techniques

The present investigation was undertaken to study the gillnet catch efficiency of sardines in the coastal waters of Sri Lanka using commercial catch and effort data. Commercial catch and effort data of small mesh gillnet fishery were collected in five fisheries districts during the period May 1999–August 2002. Gillnet catch efficiency of sardines was investigated by developing catch rates predictive models using data on commercial fisheries and environmental variables. Three statistical techniques [multiple linear regression, generalized additive model and regression tree model (RTM)] were employed to predict the catch rates of trenched sardine Amblygaster sirm (key target species of small mesh gillnet fishery) and other sardines (Sardinella longiceps, S. gibbosa, S. albella and S. sindensis). The data collection programme was conducted for another six months and the models were tested on new data. RTMs were found to be the strongest in terms of reliability and accuracy of the predictions. The two operational characteristics used here for model formulation (i.e. depth of fishing and number of gillnet pieces used per fishing operation) were more useful as predictor variables than the environmental variables. The study revealed a rapid tendency of increasing the catch rates of A. sirm with increased sea depth up to around 32 m.     

Mixtures of regression models with incomplete and noisy data

The estimation of the mixtures of regression models is usually based on the normal assumption of components and maximum likelihood estimation of the normal components is sensitive to noise, outliers, or high-leverage points. Missing values are inevitable in many situations and parameter estimates could be biased if the missing values are not handled properly. In this article, we propose the mixtures of regression models for contaminated incomplete heterogeneous data. The proposed models provide robust estimates of regression coefficients varying across latent subgroups even under the presence of missing values. The methodology is illustrated through simulation studies and a real data analysis.     

Mean and cell-mean imputation resulting in the use of a semicontinuous distribution and a mixture of semicontinuous distributions

Zero-inflated models are commonly used for modeling count and continuous data with extra zeros. Inflations at one point or two points apart from zero for modeling continuous data have been discussed less than that of zero inflation. In this article, inflation at an arbitrary point α as a semicontinuous distribution is presented and the mean imputation for a continuous response is discussed as a cause of having semicontinuous data. Also, inflation at two points and generally at k arbitrary points and their relation to cell-mean imputation in the mixture of continuous distributions are studied. To analyze the imputed data, a mixture of semicontinuous distributions is used. The effects of covariates on the dependent variable in a mixture of k semicontinuous distributions with inflation at k points are also investigated. In order to find the parameter estimates, the method of expectation–maximization (EM) algorithm is used. In a real data of Iranian Households Income and Expenditure Survey (IHIES), it is shown how to obtain a proper estimate of the population variance when continuous missing at random responses are mean imputed.     

Modelling paired categorical outcomes in clinical trials

The goal of this paper is to discuss methods for testing the homogeneity of treatment‐induced changes in trials with paired categorical responses. Widely used marginal homogeneity tests ignore the information contained in concordant pairs of observations and become highly underpowered for configurations of parameters encountered in real trials. This paper considers models for paired binary or ordinal outcomes based on both discordant and concordant pairs that provide a natural extension of marginal models. Likelihood‐ratio tests associated with these models are developed and are demonstrated to be at least as powerful as or more powerful than marginal homogeneity tests. The proposed models are easy to fit using standard statistical software. Copyright © 2003 John Wiley & Sons, Ltd.     

Sparse structure selection and estimation

This paper studies the sparsity selection and estimation in nonparametric additive models. The sparsity refers to two types — across and within variables. Sparsity across variables corresponds to the irrelevant components in the models; sparsity within variables corresponds to zero function values over the sub-domains of the relevant components. To select and estimate the sparsity, I approximate each component by B-splines and propose a group bridge penalized method, which can simultaneously identify the zero functions and zero structures of the nonzero functions. Simulation studies demonstrate the effectiveness of the proposed method in sparsity selection and estimation across and within variables.     

Simultaneous confidence interval construction for many-to-one comparisons of proportion differences based on correlated paired data

In some medical researches such as ophthalmological, orthopaedic and otolaryngologic studies, it is often of interest to compare multiple groups with a control using data collected from paired organs of patients. The major difficulty in performing the data analysis is to adjust the multiplicity between the comparison of multiple groups, and the correlation within the same patient''s paired organs. In this article, we construct asymptotic simultaneous confidence intervals (SCIs) for many-to-one comparisons of proportion differences adjusting for multiplicity and the correlation. The coverage probabilities and widths of the proposed CIs are evaluated by Monte Carlo simulation studies. The methods are illustrated by a real data example.     

Power and sample size calculation for paired right-censored data based on survival copula models

Sample size determination is essential during the planning phases of clinical trials. To calculate the required sample size for paired right-censored data, the structure of the within-paired correlations needs to be pre-specified. In this article, we consider using popular parametric copula models, including the Clayton, Gumbel, or Frank families, to model the distribution of joint survival times. Under each copula model, we derive a sample size formula based on the testing framework for rank-based tests and non-rank-based tests (i.e., logrank test and Kaplan–Meier statistic, respectively). We also investigate how the power or the sample size was affected by the choice of testing methods and copula model under different alternative hypotheses. In addition to this, we examine the impacts of paired-correlations, accrual times, follow-up times, and the loss to follow-up rates on sample size estimation. Finally, two real-world studies are used to illustrate our method and R code is available to the user.     

Log linear models for multivariate paired comparison experiments with ties

A log linear multivariate paired comparison model for ties is proposed in which the cell probabilities under independence are those given by Davidson (1970). Altham's (1970) generalized measure of association (iv) is used to compare the association structure between two models, one having full, the other having reduced association structure. Based on the model with reduced association structure, the analysis of data from a consumer preference experiment is presented.     

The bahadur efficiency of paired versus joint ranking procedures for pa1rwtse multiple comparisons

The performance of paired versus joint ranking procedures for pairwise multiple comparisons is investigated using approxiirete Bahadur efficiency, When the populations to be compared are widely separated, or-when the. data arise from a shift model with an underlying unimodal density, the paired ranking procedure is found to be better for comparing two adjacent populations while the joint ranking procedure is more efficient for comparing the two most distant populations