Analysis of the joint action of two biological compounds on the gypsy moth

Methods for the analysis of data from a complex bioassay are described. The bioassay was carried out to study the effects of the joint action of two compounds on the mortality of the gypsy moth. It was carried out by first determining a stimulus-response model based on a putative biological mode of action of the mixture. Next, a statistical procedure is described for the analysis of correlated binary data observed over time. These procedures were then used to estimate parameters of interest to biologists, such as estimates for the concentrations of the compounds that cause a certain percentage of the insects to die by a given time.     

Gaussian copula distributions for mixed data,with application in discrimination

The construction of a joint model for mixed discrete and continuous random variables that accounts for their associations is an important statistical problem in many practical applications. In this paper, we use copulas to construct a class of joint distributions of mixed discrete and continuous random variables. In particular, we employ the Gaussian copula to generate joint distributions for mixed variables. Examples include the robit-normal and probit-normal-exponential distributions, the first for modelling the distribution of mixed binary-continuous data and the second for a mixture of continuous, binary and trichotomous variables. The new class of joint distributions is general enough to include many mixed-data models currently available. We study properties of the distributions and outline likelihood estimation; a small simulation study is used to investigate the finite-sample properties of estimates obtained by full and pairwise likelihood methods. Finally, we present an application to discriminant analysis of multiple correlated binary and continuous data from a study involving advanced breast cancer patients.     

The Analysis of Methadone Clinic Data Using Marginal and Conditional Logistic Models with Mixture or Random Effects

The paper develops methods for the statistical analysis of outcomes of methadone maintenance treatment (MMT). Subjects for this study were a cohort of patients entering MMT in Sydney in 1986. Urine drug tests on these subjects were performed weekly during MMT, and were reported as either positive or negative for morphine, the marker of recent heroin use. To allow correlation between the repeated binary measurements, a marginal logistic model was fitted using the generalized estimating equation (GEE) approach and the alternating logistic regression approach. Conditional logistic models are also considered. Results of separate fitting to each patient and score tests suggest that there is substantial between-patient variation in response to MMT. To account for the population heterogeneity and to facilitate subject-specific inference, the conditional logistic model is extended by introducing random intercepts. The two, three and four group mixture models are also investigated. The model of best fit is a three group mixture model, in which about a quarter of the subjects have a poor response to MMT, with continued heroin use independent of daily dose of methadone; about a quarter of the subjects have a very good response, with little or no heroin use, again independent of dose; and about half the subjects responded in a dose-dependent fashion, with reduced heroin use while receiving higher doses of methadone. These findings are consistent with clinical experience. There is also an association between reduced drug use and increased duration in treatment. The mixture model is recommended since it is quite tractable in terms of estimation and model selection as well as being supported by clinical experience.     

Statistical Analysis of Uncertainties in Deterministic Computational Modeling – Application to Composite Process Resin Infusion Flow Model

Deterministic physics-based flow modeling provides an effective way to simulate and understand the resin flow infusion process in liquid composite molding processes and its variants. These are effective to provide optimal injection time and locations prior to gelation for given process parameters of resin viscosity and preform permeability. However, there could be significant variations in these two parameters during actual manufacturing. This paper presents simulation-based statistical analysis of uncertainties of these process parameters involved in the resin flow infusion. Two key process parameters, viscosity and permeability, and their statistical variations are examined individually and subsequently in combination for their impact on the associated injection time. Values from statistical probability distribution of the process parameters were employed to find the solution space for this engineering application through deterministic physics-based process flow modeling simulations. A bivariate confidence envelope was developed using the appropriate Cumulative Density Function for a 95% probability of successfully completing resin infusion prior to physical resin gelation time. A logistic regression model for the influence of resin viscosity and permeability on the binary response of successful resin infusion is presented and conforms well to the sensitivity analysis inferences.     

Optimal sampling for repeated binary measurements

The authors consider the optimal design of sampling schedules for binary sequence data. They propose an approach which allows a variety of goals to be reflected in the utility function by including deterministic sampling cost, a term related to prediction, and if relevant, a term related to learning about a treatment effect To this end, they use a nonparametric probability model relying on a minimal number of assumptions. They show how their assumption of partial exchangeability for the binary sequence of data allows the sampling distribution to be written as a mixture of homogeneous Markov chains of order k. The implementation follows the approach of Quintana & Müller (2004), which uses a Dirichlet process prior for the mixture.     

The Muscatine children's obesity data reanalysed using pattern mixture models

A set of longitudinal binary, partially incomplete, data on obesity among children in the USA is reanalysed. The multivariate Bernoulli distribution is parameterized by the univariate marginal probabilities and dependence ratios of all orders, which together support maximum likelihood inference. The temporal association of obesity is strong and complex but stationary. We fit a saturated model for the distribution of response patterns and find that non-response is missing completely at random for boys but that the probability of obesity is consistently higher among girls who provided incomplete records than among girls who provided complete records. We discuss the statistical and substantive features of, respectively, pattern mixture and selection models for this data set.     

Hierarchical logistic regression models for imputation of unresolved enumeration status in undercount estimation

"In this article we describe a logistic regression modeling approach for nonresponse in the [U.S.] Post-Enumeration Survey (PES) that has desirable theoretical properties and that has performed well in practice.... In the 1990 PES, interviews were not obtained from approximately 1.2% of households in the sample, and approximately 2.1% of the individuals in interviewed households were considered unresolved after follow-up....The missing binary enumeration statuses for these unresolved cases were replaced with probabilities estimated under a statistical model that incorporated covariate information observed for these cases. This article describes an approach to modeling missing binary outcomes when there are a large number of covariates."     

Testing for randomness in stream ciphers using the binary derivative

The binary derivative has been used to measure the randomness of a binary string formed by a pseudorandom number generator for use in cipher systems. In this paper we develop statistical properties of the binary derivative and show that certain types of randomness testing in binary derivatives are equivalent to well-established tests for randomness in the original string. A uniform method of testing randomness in binary strings is described based on using the binary derivative. We show that the new tests are faster and more powerful than several of the well-established tests for randomness.     

Bayesian analysis of correlated mixed categorical data by incorporating historical prior information

In this article, we develop statistical models for analysis of correlated mixed categorical (binary and ordinal) response data arising in medical and epidemi-ologic studies. There is evidence in the literature to suggest that models including correlation structure can lead to substantial improvement in precision of estimation or are more appropriate (accurate). We use a very rich class of scale mixture of multivariate normal (SMMVN) iink functions to accommodate heavy tailed distributions. In order to incorporate available historical information, we propose a unified prior elicitation scheme based on SMMVN-link models. Further, simulation-based techniques are developed to assess model adequacy. Finally, a real data example from prostate cancer studies is used to illustrate the proposed methodologies.     

Designing and analyzing a mixture experiment to optimize the mixing proportions of polyvinyl chloride composites

Polyvinyl chloride (PVC) products are typically complex composites, whose quality characteristics vary widely depending on the types and proportions of their components, as well as other processing factors. It is often required to optimize PVC production for specific applications at the highest cost efficiency. This study describes the design and analysis of a statistical experiment to investigate the effects of different parameters over the mechanical properties of PVC intended for use in electrical wire insulation. Four commonly used mixture components, namely, virgin PVC, recycled PVC, calcium carbonate, and a plasticizer, and two process variables, type of plasticizer and filler particle size, were examined. Statistical tools were utilized to analyze and optimize the mixture while simultaneously finding the proper process parameters. The mix was optimized to achieve required strength and ductility, as per ASTM D6096 while minimizing cost. The paper demonstrates how statistical models can help tailor complex polymeric composites in the presence of variations created by process variables.     

Simulation-based Inference in a Zero-inflated Bernoulli Regression Model

The logistic regression model has become a standard tool to investigate the relationship between a binary outcome and a set of potential predictors. When analyzing binary data, it often arises that the observed proportion of zeros is greater than expected under the postulated logistic model. Zero-inflated binomial (ZIB) models have been developed to fit binary data that contain too many zeros. Maximum likelihood estimators in these models have been proposed and their asymptotic properties established. Several aspects of ZIB models still deserve attention however, such as the estimation of odds-ratios and event probabilities. In this article, we propose estimators of these quantities and we investigate their properties both theoretically and via simulations. Based on these results, we provide recommendations about the range of conditions (minimum sample size, maximum proportion of zeros in excess) under which a reliable statistical inference on the odds-ratios and event probabilities can be obtained in a ZIB regression model. A real-data example illustrates the proposed estimators.     

Conservative confidence intervals for the intraclass correlation coefficient for clustered binary data

Asymptotic approaches are traditionally used to calculate confidence intervals for intraclass correlation coefficient in a clustered binary study. When sample size is small to medium, or correlation or response rate is near the boundary, asymptotic intervals often do not have satisfactory performance with regard to coverage. We propose using the importance sampling method to construct the profile confidence limits for the intraclass correlation coefficient. Importance sampling is a simulation based approach to reduce the variance of the estimated parameter. Four existing asymptotic limits are used as statistical quantities for sample space ordering in the importance sampling method. Simulation studies are performed to evaluate the performance of the proposed accurate intervals with regard to coverage and interval width. Simulation results indicate that the accurate intervals based on the asymptotic limits by Fleiss and Cuzick generally have shorter width than others in many cases, while the accurate intervals based on Zou and Donner asymptotic limits outperform others when correlation and response rate are close to their boundaries.     

A simple approach for generating correlated binary variates ∗

Correlated binary data arise frequently in medical as well as other scientific disciplines; and statistical methods, such as generalized estimating equation (GEE), have been widely used for their analysis. The need for simulating correlated binary variates arises for evaluating small sample properties of the GEE estimators when modeling such data. Also, one might generate such data to simulate and study biological phenomena such as tooth decay or periodontal disease. This article introduces a simple method for generating pairs of correlated binary data. A simple algorithm is also provided for generating an arbitrary dimensional random vector of non-negatively correlated binary variates. The method relies on the idea that correlations among the random variables arise as a result of their sharing some common components that induce such correlations. It then uses some properties of the binary variates to represent each variate in terms of these common components in addition to its own elements. Unlike most previous approaches that require solving nonlinear equations or use some distributional properties of other random variables, this method uses only some properties of the binary variate. As no intermediate random variables are required for generating the binary variates, the proposed method is shown to be faster than the other methods. To verify this claim, we compare the computational efficiency of the proposed method with those of other procedures.     

Joint analysis of nonlinear heterogeneous longitudinal data and binary outcome: an application to AIDS clinical studies

Finite mixture models are currently used to analyze heterogeneous longitudinal data. By releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, finite mixture models not only can estimate model parameters but also cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, which might be associated with a clinically important binary outcome. This article develops a joint modeling of a finite mixture of NLME models for longitudinal data in the presence of covariate measurement errors and a logistic regression for a binary outcome, linked by individual latent class indicators, under a Bayesian framework. Simulation studies are conducted to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and logistic regression are fitted separately, followed by an application to a real data set from an AIDS clinical trial, in which the viral dynamics and dichotomized time to the first decline of CD4/CD8 ratio are analyzed jointly.     

A hierarchical Bayesian model for binary data incorporating selection bias

We consider a Bayesian nonignorable model to accommodate a nonignorable selection mechanism for predicting small area proportions. Our main objective is to extend a model on selection bias in a previously published paper, coauthored by four authors, to accommodate small areas. These authors assume that the survey weights (or their reciprocals that we also call selection probabilities) are available, but there is no simple relation between the binary responses and the selection probabilities. To capture the nonignorable selection bias within each area, they assume that the binary responses and the selection probabilities are correlated. To accommodate the small areas, we extend their model to a hierarchical Bayesian nonignorable model and we use Markov chain Monte Carlo methods to fit it. We illustrate our methodology using a numerical example obtained from data on activity limitation in the U.S. National Health Interview Survey. We also perform a simulation study to assess the effect of the correlation between the binary responses and the selection probabilities.     

Mixture of the Riesz distribution with respect to the generalized multivariate gamma distribution

Wishart natural exponential families (NEFs) characterized by Letac (1989) are extended to the Riesz NEFs on symmetric matrices. These families are characterized by their variance functions defined in Hassairi and Lajmi (2001). This work uses a particular basis of these NEFs to describe the class of the generalized multivariate gamma distributions and then to study the statistical model obtained by the mixture of this distribution with the Riesz one on the space of symmetric matrices.     

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model. The authors would like to thank the editor and referees for their helpful comments. This work was supported by CNPq, Brazil.     

Compositional Tables Analysis in Coordinates

Compositional tables – a continuous counterpart to the contingency tables – carry relative information about relationships between row and column factors; thus, for their analysis, only ratios between cells of a table are informative. Consequently, the standard Euclidean geometry should be replaced by the Aitchison geometry on the simplex that enables decomposition of the table into its independent and interactive parts. The aim of the paper is to find interpretable coordinate representation for independent and interaction tables (in sense of balances and odds ratios of cells, respectively), where further statistical processing of compositional tables can be performed. Theoretical results are applied to real‐world problems from a health survey and in macroeconomics.     

Comparison of several imputation methods for missing baseline data in propensity scores analysis of binary outcome

We performed a simulation study comparing the statistical properties of the estimated log odds ratio from propensity scores analyses of a binary response variable, in which missing baseline data had been imputed using a simple imputation scheme (Treatment Mean Imputation), compared with three ways of performing multiple imputation (MI) and with a Complete Case analysis. MI that included treatment (treated/untreated) and outcome (for our analyses, outcome was adverse event [yes/no]) in the imputer's model had the best statistical properties of the imputation schemes we studied. MI is feasible to use in situations where one has just a few outcomes to analyze. We also found that Treatment Mean Imputation performed quite well and is a reasonable alternative to MI in situations where it is not feasible to use MI. Treatment Mean Imputation performed better than MI methods that did not include both the treatment and outcome in the imputer's model. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of rounded data in mixture normal model

Rounding errors have a considerable impact on statistical inferences, especially when the data size is large and the finite normal mixture model is very important in many applied statistical problems, such as bioinformatics. In this article, we investigate the statistical impacts of rounding errors to the finite normal mixture model with a known number of components, and develop a new estimation method to obtain consistent and asymptotically normal estimates for the unknown parameters based on rounded data drawn from this kind of models.