Analysis Of Binary Longitudinal Data Research Articles

Functional clustering methods for binary longitudinal data with temporal heterogeneity

In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a novel generalized varying-coefficient model that accounts for within-subject variability and simultaneously clusters varying-coefficient functions, without restricting the number of clusters nor overfitting the data. In the analysis of a heterogeneous series of binary data, the model extracts population-level fixed effects, cluster-level varying effects, and subject-level random effects. Various simulation studies show the validity and utility of the proposed method to correctly specify cluster-specific varying-coefficients when the number of clusters is unknown. The proposed method is applied to a heterogeneous series of binary data in the German Socioeconomic Panel (GSOEP) study, where we identify three major clusters demonstrating the different varying effects of socioeconomic predictors as a function of age on the working status.

Optimal shrinkage estimations in partially linear single-index models for binary longitudinal data

This paper focuses on the optimal estimation strategies of partially linear single-index models (PLSIM) for binary longitudinal data. Fitting model between the response and covariates may cause complexity and the linear terms may not be adequate to represent the relationship. In this situation, the PLSIM containing both linear and nonlinear terms is preferable. The objective of this paper is to develop optimal estimation strategies such as, pretest and shrinkage methods, for the analysis of binary longitudinal data under the PLSIM where some regression parameters are subject to restrictions. We estimate the nonparametric component using kernel estimating equations, and then use profile estimating equations to estimate the unrestricted and restricted estimators. To apply the pretest and shrinkage methods, we fit two models: one includes all covariates and the other restricts the regression parameters based on the auxiliary information. The unrestricted and restricted estimators are then combined optimally to get the pretest and shrinkage estimators. We also derive the asymptotic properties of the estimators in terms of biases and risks. Monte Carlo simulations are also conducted to examine the relative performance of the proposed estimators to the unrestricted estimator. An empirical application is also be used to illustrate the usefulness of our methodology.

A Comparison of Three Models in Multivariate Binary Longitudinal Data Analysis: Application to FDCS Study

Multivariate longitudinal data analysis plays an important role in many biomedical and social problems. In this article, we present three methods for analyzing multiple and correlated binary outcomes; each one can be beneficial for determined aims. We review methods one and two, and we proposed method three. The three methods estimate the marginal means using the GEE approach for multivariate binary longitudinal data. The first method addresses the question of estimating one group of covariate parameters for many binary outcomes while accounting for their multivariate structure. The second method addresses the question of estimating the covariate parameters for each binary outcome separately. The third method is an estimation of the covariate parameters for each combination of outcomes. Our goal is to investigate the differences among the parameter estimations of the three methods. In the application element, we present a follow-up study (Florida Dental Care Study) that measured three binary outcomes and five covariates at four intervals. The FDCS study is useful explanation of the variation between outcomes since the outcomes were highly correlated.

Analysis of binary longitudinal data with time-varying effects

This paper considers the analysis of longitudinal data where a binary response variable is observed repeatedly for each subject over time. In analyzing such data, regression coefficients are commonly assumed constant over time, which may not properly account for the time-varying effects of some subject characteristics on a sequence of binary outcomes. This paper proposes a Bayesian method for the analysis of binary longitudinal data with time-varying regression coefficients and random effects to account for nonlinear subject-specific effects over time as well as between-subject variation. The proposed method facilitates posterior computation via the method of partial collapse and accommodates spatially inhomogeneous smoothness of nonparametric functions without overfitting via a basis search technique. The proposed method is illustrated with a simulated study and the binary longitudinal data from the German socioeconomic panel study.

A Longitudinal Study of Possible Links between Tax Imputation and Dividend Reinvestment Plans: Australian Evidence

This study focuses on the relationship between dividend payout ratio and DRP (Dividend Reinvestment Plan) adoption within the framework of the Australian dividend tax imputation system. Since the decision to adopt the DRP (Dividend Reinvestment Plan) is effected through the distribution of dividends, a longitudinal study of dividend payout ratios and DRP adoptions over time during the sample period (1995-2009), places the DRP decision in the right perspective. We also look at the DRP effect on certain firm characteristics over time using cross-sectional longitudinal data. The study addresses the binary longitudinal data analysis, using the trend and GEE (General Estimating Equation) approaches, to examine the DRP effect on dividend payout ratio and other firm characteristics. The results of both the trend analysis and GEE approach indicate that DRP decisions are prompted by high dividend payout ratio, low profitability and low liquidity over time. The highly significant time coefficient in GEE estimates shows the longitudinal effect on the DRP decision.

The analysis of binary longitudinal data with time‐dependent covariates

We consider longitudinal studies with binary outcomes that are measured repeatedly on subjects over time. The goal of our analysis was to fit a logistic model that relates the expected value of the outcomes with explanatory variables that are measured on each subject. However, additional care must be taken to adjust for the association between the repeated measurements on each subject. We propose a new maximum likelihood method for covariates that may be fixed or time varying. We also implement and make comparisons with two other approaches: generalized estimating equations, which may be more robust to misspecification of the true correlation structure, and alternating logistic regression, which models association via odds ratios that are subject to less restrictive constraints than are correlations. The proposed estimation procedure will yield consistent and asymptotically normal estimates of the regression and correlation parameters if the correlation on consecutive measurements on a subject is correctly specified. Simulations demonstrate that our approach can yield improved efficiency in estimation of the regression parameter; for equally spaced and complete data, the gains in efficiency were greatest for the parameter associated with a time-by-group interaction term and for stronger values of the correlation. For unequally spaced data and with dropout according to a missing-at-random mechanism, MARK1ML with correctly specified consecutive correlations yielded substantial improvements in terms of both bias and efficiency. We present an analysis to demonstrate application of the methods we consider. We also offer an R function for easy implementation of our approach.

TheRPackagebildfor the Analysis of Binary Longitudinal Data

We present the R package bild for the parametric and graphical analysis of binary longitudinal data. The package performs logistic regression for binary longitudinal data, allowing for serial dependence among observations from a given individual and a random intercept term. Estimation is via maximization of the exact likelihood of a suitably defined model. Missing values and unbalanced data are allowed, with some restrictions. The code of bild is written partly in R language, partly in Fortran 77, interfaced through R. The package is built following the S4 formulation of R methods.

Assessment of School Performance Through a Multilevel Latent Markov Rasch Model

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to which he or she belongs. The latter effect is modeled by a discrete latent variable associated to each cluster. For the maximum likelihood estimation of the model parameters, an Expectation-Maximization algorithm is outlined. Through the analysis of a data set collected in the Lombardy Region (Italy), it is shown how the proposed model may be used for assessing the development of cognitive achievement. The data set is based on test scores in mathematics observed over 3 years on middle school students attending public and non-state schools. Manuscript received March 20, 2009 Revision received July 2, 2010 Accepted July 10, 2010

Doubly Robust Estimates for Binary Longitudinal Data Analysis with Missing Response and Missing Covariates

Longitudinal studies often feature incomplete response and covariate data. Likelihood-based methods such as the expectation-maximization algorithm give consistent estimators for model parameters when data are missing at random (MAR) provided that the response model and the missing covariate model are correctly specified; however, we do not need to specify the missing data mechanism. An alternative method is the weighted estimating equation, which gives consistent estimators if the missing data and response models are correctly specified; however, we do not need to specify the distribution of the covariates that have missing values. In this article, we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are MAR. This method is appealing in that it can provide consistent estimators if either the missing data model or the missing covariate model is correctly specified. Simulation studies demonstrate that this method performs well in a variety of situations.

A modeling framework for the analysis of HPV incidence and persistence: a semi-parametric approach for clustered binary longitudinal data analysis.

Human papillomavirus (HPV) infection is a common sexually transmitted disease of growing public health importance, and over 40 genotypes have been identified in genital infections. Current HPV cohort studies often follow participants at pre-determined visits, such as every 6 months, and data generated from such epidemiology studies can be described as clustered longitudinal binary data where correlation arises in two ways: the directionless clustering due to the multiple genotypes tested within an individual, and the temporal correlation among the repeated measurements on the same genotype along time. Current analyses for identification of risk factors associated with HPV incidence and persistence often either do not fully utilize information in the data set or ignore the correlation between the multiple genotypes. Given the scientific definition of incidence and persistence, conditional probability modeling provides us a natural mathematical tool. We thus present a semi-parametric regression model for such data where full specification of the joint multivariate binary distribution is avoided by using conditioning argument to handle the temporal correlation and GEE to account for the correlation between the multiple genotypes. The model is applied to the HPV data from the Rakai male circumcision (MC) trial to evaluate the as-treated efficacy of MC and also identify modifiable risk factors for incidence and persistence of oncogenic HPV types in men. A simulation study is performed to provide empirical information on the number of individuals that is needed for satisfactory power and estimation accuracy of the association parameter estimates in future studies.

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.

Hierarchical Bayesian Transition Models for the Analysis of Binary Longitudinal Data

The paper proposes a general hierarchical Bayesian methodology for the analysis of binary longitudinal data. The Bayesian method is implemented via Markov Chain Monte Carlo (MCMC) integration technique and is applied to a real dataset which was collected to study stereotyped behavior in deer mice.

Binary Longitudinal Data Analysis with Correlation a Function of Explanatory Variables

When binary responses are observed over time, the dependence between observations for an individual must be considered. If the focus of a study is to identify the relationship between the binary response and a set of explanatory variables then the dependence between observations may also depend on the explanatory variables. An extension of a model where dependence is assumed to be constant will be considered. A model previously proposed for dependent binary responses will be revisited and a robust estimate of the variance-covariance matrix of coefficient estimates will be suggested to provide estimates of standard errors. The results of simulation studies investigating the properties of coefficient estimates will be discussed. An example based on a study of the AIDS epidemic and intravenous drug use behaviour will be analyzed to illustrate the techniques.

The Analysis of Binary Longitudinal Data with Time-Independent Covariates

The Analysis of Binary Longitudinal Data with Time-Independent Covariates

The analysis of binary longitudinal data with time independent covariates

SUMMARY This paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject. We propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject's data. The efficiency of the proposed estimators is examined. An analysis of stress in mothers with infants is presented to illustrate the proposed method.