Analysis Of Clustered Binary Data Research Articles

Analysis of GEE with a mixture working correlation matrix for diverging number of covariates

The generalized estimating equations (GEE) method has been widely used for longitudinal data analysis. Wang [GEE analysis of clustered binary data with diverging number of covariates. Ann Stat. 2011;39:389–417] developed an asymptotic theory for GEE analysis of clustered binary data with diverging number of covariates. She suggested several moment estimators of the nuisance parameter in the working correlation matrix. However, these estimators might not exist when the working correlation structure is misspecified. When the number of covariates is finite, Xu et al. [A finite mixture model for working correlation matrices in generalized estimating equations. Stat Sin. 2012;22:755–776] proposed a mix-GEE method based on a finite mixture model to capture correlations among repeated measurements. In this paper, we develop an asymptotic theory for the mix-GEE estimator with diverging number of covariates. Simulation studies are used to demonstrate the performance of the mix-GEE with diverging number of covariates, which indicate this method is more numerically stable and has a higher efficiency than the GEE with a specified working correlation matrix in diverging number of covariates framework. Finally, a real dataset is used for illustration.

GEECORR: A SAS macro for regression models of correlated binary responses and within-cluster correlation using generalized estimating equations

Background and objectives: Generalized estimating equations (GEE) provide population-averaged model inference for longitudinal and clustered outcomes via a generalized linear model for the effect of explanatory variables on the marginal mean, while intra-cluster correlations are ordinarily treated as nuisance parameters. Software to richly parameterize and conduct inference for complex correlation structures in the marginal modeling framework is scarce.Methods: A SAS macro, GEECORR, has been developed for the analysis of clustered binary data based on GEE to include additional estimating equations for modeling pairwise correlation between binary variates as a function of covariates.Results: We illustrate the macro in a surveillance study with repeated measures, a longitudinal study, and a study with biological clustering.Conclusions: This article provides an overview of the GEE method consisting of a pair of estimating equations, describes the features and capabilities of the GEECORR macro including regression diagnostics and finite-sample bias-corrected covariance estimators, and demonstrates the macro usage for three studies.

Relative Efficiency of Unequal Versus Equal Cluster Sizes for the Nonparametric Weighted Sign Test Estimators in Clustered Binary Data

We consider analysis of clustered binary data from multiple observations for each subject in which any two observations from a subject are assumed to have a common correlation coefficient. In the weighted sign test on proportion in clustered binary data, three weighting schemes are considered: equal weights to observations, equal weights to clusters and the optimal weights that minimize the variance of the estimator. Since the distribution of cluster sizes may not be exactly specified before the trial starts, the sample size is usually determined using an average cluster size without taking into account any potential imbalance in cluster size even though cluster size usually varies among clusters. In this paper we investigate the relative efficiency (RE) of unequal versus equal cluster sizes for clustered binary data using the weighted sign test estimators. The REs are computed as a function of correlation among observations within each subject and the various cluster size distributions. The required sample size for unequal cluster sizes will not exceed the sample size for an equal cluster size multiplied by the maximum RE. It is concluded that the maximum RE for various cluster size distributions considered here does not exceed 1.50, 1.61 and 1.12 for equal weights to observations, equal weights to clusters and optimal weights, respectively. It suggests sampling 50%, 61% and 12% more clusters depending on the weighting schemes than the number of clusters computed using an average cluster size.

Analysis of proportions for clustered binary data in the presence of unequal dispersions

This paper investigates the test procedures for testing the homogeneity of the proportions in the analysis of clustered binary data in the context of unequal dispersions across the treatment groups. We introduce a simple test procedure based on adjusted proportions using a sandwich estimator of the variance of the proportion estimators obtained by the generalized estimating equations approach of Zeger and Liang (1986) [Biometrics 42, 121–130]. We also extend the exiting test procedures of testing the hypothesis of proportions in this context. These test procedures are then compared, by simulations, in terms of size and power. Moreover, we derive the score test for testing the homogeneity of the dispersion parameters among several groups of clustered binary data. An illustrative application of the recommended test procedures is also presented.

GEE analysis of clustered binary data with diverging number of covariates

Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. This paper develops an asymptotic theory for generalized estimating equations (GEE) analysis of clustered binary data when the number of covariates grows to infinity with the number of clusters. In this “large n, diverging p” framework, we provide appropriate regularity conditions and establish the existence, consistency and asymptotic normality of the GEE estimator. Furthermore, we prove that the sandwich variance formula remains valid. Even when the working correlation matrix is misspecified, the use of the sandwich variance formula leads to an asymptotically valid confidence interval and Wald test for an estimable linear combination of the unknown parameters. The accuracy of the asymptotic approximation is examined via numerical simulations. We also discuss the “diverging p” asymptotic theory for general GEE. The results in this paper extend the recent elegant work of Xie and Yang [Ann. Statist. 31 (2003) 310–347] and Balan and Schiopu-Kratina [Ann. Statist. 32 (2005) 522–541] in the “fixed p” setting.

Nonparametric Sample Size Estimation for Sensitivity and Specificity with Multiple Observations per Subject

We propose a sample size calculation approach for the estimation of sensitivity and specificity of diagnostic tests with multiple observations per subjects. Many diagnostic tests such as diagnostic imaging or periodontal tests are characterized by the presence of multiple observations for each subject. The number of observations frequently varies among subjects in diagnostic imaging experiments or periodontal studies. Nonparametric statistical methods for the analysis of clustered binary data have been recently developed by various authors. In this paper, we derive a sample size formula for sensitivity and specificity of diagnostic tests using the sign test while accounting for multiple observations per subjects. Application of the sample size formula for the design of a diagnostic test is discussed. Since the sample size formula is based on large sample theory, simulation studies are conducted to evaluate the finite sample performance of the proposed method. We compare the performance of the proposed sample size formula with that of the parametric sample size formula that assigns equal weight to each observation. Simulation studies show that the proposed sample size formula generally yields empirical powers closer to the nominal level than the parametric method. Simulation studies also show that the number of subjects required increases as the variability in the number of observations per subject increases and the intracluster correlation increases.

Analysis of Clustered Binary Data With Unequal Cluster Sizes: A Semiparametric Bayesian Approach

The analysis of clustered binary data is a common task in many areas of application. Parametric approaches to the analysis of such data are numerous, but there has been much recent interest in nonparametric and semiparametric approaches. When cluster sizes are unequal, an assumption is often made of compatibility of marginal distributions in order for semiparametric approaches to be developed when there is little replication for different cluster sizes. Here, we use the marginal compatibility assumption to extend flexible semiparametric Bayesian methods able to shrink towards a “parametric backbone” to the situation where there are few replicated observations for distinct cluster sizes and each distinct value of a covariate. A motivating application is the analysis of developmental toxicology data where pregnant laboratory animals are exposed to a dose of some potentially toxic compound and interest lies in describing the distribution, as a function of the dose level, of the number of fetuses exhibiting some characteristic abnormality. Flexible semiparametric methods are required here, as the data typically exhibit overdispersion and complex structure. We also consider a further extension appropriate to the analysis of clustered binary data in the situation where there is little or no replication for distinct covariate values.

Bayesian inference for generalized linear mixed models

Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.

Clustered binary data with random cluster sizes

In the analysis of clustered binary data with random cluster sizes, traditional approaches assuming fixed cluster sizes are generally used. Appropriate inference should take account of both intra-cluster correlation and extra-variation arising from the random cluster sizes. We introduce a dual Poisson random effects model for performing appropriate analyses of such data. Our orthodox best linear unbiased predictor approach to this model depends only on the first- and second- moment assumptions of unobserved random effects. This approach is illustrated with analyses of seed germination data and developmental toxicity data.

HGLM versus conditional estimators for the analysis of clustered binary data

Clustered binary data arise frequently in medical research such as cross-over clinical trials and twin studies. For the analysis of such data either a random-effects model or a conditional likelihood approach can be used. In this paper, we compare numerically the random-effects model estimator and the conditional likelihood estimator and discuss their relative merits for the analysis of binary data.

A simple method for analysing overdispersion in clustered Poisson data.

A simple method is proposed for analysing grouped count data exhibiting overdispersion relative to a Poisson model. The method is similar to the approach suggested for the analysis of clustered binary data in Rao and Scott (1992). It requires no specific model for the overdispersion and it can be implemented easily using standard programs designed to handle independent Poisson counts, after a small amount of preprocessing.

A comparison of methods for testing homogeneity of proportions in teratologic studies

We consider teratologic studies in which the aim is to compare the survival rate of animals in a treatment group to the corresponding rate in a control group. The design of such studies often involves the allocation of intact litters of animals to treatment, invalidating the application of standard statistical methods. We review the strengths and weaknesses of several approaches for dealing with this problem including methodology recently developed for the analysis of clustered binary data. A simulation study is conducted in which litter sizes are generated from a distribution having specified mean and degree of imbalance. It is recommended on the basis of this study and on theoretical considerations that the choice of method should depend on whether the comparison of interest is experimental or observational. For experimental comparisons, involving the random assignment of litters to different treatment groups, methods based on the adjustment of standard chi-square statistics are recommended unless the number of litters in each group is very large.

Multivariate Methods for Clustered Binary Data with Multiple Subclasses, with Application to Binary Longitudinal Data

Clustered binary data occur frequently in biostatistical work. Several approaches have been proposed for the analysis of clustered binary data. In Rosner (1984, Biometrics 40, 1025-1035), a polychotomous logistic regression model was proposed that is a generalization of the beta-binomial distribution and allows for unit- and subunit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of subunits within a cluster are equally correlated. This is appropriate for ophthalmologic work where clusters are generally of size 2, but may be inappropriate for larger cluster sizes. A beta-binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of unit-, class-, and subunit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, Massachusetts, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.

Multivariate methods for binary longitudinal data with heterogeneous correlation over time.

Clustered binary data occur frequently in biostatistical work. One particular application is in binary longitudinal data, where several visits are available for the same individual. Several approaches have been proposed for the analysis of clustered binary data. In Rosner, a polychotomous logistic regression model was proposed which is a generalization of the beta-binomial distribution and allows for person- and visit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of visits within an individual are equally correlated, which may be inappropriate if several visits are available over a long follow-up period. In this paper, this approach is extended to allow for heterogeneous correlation over time. The total time period is divided into subintervals and a beta-binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of person-, subinterval-, and visit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, MA, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.