Clustered Binary Data Research Articles

A novel case-control subsampling approach for rapid model exploration of large clustered binary data.

In many settings, an analysis goal is the identification of a factor, or set of factors associated with an event or outcome. Often, these associations are then used for inference and prediction. Unfortunately, in the big data era, the model building and exploration phases of analysis can be time-consuming, especially if constrained by computing power (ie, a typical corporate workstation). To speed up this model development, we propose a novel subsampling scheme to enable rapid model exploration of clustered binary data using flexible yet complex model set-ups (GLMMs with additive smoothing splines). By reframing the binary response prospective cohort study into a case-control-type design, and using our knowledge of sampling fractions, we show one can approximate the model estimates as would be calculated from a full cohort analysis. This idea is extended to derive cluster-specific sampling fractions and thereby incorporate cluster variation into an analysis. Importantly, we demonstrate that previously computationally prohibitive analyses can be conducted in a timely manner on a typical workstation. The approach is applied to analysing risk factors associated with adverse reactions relating to blood donation.

R package to estimate intracluster correlation coefficient with confidence interval for binary data

Background and ObjectiveThe Intracluster Correlation Coefficient (ICC) is a major parameter of interest in cluster randomized trials that measures the degree to which responses within the same cluster are correlated. There are several types of ICC estimators and its confidence intervals (CI) suggested in the literature for binary data. Studies have compared relative weaknesses and advantages of ICC estimators as well as its CI for binary data and suggested situations where one is advantageous in practical research. The commonly used statistical computing systems currently facilitate estimation of only a very few variants of ICC and its CI. To address the limitations of current statistical packages, we developed an R package, ICCbin, to facilitate estimating ICC and its CI for binary responses using different methods. MethodsThe ICCbin package is designed to provide estimates of ICC in 16 different ways including analysis of variance methods, moments based estimation, direct probabilistic methods, correlation based estimation, and resampling method. CI of ICC is estimated using 5 different methods. It also generates cluster binary data using exchangeable correlation structure. ResultsICCbin package provides two functions for users. The function rcbin() generates cluster binary data and the function iccbin() estimates ICC and it’s CI. The users can choose appropriate ICC and its CI estimate from the wide selection of estimates from the outputs. ConclusionsThe R package ICCbin presents very flexible and easy to use ways to generate cluster binary data and to estimate ICC and it’s CI for binary response using different methods. The package ICCbin is freely available for use with R from the CRAN repository (https://cran.r-project.org/package=ICCbin). We believe that this package can be a very useful tool for researchers to design cluster randomized trials with binary outcome.

Estimating multiple-membership logit models with mixed effects: indirect inference versus data cloning

ABSTRACTMultiple-membership logit models with random effects are models for clustered binary data, where each statistical unit can belong to more than one group. The likelihood function of these models is analytically intractable. We propose two different approaches for parameter estimation: indirect inference and data cloning (DC). The former is a non-likelihood-based method which uses an auxiliary model to select reasonable estimates. We propose an auxiliary model with the same dimension of parameter space as the target model, which is particularly convenient to reach good estimates very fast. The latter method computes maximum likelihood estimates through the posterior distribution of an adequate Bayesian model, fitted to cloned data. We implement a DC algorithm specifically for multiple-membership models. A Monte Carlo experiment compares the two methods on simulated data. For further comparison, we also report Bayesian posterior mean and Integrated Nested Laplace Approximation hybrid DC estimates. Simulations show a negligible loss of efficiency for the indirect inference estimator, compensated by a relevant computational gain. The approaches are then illustrated with two real examples on matched paired data.

BayesBinMix: an R Package for Model Based Clustering of Multivariate Binary Data

The BayesBinMix package offers a Bayesian framework for clustering binary data with or without missing values by fitting mixtures of multivariate Bernoulli distributions with an unknown number of components. It allows the joint estimation of the number of clusters and model parameters using Markov chain Monte Carlo sampling. Heated chains are run in parallel and accelerate the convergence to the target posterior distribution. Identifiability issues are addressed by implementing label switching algorithms. The package is demonstrated and benchmarked against the Expectation-Maximization algorithm using a simulation study as well as a real dataset.

Modeling clustered binary data with excess zero clusters.

We establish a zero-inflated (random-effects) logistic-Gaussian model for clustered binary data in which members of clusters in one latent class have a zero response with probability one, and members of clusters in a second latent class yield correlated outcomes. Response probabilities in terms of random-effects models are formulated, and maximum marginal likelihood estimation procedures based on Gaussian quadrature are developed. Application to esophageal cancer data in Chinese families is presented.

A comparison of methods for the analysis of binomial clustered outcomes in behavioral research

BackgroundIn behavioral research, data consisting of a per-subject proportion of “successes” and “failures” over a finite number of trials often arise. This clustered binary data are usually non-normally distributed, which can distort inference if the usual general linear model is applied and sample size is small. A number of more advanced methods is available, but they are often technically challenging and a comparative assessment of their performances in behavioral setups has not been performed. MethodWe studied the performances of some methods applicable to the analysis of proportions; namely linear regression, Poisson regression, beta-binomial regression and Generalized Linear Mixed Models (GLMMs). We report on a simulation study evaluating power and Type I error rate of these models in hypothetical scenarios met by behavioral researchers; plus, we describe results from the application of these methods on data from real experiments. ResultsOur results show that, while GLMMs are powerful instruments for the analysis of clustered binary outcomes, beta-binomial regression can outperform them in a range of scenarios. Linear regression gave results consistent with the nominal level of significance, but was overall less powerful. Poisson regression, instead, mostly led to anticonservative inference. Comparison with existing methodsGLMMs and beta-binomial regression are generally more powerful than linear regression; yet linear regression is robust to model misspecification in some conditions, whereas Poisson regression suffers heavily from violations of the assumptions when used to model proportion data. ConclusionsWe conclude providing directions to behavioral scientists dealing with clustered binary data and small sample sizes.

Resampling method to estimate intra-cluster correlation for clustered binary data

ABSTRACTVarious methods have been proposed to estimate intra-cluster correlation coefficients (ICCs) for correlated binary data, and many are very sensitive to the type of design and underlying distributional assumptions. We proposed a new method to estimate ICC and its 95% confidence intervals based on resampling principles and U-statistics, where we resampled with replacement pairs of individuals from within and between clusters. We concluded from our simulation study that the resampling-based estimates approximate the population ICC more precisely than the analysis of variance and method of moments techniques for different event rates, varying number of clusters, and cluster sizes.

Impact of Young and Strong on physical activity in young breast cancer survivors.

175 Background: Inactivity is common in breast cancer survivors and has been linked to poor outcomes. Few trials have tested physical activity (PA) interventions in young women with breast cancer, who may face unique PA barriers due to demands of jobs and young families. Methods: Young and Strong was a cluster-randomized study evaluating the effect of education interventions for young breast cancer survivors.Sites were randomized 1:1 to a young women’s intervention (YWI), focused on fertility and other issues facing young women, or to a physical activity intervention (PAI). At PAI sites, providers were instructed to discuss PA with patients, and participants were given materials to encourage PA. PA was measured with the modified Godin Leisure Score Index at baseline, and 3, 6, and 12 months. Medical records were reviewed to assess provider attention to PA. Changes in weekly min of PA were compared between the PAI and YWI groups using general estimating equations to evaluate clustered binary and Gaussian data. Results: 467 patients enrolled between 7/12 -12/13 across 54 sites. Median age at dx was 40yrs (range 22-45). At baseline, participants were moderately active. PA increased in both groups over time (Table); there was no significant difference in PA between groups at any time (all p > 0.1). Provider attention to PA was documented in 74% of participants on PAI and 61% on YWI (p = 0.15), and correlated with PA at 12 months (median 100 min/wk of PA in participants with provider attention to PA vs. 60 min/wk in those without, p = 0.016). Participants who reported reading all or most the PAI materials reported higher levels of PA vs. those who read less (78% vs. 64%, p = 0.05) Conclusions: Young breast cancer survivors assigned to a PA intervention did not increase PA more than those assigned to an intervention focused on young women’s issues. However, the higher levels of PA among women who engaged with the PAI materials and those whose oncology providers addressed PA suggests the importance of enhancing patient and provider engagement with healthy lifestyle information and recommendations. Clinical trial information: NCT01647607. [Table: see text]

CL-AntInc Algorithm for Clustering Binary Data Streams Using the Ants Behavior

In this paper, we present a new approach using a non-hierarchical method in graph environment and the concept of artificial ants for both clustering and visualization using Tulip framework. This model can be presented to take into account data in blocks in an incremental way. It seems especially interesting to process binary data streaming. In this algorithm, we also suggest to apply swarm intelligence techniques for the incremental processing of this new challenging data type. The main novelty of this research work resides on the adaptation of CL-AntInc to perform clustering binary data streams and building growing graphs increasingly for this type of data.The proposed algorithm performance is evaluated using real world data sets extracted from Machine Learning Repository. Our algorithm is competitive when compared with other stream clustering methods.

Separation Issues and Possible Solutions: Part I – Systematic Literature Review on Logistic Models ‐ Part II – Comparison of different methods for separation in logistic regression

Separation Issues and Possible Solutions: Part I – Systematic Literature Review on Logistic Models ‐ Part II – Comparison of different methods for separation in logistic regression

Mixed model and estimating equation approaches for zero inflation in clustered binary response data with application to a dating violence study

The NEXT Generation Health study investigates the dating violence of adolescents using a survey questionnaire. Each student is asked to affirm or deny multiple instances of violence in his/her dating relationship. There is, however, evidence suggesting that students not in a relationship responded to the survey, resulting in excessive zeros in the responses. This paper proposes likelihood-based and estimating equation approaches to analyze the zero-inflated clustered binary response data. We adopt a mixed model method to account for the cluster effect, and the model parameters are estimated using a maximum-likelihood (ML) approach that requires a Gaussian-Hermite quadrature (GHQ) approximation for implementation. Since an incorrect assumption on the random effects distribution may bias the results, we construct generalized estimating equations (GEE) that do not require the correct specification of within-cluster correlation. In a series of simulation studies, we examine the performance of ML and GEE methods in terms of their bias, efficiency and robustness. We illustrate the importance of properly accounting for this zero inflation by reanalyzing the NEXT data where this issue has previously been ignored.

Testing the homogeneity of proportions for clustered binary data without knowing the correlation structure

A robust generalized score test for comparing groups of cluster binary data is proposed. This novel test is asymptotically valid for practically any underlying correlation configurations including the situation when correlation coefficients vary within or between clusters. This structure generally undermines the validity of the typical large sample properties of the method of maximum likelihood. Simulations and real data analysis are used to demonstrate the merit of this parametric robust method. Results show that our test is superior to two recently proposed test statistics advocated by other researchers.

Simultaneous model selection and estimation for mean and association structures with clustered binary data

This paper investigates the property of the penalized estimating equations when both the mean and association structures are modelled. To select variables for the mean and association structures sequentially, we propose a hierarchical penalized generalized estimating equations (HPGEE2) approach. The first set of penalized estimating equations is solved for the selection of significant mean parameters. Conditional on the selected mean model, the second set of penalized estimating equations is solved for the selection of significant association parameters. The hierarchical approach is designed to accommodate possible model constraints relating the inclusion of covariates into the mean and the association models. This two‐step penalization strategy enjoys a compelling advantage of easing computational burdens compared to solving the two sets of penalized equations simultaneously. HPGEE2 with a smoothly clipped absolute deviation (SCAD) penalty is shown to have the oracle property for the mean and association models. The asymptotic behavior of the penalized estimator under this hierarchical approach is established. An efficient two‐stage penalized weighted least square algorithm is developed to implement the proposed method. The empirical performance of the proposed HPGEE2 is demonstrated through Monte‐Carlo studies and the analysis of a clinical data set. Copyright © 2013 John Wiley & Sons Ltd

Estimation of intra-cluster correlation coefficient via the failure of Bartlett’s second identity

A new means of estimating the correlation coefficient for cluster binary data in the regression settings is introduced. The creation of this method is founded upon the violation of Bartlett's second identity when adopting the binomial distributions to model binary data that are correlated. The new methodology applies to any sensible link functions that connect the success probability and covariates. One can easily implement the procedure by using any statistical software providing the naive and the sandwich covariance matrices for regression parameter estimates. Simulations and real data analyses are used to demonstrate the efficacy of our new procedure.

Sample size estimation to substantiate freedom from disease for clustered binary data with a specific risk profile

Disease cases are often clustered within herds or generally groups that share common characteristics. Sample size formulae must adjust for the within-cluster correlation of the primary sampling units. Traditionally, the intra-cluster correlation coefficient (ICC), which is an average measure of the data heterogeneity, has been used to modify formulae for individual sample size estimation. However, subgroups of animals sharing common characteristics, may exhibit excessively less or more heterogeneity. Hence, sample size estimates based on the ICC may not achieve the desired precision and power when applied to these groups. We propose the use of the variance partition coefficient (VPC), which measures the clustering of infection/disease for individuals with a common risk profile. Sample size estimates are obtained separately for those groups that exhibit markedly different heterogeneity, thus, optimizing resource allocation. A VPC-based predictive simulation method for sample size estimation to substantiate freedom from disease is presented. To illustrate the benefits of the proposed approach we give two examples with the analysis of data from a risk factor study on Mycobacterium avium subsp. paratuberculosis infection, in Danish dairy cattle and a study on critical control points for Salmonella cross-contamination of pork, in Greek slaughterhouses.

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.

Comparisons of computational methods for clustered binary data

Clustered binary data are common in medical research and can be fitted to the logistic regression model with random effects which belongs to a wider class of models called the generalized linear mixed model. The likelihood-based estimation of model parameters often has to handle intractable integration which leads to several estimation methods to overcome such difficulty. The penalized quasi-likelihood (PQL) method is the one that is very popular and computationally efficient in most cases. The expectation–maximization (EM) algorithm allows to estimate maximum-likelihood estimates, but requires to compute possibly intractable integration in the E-step. The variants of the EM algorithm to evaluate the E-step are introduced. The Monte Carlo EM (MCEM) method computes the E-step by approximating the expectation using Monte Carlo samples, while the Modified EM (MEM) method computes the E-step by approximating the expectation using the Laplace's method. All these methods involve several steps of approximation so that corresponding estimates of model parameters contain inevitable errors (large or small) induced by approximation. Understanding and quantifying discrepancy theoretically is difficult due to the complexity of approximations in each method, even though the focus is on clustered binary data. As an alternative competing computational method, we consider a non-parametric maximum-likelihood (NPML) method as well. We review and compare the PQL, MCEM, MEM and NPML methods for clustered binary data via simulation study, which will be useful for researchers when choosing an estimation method for their analysis.

A solution to separation for clustered binary data

The presence of one or more covariates that perfectly or almost perfectly predict the outcome of interest (which is referred to as complete or quasi-complete separation, the latter denoting the case when such perfect prediction occurs only for a subset of observations in the data) has been extensively studied in the last four decades. Since 1984, when Albert and Anderson (1984) differentiated between complete and quasi-complete separation, several authors have studied this phenomenon and tried to provide answers or ways of identifying the problem (Lesaffre and Albert, 1989; Firth, 1993; Christmann and Rousseeuw, 2001; Rousseeuw and Christmann, 2003; Allison, 2004; Zorn, 2005; Heinze, 2006). From an estimation perspective, separation leads to infinite coefficients and standard errors, which makes the algorithm collapse or give inappropriate results. As a practical matter, separation forces the analyst to choose from a number of problematic alternatives for dealing with the problem, and in the past the elimination of such problematic variables were common practice to deal with such situations. In the last decade, solutions using penalized likelihood have been proposed, but always dealing with independent binary data. Here we will propose a Bayesian solution to the problem when we deal with clustered binary data using informative priors that are supported by the data and compare it with an alternative procedure proposed by Gelman et al. (2008).

Testing non-inferiority for clustered matched-pair binary data in diagnostic medicine

Testing non-inferiority in active-controlled clinical trials examines whether a new procedure is, to a pre-specified amount, no worse than an existing procedure. To assess non-inferiority between two procedures using clustered matched-pair binary data, two new statistical tests are systematically compared to existing tests. The calculation of corresponding confidence interval is also proposed. None of the tests considered requires structural within-cluster correlation or distributional assumptions. The results of an extensive Monte Carlo simulation study illustrate that the performance of the statistics depends on several factors including the number of clusters, cluster size, probability of success in the test procedure, the homogeneity of the probability of success across clusters, and the intra-cluster correlation coefficient (ICC). In evaluating non-inferiority for a clustered matched-pair study, one should consider all of these issues when choosing an appropriate test statistic. The ICC-adjusted test statistic is generally recommended to effectively control the nominal level when there is constant or small variability of cluster sizes. For a greater number of clusters, the other test statistics maintain the nominal level reasonably well and have higher power. Therefore, with the carefully designed clustered matched-pair study, a combination of the statistics investigated may serve best in data analysis. Finally, to illustrate the practical application of the recommendations, a real clustered matched-pair collection of data is used to illustrate testing non-inferiority.

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.