Longitudinal Binary Data Research Articles

Joint mean-correlation model and its application to NorStOP binary data

In this paper we propose a generalized estimating equations method to joint model the mean and correlation structures for longitudinal binary data based on Gaussian copula, and apply it to a large cohort study for the UK’s North Staffordshire Osteoarthritis Project (NorStOP), where the responses can be pre-processed to binary variables. The resulting estimators for the mean and correlation parameters are proven to be consistent and asymptotically normally distributed. Since the theory and simulation results were studied in our previous manuscript [1], we give a brief introduction of our approach but mainly focus on its application to the NorStOP data.

Reference-based pattern-mixture models for analysis of longitudinal binary data

Pattern-mixture model (PMM)-based controlled imputations have become a popular tool to assess the sensitivity of primary analysis inference to different post-dropout assumptions or to estimate treatment effectiveness. The methodology is well established for continuous responses but less well established for binary responses. In this study, we formulate the copy-reference and jump-to-reference PMMs for longitudinal binary data using a multivariate probit model with latent variables. We discuss the maximum likelihood, Bayesian, and multiple imputation methods for estimating the treatment effect under the specified PMM. Simulation studies are conducted to evaluate the performance of these methods. These methods are also illustrated using data from a bipolar mania study.

Power difference in a \u03c72 test vs generalized linear mixed model in the presence of missing data \u2013 a simulation study

BackgroundLongitudinal randomized controlled trials (RCTs) often aim to test and measure the effect of treatment between arms at a single time point. A two-sample χ2 test is a common statistical approach when outcome data are binary. However, only complete outcomes are used in the analysis. Missing responses are common in longitudinal RCTs and by only analyzing complete data, power may be reduced and estimates could be biased. Generalized linear mixed models (GLMM) with a random intercept can be used to test and estimate the treatment effect, which may increase power and reduce bias.MethodsWe simulated longitudinal binary RCT data to compare the performance of a complete case χ2 test to a GLMM in terms of power, type I error, relative bias, and coverage under different missing data mechanisms (missing completely at random and missing at random). We considered how the baseline probability of the event, within subject correlation, and dropout rates under various missing mechanisms impacted each performance measure.ResultsWhen outcome data were missing completely at random, both χ2 and GLMM produced unbiased estimates; however, the GLMM returned an absolute power gain up to from 12.0% as compared to the χ2 test. When outcome data were missing at random, the GLMM yielded an absolute power gain up to 42.7% and estimates were unbiased or less biased compared to the χ2 test.ConclusionsInvestigators wishing to test for a treatment effect between treatment arms in longitudinal RCTs with binary outcome data in the presence of missing data should use a GLMM to gain power and produce minimally unbiased estimates instead of a complete case χ2 test.

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.

Retrospective Association Analysis of Longitudinal Binary Traits Identifies Important Loci and Pathways in Cocaine Use.

Longitudinal phenotypes have been increasingly available in genome-wide association studies (GWAS) and electronic health record-based studies for identification of genetic variants that influence complex traits over time. For longitudinal binary data, there remain significant challenges in gene mapping, including misspecification of the model for phenotype distribution due to ascertainment. Here, we propose L-BRAT (Longitudinal Binary-trait Retrospective Association Test), a retrospective, generalized estimating equation-based method for genetic association analysis of longitudinal binary outcomes. We also develop RGMMAT, a retrospective, generalized linear mixed model-based association test. Both tests are retrospective score approaches in which genotypes are treated as random conditional on phenotype and covariates. They allow both static and time-varying covariates to be included in the analysis. Through simulations, we illustrated that retrospective association tests are robust to ascertainment and other types of phenotype model misspecification, and gain power over previous association methods. We applied L-BRAT and RGMMAT to a genome-wide association analysis of repeated measures of cocaine use in a longitudinal cohort. Pathway analysis implicated association with opioid signaling and axonal guidance signaling pathways. Lastly, we replicated important pathways in an independent cocaine dependence case-control GWAS. Our results illustrate that L-BRAT is able to detect important loci and pathways in a genome scan and to provide insights into genetic architecture of cocaine use.

Functional Logistic Mixed-Effects Models for Learning Curves From Longitudinal Binary Data.

Purpose We present functional logistic mixed-effects models (FLMEMs) for estimating population and individual-level learning curves in longitudinal experiments. Method Using functional analysis tools in a Bayesian hierarchical framework, the FLMEM captures nonlinear, smoothly varying learning curves, appropriately accommodating uncertainty in various aspects of the analysis while also borrowing information across different model layers. An R package implementing our method is available as part of the Supplemental Materials . Results Application to speech learning data from Reetzke, Xie, Llanos, and Chandrasekaran (2018) and a simulation study demonstrate the utility of FLMEM and its many advantages over linear and logistic mixed-effects models. Conclusion The FLMEM is highly flexible and efficient in improving upon the practical limitations of linear models and logistic linear mixed-effects models. We expect the FLMEM to be a useful addition to the speech, language, and hearing scientist's toolkit. Supplemental Material https://doi.org/10.23641/asha.7822568.

Bias-reduced and separation-proof GEE with small or sparse longitudinal binary data.

Generalized estimating equation (GEE) is a popular approach for analyzing correlated binary data. However, the problems of separation in GEE are still unknown. The separation created by a covariate often occurs in small correlated binary data and even in large data with rare outcome and/or high intra-cluster correlation and a number of influential covariates. This paper investigated the consequences of separation in GEE and addressed them by introducing a penalized GEE, termed as PGEE. The PGEE is obtained by adding Firth-type penalty term, which was originally proposed for generalized linear model score equation, to standard GEE and shown to achieve convergence and provide finite estimate of the regression coefficient in the presence of separation, which are not often possible in GEE. Further, a small-sample bias correction to the sandwich covariance estimator of the PGEE estimator is suggested. Simulations also showed that the GEE failed to achieve convergence and/or provided infinitely large estimate of the regression coefficient in the presence of complete or quasi-complete separation, whereas the PGEE showed significant improvement by achieving convergence and providing finite estimate. Even in the presence of near-to-separation, the PGEE also showed superior properties over the GEE. Furthermore, the bias-corrected sandwich estimator for the PGEE estimator showed substantial improvement over the standard sandwich estimator by reducing bias in estimating type I error rate. An illustration using real data also supported the findings of simulation. The PGEE with bias-corrected sandwich covariance estimator is recommended to use for small-to-moderate size sample (N ≤ 50) and even can be used for large sample if there is any evidence of separation or near-to-separation.

A Data Analysis Method for Using Longitudinal Binary Outcome Data from a SMART to Compare Adaptive Interventions

Sequential multiple assignment randomized trials (SMARTs) are a useful and increasingly popular approach for gathering information to inform the construction of adaptive interventions to treat psychological and behavioral health conditions. Until recently, analysis methods for data from SMART designs considered only a single measurement of the outcome of interest when comparing the efficacy of adaptive interventions. Lu et al. proposed a method for considering repeated outcome measurements to incorporate information about the longitudinal trajectory of change. While their proposed method can be applied to many kinds of outcome variables, they focused mainly on linear models for normally distributed outcomes. Practical guidelines and extensions are required to implement this methodology with other types of repeated outcome measures common in behavioral research. In this article, we discuss implementation of this method with repeated binary outcomes. We explain how to compare adaptive interventions in terms of various summaries of repeated binary outcome measures, including average outcome (area under the curve) and delayed effects. The method is illustrated using an empirical example from a SMART study to develop an adaptive intervention for engaging alcohol- and cocaine-dependent patients in treatment. Monte Carlo simulations are provided to demonstrate the good performance of the proposed technique.

Modeling of the ARMA random effects covariance matrix in logistic random effects models

Logistic random effects models (LREMs) have been frequently used to analyze longitudinal binary data. When a random effects covariance matrix is used to make proper inferences on covariate effects, the random effects in the models account for both within-subject association and between-subject variation, but the covariance matix is difficult to estimate because it is high-dimensional and should be positive definite. To overcome these limitations, two Cholesky decomposition approaches were proposed for precision matrix and covariance matrix: modified Cholesky decomposition and moving average Cholesky decomposition, respectively. However, the two approaches may not work when there are non-trivial and complicated correlations of repeated outcomes. In this paper, we combined the two decomposition approaches to model the random effects covariance matrix in the LREMs, thereby capturing a wider class of sophisticated dependence structures while achieving parsimony in parametrization. We then used our proposed model to analyze lung cancer data.

Sensitivity analysis for non-monotone missing binary data in longitudinal studies: Application to the NIDA collaborative cocaine treatment study.

Conventional approaches for handling missingness in substance use disorder trials commonly rely upon a single deterministic "worst value" imputation that posits a perfect relationship between missingness and drug use ("missing value = presumed drug use"); this yields biased estimates of treatment effects and their standard errors. Instead, deterministic imputations should be replaced by probabilistic versions that encode researchers prior beliefs that those with missing data are more likely to be using drugs at those occasions. Motivated by this problem, we present a method for handling non-monotone missing binary data in longitudinal studies. Specifically, we consider a joint model that combines a not missing at random (NMAR) selection model with a generalized linear mixed model for longitudinal binary data. The selection model links the distribution of a missing outcome to the corresponding distribution of the outcome for those observed at that occasion via a fixed and known sensitivity parameter. The mixed model for longitudinal binary data assumes the random effects have bridge distributions; the latter yields regression parameters that have both subject-specific and marginal interpretations. This approach is completely transparent about what is being assumed about missing data and can be used as the basis for sensitivity analysis.

Misspecification of Multimodal Random-Effect Distributions in Logistic Mixed Models for Panel Survey Data

Summary Logistic mixed models for longitudinal binary data typically assume normally distributed random effects, which may be too restrictive if an underlying subpopulation structure exists. The paper illustrates the ease of implementing diagnostic tests and fitting random effects as a mixture of normal distributions to detect and address distributional misspecification of the random effects in a potential mover–stayer scenario. Methods are illustrated by using data from the Household, Income and Labour Dynamics in Australia panel survey. The robustness of the normality assumption to violations characterized by a three-component mixture of normal distributions was assessed via a simulation study. Adverse inferential impact of incorrectly assuming normality was identified for parameters directly related to the random effects, resulting in biased estimates and poor coverage rates for confidence intervals. The results support the general robustness of fixed effect parameters to non-extreme distributional violations of the random effects.

Bayesian Analysis of Markov Based Logistic Model

In analyzing longitudinal data the correlations between responses obtained from same individual need to be taken into account. Various models can be used to handle such correlations. This article focuses on the application of transition modeling using Bayesian approach for analyzing longitudinal binary data. For Bayesian estimation asymmetric loss functions, such as, linear exponential (LINEX) and modified linear exponential (MLINEX) loss function and Tierney and Kadnae (T.K.) approximation has been used. Comparison is made using Bayes factor and Bayesian approach under LINEX loss function can be suggested to estimate the parameters of transition model.

Outcome-related, Auxiliary Variable Sampling Designs for Longitudinal Binary Data.

Epidemiologists have long used case-control and related study designs to enhance variability of response and information available to estimate exposure-disease associations. Less has been done for longitudinal data. We discuss an epidemiological study design and analysis approach for longitudinal binary response data. We seek to gain statistical efficiency by oversampling relatively informative subjects for inclusion into the sample. In this methodological demonstration, we develop this concept by sampling repeatedly from an existing cohort study to estimate the relationship of chronic obstructive pulmonary disease to past-year smoking in a panel of baseline smokers. To account for oversampling, we describe a sequential offsetted regressions approach for valid inferences in this setting. Targeted sampling can lead to increased statistical efficiency when combined with sequential offsetted regressions. Efficiency gains are degraded with increased prevalence of the disease response variable, with decreased association between the sampling variable and the response, and with other design and analysis parameters, providing guidance to those wishing to use these types of designs in the future. These designs hold promise for efficient use of resources in longitudinal cohort studies.

Extending the Case-Control Design to Longitudinal Data: Stratified Sampling Based on Repeated Binary Outcomes.

We detail study design options that generalize case-control sampling when longitudinal outcome data are already collected as part of a primary cohort study, but new exposure data must be retrospectively processed for a secondary analysis. Furthermore, we assume that cost will limit the size of the subsample that can be evaluated. We describe a novel class of stratified outcome-dependent sampling designs for longitudinal binary response data where distinct strata are created for subjects who never, sometimes, and always experienced the event of interest during longitudinal follow-up. Individual designs within this class are differentiated by the stratum-specific sampling probabilities. We show for parameters associated with time-varying exposures, subjects who experience the event/outcome at some but not at all of the follow-up times (i.e., those who exhibit response variation) are highly informative. If the time-varying exposure varies exclusively within individuals (i.e., intraclass correlation coefficient is 0), then sampling all subjects with response variability can yield highly precise parameter estimates even when compared with an analysis of the original cohort. The flexibility of the designs and analysis procedures also permits estimation of parameters that correspond to time-fixed covariates, and we show that with an imputation-based estimation procedure, baseline covariate associations can be estimated with very high precision irrespective of the design. We demonstrate features of the designs and analysis procedures via a plasmode simulation using data from the Lung Health Study.

Bayesian Modeling and Inference for Nonignorably Missing Longitudinal Binary Response Data with Applications to HIV Prevention Trials.

Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, one must handle the missing data appropriately and examine whether the missing data mechanism is ignorable or nonignorable. In this article, we develop a new probit model for longitudinal binary response data. It resolves a challenging issue for estimating the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We show that when improper uniform priors are specified for the regression coefficients of the joint multinomial model via a sequence of one-dimensional conditional distributions for the missing data indicators under nonignorable missingness, the joint posterior distribution is improper. A variation of Jeffreys prior is thus established as a remedy for the improper posterior distribution. In addition, an efficient Gibbs sampling algorithm is developed using a collapsing technique. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to guide the choices of prior specifications and to compare the models under different missing data mechanisms. We report on extensive simulations conducted to investigate the empirical performance of the proposed methods. The proposed methodology is further illustrated using data from an HIV prevention clinical trial.

A comparison of multiple imputation methods for incomplete longitudinal binary data

ABSTRACTLongitudinal binary data are commonly encountered in clinical trials. Multiple imputation is an approach for getting a valid estimation of treatment effects under an assumption of missing at random mechanism. Although there are a variety of multiple imputation methods for the longitudinal binary data, a limited number of researches have reported on relative performances of the methods. Moreover, when focusing on the treatment effect throughout a period that has often been used in clinical evaluations of specific disease areas, no definite investigations comparing the methods have been available. We conducted an extensive simulation study to examine comparative performances of six multiple imputation methods available in the SAS MI procedure for longitudinal binary data, where two endpoints of responder rates at a specified time point and throughout a period were assessed. The simulation study suggested that results from naive approaches of a single imputation with non-responders and a complete case analysis could be very sensitive against missing data. The multiple imputation methods using a monotone method and a full conditional specification with a logistic regression imputation model were recommended for obtaining unbiased and robust estimations of the treatment effect. The methods were illustrated with data from a mental health research.

Pairwise residuals and diagnostic tests for misspecified dependence structures in models for binary longitudinal data.

Maximum likelihood estimation of models for binary longitudinal data is typically inconsistent if the dependence structure is misspecified. Unfortunately, diagnostics specifically designed for detecting such misspecifications are scant. We develop residuals and diagnostic tests based on comparing observed and expected frequencies of response patterns over time in the presence of arbitrary time-varying and time-invariant covariates. To overcome the sparseness problem, we use lower-order marginal tables, such as two-way tables for pairs of time-points, aggregated over covariate patterns. Our proposed pairwise concordance residuals are valuable for exploratory diagnostics and for constructing both generic tests for misspecified dependence structure as well as targeted adjacent pair concordance tests for excess serial dependence. The proposed methods are straightforward to implement and work well for general situations, regardless of the number of time-points and the number and types of covariates.

A pseudo likelihood approach to analyze rate difference of binary response data in longitudinal factorial studies

ABSTRACTAlthough Fan showed that the mixed-effects model for repeated measures (MMRM) is appropriate to analyze complete longitudinal binary data in terms of the rate difference, they focused on using the generalized estimating equations (GEE) to make statistical inference. The current article emphasizes validity of the MMRM when the normal-distribution-based pseudo likelihood approach is used to make inference for complete longitudinal binary data. For incomplete longitudinal binary data with missing at random missing mechanism, however, the MMRM, using either the GEE or the normal-distribution-based pseudo likelihood inferential procedure, gives biased results in general and should not be used for analysis.

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 marginalized multilevel model for bivariate longitudinal binary data

This study considers analysis of bivariate longitudinal binary data. We propose a model based on marginalized multilevel model framework. The proposed model consists of two levels such that the first level associates the marginal mean of responses with covariates through a logistic regression model and the second level includes subject/time specific random intercepts within a probit regression model. The covariance matrix of multiple correlated time-specific random intercepts for each subject is assumed to represent the within-subject association. The subject-specific random effects covariance matrix is further decomposed into its dependence and variance components through modified Cholesky decomposition method and then the unconstrained version of resulting parameters are modelled in terms of covariates with low-dimensional regression parameters. This provides better explanations related to dependence and variance parameters and a reduction in the number of parameters to be estimated in random effects covariance matrix to avoid possible identifiability problems. Marginal correlations between responses of subjects and within the responses of a subject are derived through a Taylor series-based approximation. Data cloning computational algorithm is used to compute the maximum likelihood estimates and standard errors of the parameters in the proposed model. The validity of the proposed model is assessed through a Monte Carlo simulation study, and results are observed to be at acceptable level. Lastly, the proposed model is illustrated through Mother’s Stress and Children’s Morbidity study data, where both population-averaged and subject-specific interpretations are drawn through Emprical Bayes estimation of random effects.