Analysis of clustered and longitudinal binary data subject to response misclassification

Misclassified clustered and longitudinal data arise in studies where the response indicates a condition identified through an imperfect diagnostic procedure. Examples include longitudinal studies that use an imperfect diagnostic test to assess whether or not an individual has been infected with a specific virus. This article presents methods to implement both population-averaged and cluster-specific analyses of such data when the misclassification rates are known. The methods exploit the fact that the class of generalized linear models enjoys a closure property in the case of misclassified responses. Data from longitudinal studies of infectious disease will illustrate the findings.     

A latent autoregressive model for longitudinal binary data subject to informative missingness

Longitudinal clinical trials often collect long sequences of binary data. Our application is a recent clinical trial in opiate addicts that examined the effect of a new treatment on repeated binary urine tests to assess opiate use over an extended follow-up. The dataset had two sources of missingness: dropout and intermittent missing observations. The primary endpoint of the study was comparing the marginal probability of a positive urine test over follow-up across treatment arms. We present a latent autoregressive model for longitudinal binary data subject to informative missingness. In this model, a Gaussian autoregressive process is shared between the binary response and missing-data processes, thereby inducing informative missingness. Our approach extends the work of others who have developed models that link the various processes through a shared random effect but do not allow for autocorrelation. We discuss parameter estimation using Monte Carlo EM and demonstrate through simulations that incorporating within-subject autocorrelation through a latent autoregressive process can be very important when longitudinal binary data is subject to informative missingness. We illustrate our new methodology using the opiate clinical trial data.     

Mixed effects logistic regression models for longitudinal ordinal functional response data with multiple-cause drop-out from the longitudinal study of aging

In the context of analyzing ordinal functional limitation responses from the Longitudinal Study of Aging, we investigate the association between current functional limitation and previous year's limitation and its modification by physical activity and multiple causes of drop-out. We accommodate the longitudinal nature of the multiple causes of informative drop-out (death and unknown loss-to-follow-up) with a mixed effects logistic model. Under the proposed model with a random intercept and slope, the ordinal functional outcome and multiple discrete time survival profiles share a common random effect structure. This shared parameter selection model assumes that the multiple causes of drop-out are conditionally independent of the functional limitation outcome given the underlying random effect representing an individual's trajectory of general health status across time. Although it is not possible to fully assess the adequacy of this assumption, we assess the robustness of the approach by varying the assumptions underlying the proposed model, such as the random effects distribution and the drop-out component. It appears that between-subject differences in initial functional limitation are strongly associated with future functional limitation and that this association is stronger for those who do not have physical activity regardless of the random effects and informative drop-out specifications. In contrast, the association between current functional limitation and previous trajectory of functional status within an individual is weaker and more sensitive to changes in the random effects and drop-out assumptions.     

Multiple outputation: inference for complex clustered data by averaging analyses from independent data

This article applies a simple method for settings where one has clustered data, but statistical methods are only available for independent data. We assume the statistical method provides us with a normally distributed estimate, theta, and an estimate of its variance sigma. We randomly select a data point from each cluster and apply our statistical method to this independent data. We repeat this multiple times, and use the average of the associated theta's as our estimate. An estimate of the variance is given by the average of the sigma2's minus the sample variance of the theta's. We call this procedure multiple outputation, as all "excess" data within each cluster is thrown out multiple times. Hoffman, Sen, and Weinberg (2001, Biometrika 88, 1121-1134) introduced this approach for generalized linear models when the cluster size is related to outcome. In this article, we demonstrate the broad applicability of the approach. Applications to angular data, p-values, vector parameters, Bayesian inference, genetics data, and random cluster sizes are discussed. In addition, asymptotic normality of estimates based on all possible outputations, as well as a finite number of outputations, is proven given weak conditions. Multiple outputation provides a simple and broadly applicable method for analyzing clustered data. It is especially suited to settings where methods for clustered data are impractical, but can also be applied generally as a quick and simple tool.     

Marginal models for longitudinal continuous proportional data

Summary. Continuous proportional data arise when the response of interest is a percentage between zero and one, e.g., the percentage of decrease in renal function at different follow‐up times from the baseline. In this paper, we propose methods to directly model the marginal means of the longitudinal proportional responses using the simplex distribution of Barndorff‐Nielsen and Jørgensen that takes into account the fact that such responses are percentages restricted between zero and one and may as well have large dispersion. Parameters in such a marginal model are estimated using an extended version of the generalized estimating equations where the score vector is a nonlinear function of the observed response. The method is illustrated with an ophthalmology study on the use of intraocular gas in retinal repair surgeries.     

Behavioral testing of antidepressant compounds: an analysis of crossover design for correlated binary data

The differential reinforcement of low-rate 72 seconds schedule (DRL-72) is a standard behavioral test procedure for screening potential antidepressant compounds. The protocol for the DRL-72 experiment, proposed by Evenden et al. (1993), consists of using a crossover design for the experiment and one-way ANOVA for the statistical analysis. In this paper we discuss the choice of several crossover designs for the DRL-72 experiment and propose to estimate the treatment effects using either generalized linear mixed models (GLMM) or generalized estimating equation (GEE) models for clustered binary data.     

A statistical model for under- or overdispersed clustered and longitudinal count data

We propose a likelihood-based model for correlated count data that display under- or overdispersion within units (e.g. subjects). The model is capable of handling correlation due to clustering and/or serial correlation, in the presence of unbalanced, missing or unequally spaced data. A family of distributions based on birth-event processes is used to model within-subject underdispersion. A computational approach is given to overcome a parameterization difficulty with this family, and this allows use of common Markov Chain Monte Carlo software (e.g. WinBUGS) for estimation. Application of the model to daily counts of asthma inhaler use by children shows substantial within-subject underdispersion, between-subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. The model provides a major improvement over Poisson longitudinal models, and diagnostics show that the model fits well.     

Overdispersed fungus germination data: statistical analysis using R

ABSTRACT

Proportion data from dose-response experiments are often overdispersed, characterised by a larger variance than assumed by the standard binomial model. Here, we present different models proposed in the literature that incorporate overdispersion. We also discuss how to select the best model to describe the data and present, using R software, specific code used to fit and interpret binomial, quasi-binomial, beta-binomial, and binomial-normal models, as well as to assess goodness-of-fit. We illustrate applications of these generalized linear models and generalized linear mixed models with a case study from a biological control experiment, where different isolates of Isaria fumosorosea (Hypocreales: Cordycipitaceae) were used to assess which ones presented higher resistance to UV-B radiation. We show how to test for differences between isolates and also how to statistically group isolates presenting a similar behaviour.     

Quantifying intraclass correlations for count and time‐to‐event data

The intraclass correlation is commonly used with clustered data. It is often estimated based on fitting a model to hierarchical data and it leads, in turn, to several concepts such as reliability, heritability, inter‐rater agreement, etc. For data where linear models can be used, such measures can be defined as ratios of variance components. Matters are more difficult for non‐Gaussian outcomes. The focus here is on count and time‐to‐event outcomes where so‐called combined models are used, extending generalized linear mixed models, to describe the data. These models combine normal and gamma random effects to allow for both correlation due to data hierarchies as well as for overdispersion. Furthermore, because the models admit closed‐form expressions for the means, variances, higher moments, and even the joint marginal distribution, it is demonstrated that closed forms of intraclass correlations exist. The proposed methodology is illustrated using data from agricultural and livestock studies.     

Modeling tumor growth with random onset

The longitudinal assessment of tumor volume is commonly used as an endpoint in small animal studies in cancer research. Groups of genetically identical mice are injected with mutant cells from clones developed with different mutations. The interest is on comparing tumor onset (i.e., the time of tumor detection) and tumor growth after onset, between mutation groups. This article proposes a class of linear and nonlinear growth models for jointly modeling tumor onset and growth in this situation. Our approach allows for interval-censored time of onset and missing-at-random dropout due to early sacrifice, which are common situations in animal research. We show that our approach has good small-sample properties for testing and is robust to some key unverifiable modeling assumptions. We illustrate this methodology with an application examining the effect of different mutations on tumorigenesis.     

Modeling clustered, discrete, or grouped time survival data with covariates

We have developed methods for modeling discrete or grouped time, right-censored survival data collected from correlated groups or clusters. We assume that the marginal hazard of failure for individual items within a cluster is specified by a linear log odds survival model and the dependence structure is based on a gamma frailty model. The dependence can be modeled as a function of cluster-level covariates. Likelihood equations for estimating the model parameters are provided. Generalized estimating equations for the marginal hazard regression parameters and pseudolikelihood methods for estimating the dependence parameters are also described. Data from two clinical trials are used for illustration purposes.     

Semiparametric frailty models for zero‐inflated event count data in the presence of informative dropout

Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow‐up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow‐up time and the subject‐specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood‐based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite‐dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes.     

Akaike's information criterion in generalized estimating equations

Correlated response data are common in biomedical studies. Regression analysis based on the generalized estimating equations (GEE) is an increasingly important method for such data. However, there seem to be few model-selection criteria available in GEE. The well-known Akaike Information Criterion (AIC) cannot be directly applied since AIC is based on maximum likelihood estimation while GEE is nonlikelihood based. We propose a modification to AIC, where the likelihood is replaced by the quasi-likelihood and a proper adjustment is made for the penalty term. Its performance is investigated through simulation studies. For illustration, the method is applied to a real data set.     

Modeling longitudinal data with ordinal response by varying coefficients

This paper presents a smooth regression model for ordinal data with longitudinal dependence structure. A marginal model with cumulative logit link is applied to cope with the ordinal scale and the main and covariate effects in the model are allowed to vary with time. Local fitting is pursued and asymptotic properties of the estimates are discussed. In a second step, the longitudinal dependence of the observations is considered. Cumulative log odds ratios are fitted locally, which allows investigation of how the longitudinal dependence of the ordinal observations changes with time.     

Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function

Typically, regression models for competing risks outcomes are based on proportional hazards models for the crude hazard rates. These estimates often do not agree with impressions drawn from plots of cumulative incidence functions for each level of a risk factor. We present a technique which models the cumulative incidence functions directly. The method is based on the pseudovalues from a jackknife statistic constructed from the cumulative incidence curve. These pseudovalues are used in a generalized estimating equation to obtain estimates of model parameters. We study the properties of this estimator and apply the technique to a study of the effect of alternative donors on relapse for patients given a bone marrow transplant for leukemia.     

Marginal Models Via GLS: A Convenient Yet Neglected Tool for the Analysis of Correlated Data in the Behavioural Sciences

Behavioural research often produces data that have a complicated structure. For instance, data can represent repeated observations of the same individual and suffer from heteroscedasticity as well as other technical snags. The regression analysis of such data is often complicated by the fact that the observations (response variables) are mutually correlated. The correlation structure can be quite complex and might or might not be of direct interest to the user. In any case, one needs to take correlations into account (e.g. by means of random‐effect specification) in order to arrive at correct statistical inference (e.g. for construction of the appropriate test or confidence intervals). Over the last decade, such data have been more and more frequently analysed using repeated‐measures ANOVA and mixed‐effects models. Some researchers invoke the heavy machinery of mixed‐effects modelling to obtain the desired population‐level (marginal) inference, which can be achieved by using simpler tools – namely marginal models. This paper highlights marginal modelling (using generalized least squares [GLS] regression) as an alternative method. In various concrete situations, such marginal models can be based on fewer assumptions and directly generate estimates (population‐level parameters) which are of immediate interest to the behavioural researcher (such as population mean). Sometimes, they might be not only easier to interpret but also easier to specify than their competitors (e.g. mixed‐effects models). Using five examples from behavioural research, we demonstrate the use, advantages, limits and pitfalls of marginal and mixed‐effects models implemented within the functions of the ‘nlme’ package in R.