Marginal modeling of multilevel binary data with time-varying covariates

We propose and compare two approaches for regression analysis of multilevel binary data when clusters are not necessarily nested: a GEE method that relies on a working independence assumption coupled with a three-step method for obtaining empirical standard errors, and a likelihood-based method implemented using Bayesian computational techniques. Implications of time-varying endogenous covariates are addressed. The methods are illustrated using data from the Breast Cancer Surveillance Consortium to estimate mammography accuracy from a repeatedly screened population.     

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.     

Testing the effect of treatment in experiments with correlated binary outcomes.

This paper considers the problem of testing for treatment effect in a randomized experiment with correlated binary outcomes, representing success or failure for different "parts" of a randomized unit. Attention is restricted to tests that are based on a summary score for each individual randomized, and thus are valid regardless of the precise nature of the correlation among parts. The focus is on the efficiency of such tests under various correlation structures, with special emphasis on the case in which the correlation among parts within an individual differs across treatment groups. A class of summary score statistics is defined, and optimal testing is discussed for some simple situations. Three potential general-purpose tests also are described: (1) the ratio estimate test discussed by Henderson et al. (1988, Controlled Clinical Trials 9, 189-205); (2) a modified ratio estimate test with adjusted weighting based on the within-individual correlation between parts; (3) a test defined by applying the Mantel-Haenszel procedure to the proportion of individuals with at least one failure, stratifying by the number of parts. For these general-purpose tests, numerical calculations of asymptotic efficiency are presented under a wide range of designs and correlation structures. On the basis of these results, some practical recommendations for choosing a test are made.     

Significance levels for studies with correlated test statistics

When testing large numbers of null hypotheses, one needs to assess the evidence against the global null hypothesis that none of the hypotheses is false. Such evidence typically is based on the test statistic of the largest magnitude, whose statistical significance is evaluated by permuting the sample units to simulate its null distribution. Efron (2007) has noted that correlation among the test statistics can induce substantial interstudy variation in the shapes of their histograms, which may cause misleading tail counts. Here, we show that permutation-based estimates of the overall significance level also can be misleading when the test statistics are correlated. We propose that such estimates be conditioned on a simple measure of the spread of the observed histogram, and we provide a method for obtaining conditional significance levels. We justify this conditioning using the conditionality principle described by Cox and Hinkley (1974). Application of the method to gene expression data illustrates the circumstances when conditional significance levels are needed.     

Random-effects models for serial observations with binary response

This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a logistic model, but with regression coefficients that vary between subjects. The logistic regression parameters are assumed to be normally distributed in the population. Inference is based upon maximum likelihood estimation of fixed effects and variance components, and empirical Bayes estimation of random effects. Exact solutions are analytically and computationally infeasible, but an approximation based on the mode of the posterior distribution of the random parameters is proposed, and is implemented by means of the EM algorithm. This approximate method is compared with a simpler two-step method proposed by Korn and Whittemore (1979, Biometrics 35, 795-804), using data from a panel study of asthmatics originally described in that paper. One advantage of the estimation strategy described here is the ability to use all of the data, including that from subjects with insufficient data to permit fitting of a separate logistic regression model, as required by the Korn and Whittemore method. However, the new method is computationally intensive.     

Early glial responses in murine models of multiple sclerosis

Investigations of functional interactions among axons and glia over the last decade have revealed the extent and complexity of glial-neuronal and glial-glial communication during development, adult function and recovery from injury. These data have profound implications for the understanding of central nervous system (CNS) disorders, which until recently, have been classified as either neuronal or glial diseases. Re-evaluation of the pathological processes in a number of conditions has clearly shown involvement of both neurons and glia in early pathology. In multiple sclerosis (MS), the myelin sheath has traditionally been regarded as the primary target. However, recent evidence has clearly demonstrated axonal damage in new lesions. We have addressed the question of the role of axonal pathology in early MS by using well-characterized murine models for the relapsing-remitting (RR) or the primary progressive (PP) forms of the disease. We performed a histopathological survey of the CNS, following induction of the disease, to determine the timing of appearance, as well as the development of lesions. Then we analysed the relationship between inflammation, demyelination and axonal damage together with responses from astrocytes and microglia in each model from the earliest evidence of inflammation. We found that axonal damage begins well ahead of the appearance of motor symptoms. Pathology appears to be more closely related to the degree of inflammation than to demyelination. We also show that early astrocyte responses and the degree of axonal loss are markedly different in the two models and relate to the severity of pathology. These data support the now widely accepted hypothesis that axonal damage begins early in the disease process, but also suggest modulation of axonal loss and disease progression by the astrocytic response.     

Finite volume and asymptotic methods for stochastic neuron models with correlated inputs

We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker?CPlanck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein?CUhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation.