Paul S. Albert

Models for longitudinal data: a generalized estimating equation approach.

This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mothers smoking and childrens respiratory disease.

A generalized estimating equations approach for spatially correlated binary data: applications to the analysis of neuroimaging data.

This paper proposes a generalized estimating equations approach for the analysis of spatially correlated binary data when there are large numbers of spatially correlated observations on a moderate number of subjects. This approach is useful when the scientific focus is on modeling the marginal mean structure. Proper modeling of the spatial correlation structure is shown to provide large efficiency gains along with precise standard error estimates for inference on mean structure parameters. Generalized estimating equations for estimating the parameters of both the mean and spatial correlation structure are proposed. The use of semivariogram models for parameterizing the correlation structure is discussed, and estimation of the sample semivariogram is proposed as a technique for choosing parametric models and starting values for generalized estimating equations estimation. The methodology is illustrated with neuroimaging data collected as part of the National Institute of Neurological Disorders and Stroke (NINDS) Stroke Data Bank. A simulation study demonstrates the importance of accurate modeling of the spatial correlation structure in data with large numbers of spatially correlated observations such as those found in neuroimaging studies.

A two-state Markov mixture model for a time series of epileptic seizure counts.

This paper discusses a model for a time series of epileptic seizure counts in which the mean of a Poisson distribution changes according to an underlying two-state Markov chain. The EM algorithm (Dempster, Laird, and Rubin, 1977, Journal of the Royal Statistical Society, Series B 39, 1-38) is used to compute maximum likelihood estimators for the parameters of this two-state mixture model and extensions are made allowing for nonstationarity. The model is illustrated using daily seizure counts for patients with intractable epilepsy and results are compared with a simple Poisson distribution and Poisson regressions. Some simulation results are also presented to demonstrate the feasibility of this model.

A Random Effects Transition Model For Longitudinal Binary Data With Informative Missingness

Understanding the transitions between disease states is often the goal in studying chronic disease. These studies, however, are typically subject to a large amount of missingness either due to patient dropout or intermittent missed visits. The missing data is often informative since missingness and dropout are usually related to either an individuals underlying disease process or the actual value of the missed observation. Our motivating example is a study of opiate addiction that examined the effect of a new treatment on thrice-weekly binary urine tests to assess opiate use over follow-up. The interest in this opiate addiction clinical trial was to characterize the transition pattern of opiate use (in each treatment arm) as well as to compare both the marginal probability of a positive urine test over follow-up and the time until the first positive urine test between the treatment arms. We develop a shared random effects model that links together the propensity of transition between states and the probability of either an intermittent missed observation or dropout. This approach allows for heterogeneous transition and missing data patterns between individuals as well as incorporating informative intermittent missing data and dropout. We compare this new approach with other approaches proposed for the analysis of longitudinal binary data with informative missingness.

A Markov model for sequences of ordinal data from a relapsing-remitting disease

Many chronic diseases follow a course with multiple relapses into periods with severe symptoms alternating with periods of remission; experimental allergic encephalomyelitis, the animal model for multiple sclerosis, is an example of such a disease. A finite Markov chain is proposed as a model for analyzing sequences of ordinal data from a relapsing-remitting disease. The proposed model is one in which the state space is expanded to include information about the relapsing-remitting status as well as the ordinal severity score, and a reparameterization is suggested that reduces the number of parameters needed to be estimated. The Markov model allows for a wide range of relapsing-remitting behavior, provides an understanding of the stochastic nature of the disease process, and allows for efficient estimation of important characteristics of the disease course (such as mean first passage times, occupation times, and steady-state probabilities). These methods are applied to data from a study of the effect of a treatment (transforming growth factor-beta 1) on experimental allergic encephalomyelitis.

A Latent Process Regression Model for Spatially Correlated Count Data

This paper proposes a regression model for spatially correlated count data that generalizes the work of Zeger (1988, Biometrika 75, 621-629) developed in a time-series setting. In this approach, spatial correlation is introduced through a latent process, and the marginal mean function may contain spatial trends and covariates. Generalized estimating equations are used to estimate and perform marginal inference on the spatial trend and covariate effects. The feasibility of this approach is demonstrated using an example of the distribution of neuronal cell counts in a laboratory culture dish.

Estimating diagnostic accuracy of multiple binary tests with an imperfect reference standard

The goal in diagnostic medicine is often to estimate the diagnostic accuracy of multiple experimental tests relative to a gold standard reference. When a gold standard reference is not available, investigators commonly use an imperfect reference standard. This paper proposes methodology for estimating the diagnostic accuracy of multiple binary tests with an imperfect reference standard when information about the diagnostic accuracy of the imperfect test is available from external data sources. We propose alternative joint models for characterizing the dependence between the experimental tests and discuss the use of these models for estimating individual-test sensitivity and specificity as well as prevalence and multivariate post-test probabilities (predictive values). We show using analytical and simulation techniques that, as long as the sensitivity and specificity of the imperfect test are high, inferences on diagnostic accuracy are robust to misspecification of the joint model. The methodology is demonstrated with a study examining the diagnostic accuracy of various HIV-antibody tests for HIV.

High frequency of CDKN2A alterations in esophageal squamous cell carcinoma from a high‐risk Chinese population

Because previous studies have shown that loss of heterozygosity (LOH) is common on chromosome arm 9p in esophageal squamous cell carcinoma (ESCC) and that genetic alterations in CDKN2A and CDKN2B on 9p are also common, we sought to determine whether LOH and these genetic alterations are related. We performed LOH studies on chromosome bands 9p21–p22 and searched for genetic alterations of CDKN2A and CDKN2B in 56 ESCCs from a high‐risk Chinese population. Seventy‐three percent of patients were found to have LOH at one or more loci on chromosome bands 9p21–p22, and LOH occurred more frequently in patients with a family history of upper gastrointestinal cancer than in those with a negative family history (P = 0.01, global permutation test). CDKN2A mutations (point mutations, deletions, insertions) were observed in 25% (14 of 56) of cases, and the LOH pattern was significantly different for individuals with and without a CDKN2A mutation (P = 0.01, global test). Three new single nucleotide polymorphisms (SNPs) and 2 previously reported SNPs were identified in this group of patients. Intragenic allelic loss at polymorphic sites in CDKN2A was detected in 32% (18 of 56) of patients. Seven of the 56 (13%) cases exhibited what is considered classic evidence (n = 4) or showed potential evidence (n = 3) of biallelic inactivation. Only one alteration was observed in CDKN2B, G171A in the 5′ untranslated region. Both mutation and intragenic allelic loss in CDKN2A appear to play a role in the development of ESCC. ©2003 Wiley‐Liss, Inc.

Random effects and latent processes approaches for analyzing binary longitudinal data with missingness: a comparison of approaches using opiate clinical trial data

The analysis of longitudinal data with non-ignorable missingness remains an active area in biostatistics research. This article discusses various random effects and latent process models which have been proposed for analyzing longitudinal binary data subject to both non-ignorable intermittent missing data and dropout. These models account for non-ignorable missingness by introducing random effects or a latent process which is shared between the response model and the model for the missing-data mechanism. We discuss various random effects and latent processes approaches and compare these approaches with analyses from an opiate clinical trial data set, which had high proportion of intermittent missingness and dropout. We also compare these random effect and latent process approaches with other methods for accounting for non-ignorable missingness using this data set.

A GENERALIZED ESTIMATING EQUATION APPROACH FOR MODELING RANDOM LENGTH BINARY VECTOR DATA

A common measure in clinical trials and epidemiologic studies is the number of events such as seizures, hospitalizations, or bouts of disease. Frequently, a binary measure of severity for each event is available but is not incorporated in the analysis. This paper proposes methodology for jointly modeling the number of events and the vector of correlated binary severity measures. Our formulation exploits the notion that a given covariate may affect both outcomes in a similar way. We functionally link the regression parameters for the counts and binary means and discuss a generalized estimating equation (GEE) approach for parameter estimation. We discuss conditions under which the proposed joint modeling approach provides marked gains in efficiency relative to the common procedure of simply modeling the counts, and we illustrate the methodology with epilepsy clinical trial data.