Analysis of longitudinal data with irregular, outcome-dependent follow-up

Summary.  A frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self-selected points in time. As a result, observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and/or some auxiliary factors that are associated with the outcome. If the follow-up visit and outcome processes are correlated, then marginal regression analyses will produce biased estimates. Building on the work of Robins, Rotnitzky and Zhao, we propose a class of inverse intensity-of-visit process-weighted estimators in marginal regression models for longitudinal responses that may be observed in continuous time. This allows us to handle arbitrary patterns of missing data as embedded in a subject's visit process. We derive the large sample distribution for our inverse visit-intensity-weighted estimators and investigate their finite sample behaviour by simulation. Our approach is illustrated with a data set from a health services research study in which homeless people with mental illness were randomized to three different treatments and measures of homelessness (as percentage days homeless in the past 3 months) and other auxiliary factors were recorded at follow-up times that are not fixed by design.     

New approaches for censored longitudinal data in joint modelling of longitudinal and survival data,with application to HIV vaccine studies

In HIV vaccine studies, longitudinal immune response biomarker data are often left-censored due to lower limits of quantification of the employed immunological assays. The censoring information is important for predicting HIV infection, the failure event of interest. We propose two approaches to addressing left censoring in longitudinal data: one that makes no distributional assumptions for the censored data—treating left censored values as a “point mass” subgroup—and the other makes a distributional assumption for a subset of the censored data but not for the remaining subset. We develop these two approaches to handling censoring for joint modelling of longitudinal and survival data via a Cox proportional hazards model fit by h-likelihood. We evaluate the new methods via simulation and analyze an HIV vaccine trial data set, finding that longitudinal characteristics of the immune response biomarkers are highly associated with the risk of HIV infection.

     

Multilevel models for longitudinal data

Summary.  Repeated measures and repeated events data have a hierarchical structure which can be analysed by using multilevel models. A growth curve model is an example of a multilevel random-coefficients model, whereas a discrete time event history model for recurrent events can be fitted as a multilevel logistic regression model. The paper describes extensions to the basic growth curve model to handle auto-correlated residuals, multiple-indicator latent variables and correlated growth processes, and event history models for correlated event processes. The multilevel approach to the analysis of repeated measures data is contrasted with structural equation modelling. The methods are illustrated in analyses of children's growth, changes in social and political attitudes, and the interrelationship between partnership transitions and childbearing.     

Using the bootstrap in correlation analysis,with application to a longitudinal data set

The problem of constructing simultaneous confidence intervals for various measures of association is considered. Alternative bootstrap algorithms are given for approximating the sampling distributions of the quantities generating the confidence sets. The small sample performance of the procedures is illustrated using simulated data from 3- and 6-variate normal populations. The results are applied to a large multidimensional longitudinal data set from a study of the relationship between drug use and several behavioral attributes.     

Bayesian quantile regression for ordinal longitudinal data

Since the pioneering work by Koenker and Bassett [27], quantile regression models and its applications have become increasingly popular and important for research in many areas. In this paper, a random effects ordinal quantile regression model is proposed for analysis of longitudinal data with ordinal outcome of interest. An efficient Gibbs sampling algorithm was derived for fitting the model to the data based on a location-scale mixture representation of the skewed double-exponential distribution. The proposed approach is illustrated using simulated data and a real data example. This is the first work to discuss quantile regression for analysis of longitudinal data with ordinal outcome.     

Quantile regression-based Bayesian semiparametric mixed-effects models for longitudinal data with non-normal,missing and mismeasured covariate

Quantile regression (QR) models have received increasing attention recently for longitudinal data analysis. When continuous responses appear non-centrality due to outliers and/or heavy-tails, commonly used mean regression models may fail to produce efficient estimators, whereas QR models may perform satisfactorily. In addition, longitudinal outcomes are often measured with non-normality, substantial errors and non-ignorable missing values. When carrying out statistical inference in such data setting, it is important to account for the simultaneous treatment of these data features; otherwise, erroneous or even misleading results may be produced. In the literature, there has been considerable interest in accommodating either one or some of these data features. However, there is relatively little work concerning all of them simultaneously. There is a need to fill up this gap as longitudinal data do often have these characteristics. Inferential procedure can be complicated dramatically when these data features arise in longitudinal response and covariate outcomes. In this article, our objective is to develop QR-based Bayesian semiparametric mixed-effects models to address the simultaneous impact of these multiple data features. The proposed models and method are applied to analyse a longitudinal data set arising from an AIDS clinical study. Simulation studies are conducted to assess the performance of the proposed method under various scenarios.     

Cook's distance in linear longitudinal models

Cook's distance (1977) has become the standard influence diagnostic tool for analyzing cross–sectional regression studies. This paper introduces an analogue of Cook's distance in fixed effects models for longitudinal data. We demonstrate that this statistic is dominated by the effects of nuisance parameters, and hence its effectiveness as an influence measure in the longitudinal data setting is limited.     

Stationary state space models for longitudinal data

The authors consider a class of state space models for the analysis of non‐normal longitudinal data whose latent process follows a stationary AR(1) model with exponential dispersion model margins. They propose to estimate parameters through an estimating equation approach based on the Kalman smoother. This allows them to carry out a straightforward analysis of a wide range of non‐normal data. They illustrate their approach via a simulation study and through analyses of Brazilian precipitation and US polio infection data.     

A flexible link for joint modelling longitudinal and survival data accounting for individual longitudinal heterogeneity

Statistical Methods & Applications - This work aims at jointly modelling longitudinal and survival HIV data by considering the sharing of a set of parameters of interest. For the CD4...     

Generalized additive models for longitudinal data

We introduce a class of models for longitudinal data by extending the generalized estimating equations approach of Liang and Zeger (1986) to incorporate the flexibility of nonparametric smoothing. The algorithm provides a unified estimation procedure for marginal distributions from the exponential family. We propose pointwise standard-error bands and approximate likelihood-ratio and score tests for inference. The algorithm is formally derived by using the penalized quasilikelihood framework. Convergence of the estimating equations and consistency of the resulting solutions are discussed. We illustrate the algorithm with data on the population dynamics of Colorado potato beetles on potato plants.     

Analysis of longitudinal data with drop-out: objectives, assumptions and a proposal

Summary. The problem of analysing longitudinal data that are complicated by possibly informative drop-out has received considerable attention in the statistical literature. Most researchers have concentrated on either methodology or application, but we begin this paper by arguing that more attention could be given to study objectives and to the relevant targets for inference. Next we summarize a variety of approaches that have been suggested for dealing with drop-out. A long-standing concern in this subject area is that all methods require untestable assumptions. We discuss circumstances in which we are willing to make such assumptions and we propose a new and computationally efficient modelling and analysis procedure for these situations. We assume a dynamic linear model for the expected increments of a constructed variable, under which subject-specific random effects follow a martingale process in the absence of drop-out. Informal diagnostic procedures to assess the tenability of the assumption are proposed. The paper is completed by simulations and a comparison of our method and several alternatives in the analysis of data from a trial into the treatment of schizophrenia, in which approximately 50% of recruited subjects dropped out before the final scheduled measurement time.     

Semiparametric Bayesian classification with longitudinal markers

Summary.  We analyse data from a study involving 173 pregnant women. The data are observed values of the β human chorionic gonadotropin hormone measured during the first 80 days of gestational age, including from one up to six longitudinal responses for each woman. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from data that are available at the early stages of pregnancy. We achieve the desired classification with a semiparametric hierarchical model. Specifically, we consider a Dirichlet process mixture prior for the distribution of the random effects in each group. The unknown random-effects distributions are allowed to vary across groups but are made dependent by using a design vector to select different features of a single underlying random probability measure. The resulting model is an extension of the dependent Dirichlet process model, with an additional probability model for group classification. The model is shown to perform better than an alternative model which is based on independent Dirichlet processes for the groups. Relevant posterior distributions are summarized by using Markov chain Monte Carlo methods.     

Practical modeling strategies for unbalanced longitudinal data analysis

In practice, data are often measured repeatedly on the same individual at several points in time. Main interest often relies in characterizing the way the response changes in time, and the predictors of that change. Marginal, mixed and transition are frequently considered to be the main models for continuous longitudinal data analysis. These approaches are proposed primarily for balanced longitudinal design. However, in clinic studies, data are usually not balanced and some restrictions are necessary in order to use these models. This paper was motivated by a data set related to longitudinal height measurements in children of HIV-infected mothers that was recorded at the university hospital of the Federal University in Minas Gerais, Brazil. This data set is severely unbalanced. The goal of this paper is to assess the application of continuous longitudinal models for the analysis of unbalanced data set.     

Estimation from incomplete data in longitudinal surveys

In longitudinal surveys where a number of observations have to be made on the same sampling unit at specified time intervals, it is not uncommon that observations for some of the time stages for some of the sampled units are found missing. In the present investigation an estimation procedure for estimating the population total based on such incomplete data from multiple observations is suggested which makes use of all the available information and is seen to be more efficient than the one based on only completely observed units. Estimators are also proposed for two other situations; firstly when data is collected only for a sample of time stages and secondly when data is observed for only one time stage per sampled unit.     

Local estimation for varying-coefficient models with longitudinal data

Varying-coefficient models are very useful for longitudinal data analysis. In this paper, we focus on varying-coefficient models for longitudinal data. We develop a new estimation procedure using Cholesky decomposition and profile least squares techniques. Asymptotic normality for the proposed estimators of varying-coefficient functions has been established. Monte Carlo simulation studies show excellent finite-sample performance. We illustrate our methods with a real data example.     

Bayesian quantile regression for longitudinal data models

In this paper, we discuss a fully Bayesian quantile inference using Markov Chain Monte Carlo (MCMC) method for longitudinal data models with random effects. Under the assumption of error term subject to asymmetric Laplace distribution, we establish a hierarchical Bayesian model and obtain the posterior distribution of unknown parameters at τ-th level. We overcome the current computational limitations using two approaches. One is the general MCMC technique with Metropolis–Hastings algorithm and another is the Gibbs sampling from the full conditional distribution. These two methods outperform the traditional frequentist methods under a wide array of simulated data models and are flexible enough to easily accommodate changes in the number of random effects and in their assumed distribution. We apply the Gibbs sampling method to analyse a mouse growth data and some different conclusions from those in the literatures are obtained.     

Identification of longitudinal biomarkers for survival by a score test derived from a joint model of longitudinal and competing risks data

In this paper, we consider joint modelling of repeated measurements and competing risks failure time data. For competing risks time data, a semiparametric mixture model in which proportional hazards model are specified for failure time models conditional on cause and a multinomial model for the marginal distribution of cause conditional on covariates. We also derive a score test based on joint modelling of repeated measurements and competing risks failure time data to identify longitudinal biomarkers or surrogates for a time to event outcome in competing risks data.     

Modeling longitudinal count data with dropouts

This paper explores the utility of different approaches for modeling longitudinal count data with dropouts arising from a clinical study for the treatment of actinic keratosis lesions on the face and balding scalp. A feature of these data is that as the disease for subjects on the active arm improves their data show larger dispersion compared with those on the vehicle, exhibiting an over‐dispersion relative to the Poisson distribution. After fitting the marginal (or population averaged) model using the generalized estimating equation (GEE), we note that inferences from such a model might be biased as dropouts are treatment related. Then, we consider using a weighted GEE (WGEE) where each subject's contribution to the analysis is weighted inversely by the subject's probability of dropout. Based on the model findings, we argue that the WGEE might not address the concerns about the impact of dropouts on the efficacy findings when dropouts are treatment related. As an alternative, we consider likelihood‐based inference where random effects are added to the model to allow for heterogeneity across subjects. Finally, we consider a transition model where, unlike the previous approaches that model the log‐link function of the mean response, we model the subject's actual lesion counts. This model is an extension of the Poisson autoregressive model of order 1, where the autoregressive parameter is taken to be a function of treatment as well as other covariates to induce different dispersions and correlations for the two treatment arms. We conclude with a discussion about model selection. Published in 2009 by John Wiley & Sons, Ltd.     

Progressive multi-state models for informatively incomplete longitudinal data

Progressive multi-state models provide a convenient framework for characterizing chronic disease processes where the states represent the degree of damage resulting from the disease. Incomplete data often arise in studies of such processes, and standard methods of analysis can lead to biased parameter estimates when observation of data is response-dependent. This paper describes a joint analysis useful for fitting progressive multi-state models to data arising in longitudinal studies in such settings. Likelihood based methods are described and parameters are shown to be identifiable. An EM algorithm is described for parameter estimation, and variance estimation is carried out using the Louis’ method. Simulation studies demonstrate that the proposed method works well in practice under a variety of settings. An application to data from a smoking prevention study illustrates the utility of the method.