Grace Y. Yi

Marginal Methods for Incomplete Longitudinal Data Arising in Clusters

Inverse probability–weighted generalized estimating equations are commonly used to deal with incomplete longitudinal data arising from a missing-at-random mechanism when the marginal means are of primary interest. In many cases, however, the repeated measurements themselves may arise in clusters, which leads to both a cross-sectional and a longitudinal correlation structure. In some applications, the degree of these types of correlation may become of scientific interest. Here we develop inverse probability–weighted second-order estimating equations for monotone missing-data patterns which, under specified assumptions, facilitate consistent estimation of the marginal mean parameters and association parameters. Here the missing-data model accommodates cross-sectional clustering in the missing-data indicators, and the probabilities are estimated under a multivariate Plackett model. For computational reasons, we also consider using the alternating logistic regression algorithm for estimation of the association parameters for the responses. We investigate the importance of modeling the cross-sectional clustering in the missing-data process by simulation. An extension to deal with intermittently missing data is provided, and an application to a longitudinal cluster-randomized smoking prevention trial is presented.

Median regression models for longitudinal data with dropouts.

SUMMARY Recently, median regression models have received increasing attention. When continuous responses follow a distribution that is quite different from a normal distribution, usual mean regression models may fail to produce efficient estimators whereas median regression models may perform satisfactorily. In this article, we discuss using median regression models to deal with longitudinal data with dropouts. Weighted estimating equations are proposed to estimate the median regression parameters for incomplete longitudinal data, where the weights are determined by modeling the dropout process. Consistency and the asymptotic distribution of the resultant estimators are established. The proposed method is used to analyze a longitudinal data set arising from a controlled trial of HIV disease (Volberding et al., 1990, The New England Journal of Medicine 322, 941-949). Simulation studies are conducted to assess the performance of the proposed method under various situations. An extension to estimation of the association parameters is outlined.

Analysis of Longitudinal and Survival Data: Joint Modeling, Inference Methods, and Issues

In the past two decades, joint models of longitudinal and survival data have received much attention in the literature. These models are often desirable in the following situations: (i) survival models with measurement errors or missing data in time-dependent covariates, (ii) longitudinal models with informative dropouts, and (iii) a survival process and a longitudinal process are associated via latent variables. In these cases, separate inferences based on the longitudinal model and the survival model may lead to biased or inefficient results. In this paper, we provide a brief overview of joint models for longitudinal and survival data and commonly used methods, including the likelihood method and two-stage methods.

Weighted Generalized Estimating Functions for Longitudinal Response and Covariate Data That Are Missing at Random

Longitudinal studies often feature incomplete response and covariate data. It is well known that biases can arise from naive analyses of available data, but the precise impact of incomplete data depends on the frequency of missing data and the strength of the association between the response variables and covariates and the missing-data indicators. Various factors may influence the availability of response and covariate data at scheduled assessment times, and at any given assessment time the response may be missing, covariate data may be missing, or both response and covariate data may be missing. Here we show that it is important to take the association between the missing data indicators for these two processes into account through joint models. Inverse probability-weighted generalized estimating equations offer an appealing approach for doing this. Here we develop these equations for a particular model generating intermittently missing-at-random data. Empirical studies demonstrate that the consistent estimators arising from the proposed methods have very small empirical biases in moderate samples. Supplemental materials are available online.

Simultaneous Inference and Bias Analysis for Longitudinal Data with Covariate Measurement Error and Missing Responses

Longitudinal data arise frequently in medical studies and it is common practice to analyze such data with generalized linear mixed models. Such models enable us to account for various types of heterogeneity, including between- and within-subjects ones. Inferential procedures complicate dramatically when missing observations or measurement error arise. In the literature, there has been considerable interest in accommodating either incompleteness or covariate measurement error under random effects models. However, there is relatively little work concerning both features simultaneously. There is a need to fill up this gap as longitudinal data do often have both characteristics. In this article, our objectives are to study simultaneous impact of missingness and covariate measurement error on inferential procedures and to develop a valid method that is both computationally feasible and theoretically valid. Simulation studies are conducted to assess the performance of the proposed method, and a real example is analyzed with the proposed method.

A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error

Covariate measurement error and missing responses are typical features in longitudinal data analysis. There has been extensive research on either covariate measurement error or missing responses, but relatively little work has been done to address both simultaneously. In this paper, we propose a simple method for the marginal analysis of longitudinal data with time-varying covariates, some of which are measured with error, while the response is subject to missingness. Our method has a number of appealing properties: assumptions on the model are minimal, with none needed about the distribution of the mismeasured covariate; implementation is straightforward and its applicability is broad. We provide both theoretical justification and numerical results.

Analysis of interval‐censored disease progression data via multi‐state models under a nonignorable inspection process

Irreversible multi-state models provide a convenient framework for characterizing disease processes that arise when the states represent the degree of organ or tissue damage incurred by a progressive disease. In many settings, however, individuals are only observed at periodic clinic visits and so the precise times of the transitions are not observed. If the life history and observation processes are not independent, the observation process contains information about the life history process, and more importantly, likelihoods based on the disease process alone are invalid. With interval-censored failure time data, joint models are nonidentifiable and data analysts must rely on sensitivity analyses to assess the effect of the dependent observation times. This paper is concerned, however, with the analysis of data from progressive multi-state disease processes in which individuals are scheduled to be seen at periodic pre-scheduled assessment times. We cast the problem in the framework used for incomplete longitudinal data problems. Maximum likelihood estimation via an EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. Data from a cohort of patients with psoriatic arthritis are analyzed for illustration.

Analysis of correlated binary data under partially linear single-index logistic models

Clustered data arise commonly in practice and it is often of interest to estimate the mean response parameters as well as the association parameters. However, most research has been directed to address the mean response parameters with the association parameters relegated to a nuisance role. There is relatively little work concerning both the marginal and association structures, especially in the semiparametric framework. In this paper, our interest centers on inference on both the marginal and association parameters. We develop a semiparametric method for clustered binary data and establish the theoretical results. The proposed methodology is investigated through various numerical studies.

A simulation-based marginal method for longitudinal data with dropout and mismeasured covariates

Longitudinal data often contain missing observations and error-prone covariates. Extensive attention has been directed to analysis methods to adjust for the bias induced by missing observations. There is relatively little work on investigating the effects of covariate measurement error on estimation of the response parameters, especially on simultaneously accounting for the biases induced by both missing values and mismeasured covariates. It is not clear what the impact of ignoring measurement error is when analyzing longitudinal data with both missing observations and error-prone covariates. In this article, we study the effects of covariate measurement error on estimation of the response parameters for longitudinal studies. We develop an inference method that adjusts for the biases induced by measurement error as well as by missingness. The proposed method does not require the full specification of the distribution of the response vector but only requires modeling its mean and variance structures. Furthermore, the proposed method employs the so-called functional modeling strategy to handle the covariate process, with the distribution of covariates left unspecified. These features, plus the simplicity of implementation, make the proposed method very attractive. In this paper, we establish the asymptotic properties for the resulting estimators. With the proposed method, we conduct sensitivity analyses on a cohort data set arising from the Framingham Heart Study. Simulation studies are carried out to evaluate the impact of ignoring covariate measurement error and to assess the performance of the proposed method.

Methods for Bivariate Survival Data with Mismeasured Covariates Under an Accelerated Failure Time Model

Accelerated failure time models are useful in survival data analysis, but such models have received little attention in the context of measurement error. In this paper we discuss an accelerated failure time model for bivariate survival data with covariates subject to measurement error. In particular, methods based on the marginal and joint models are considered. Consistency and efficiency of the resultant estimators are investigated. Simulation studies are carried out to evaluate the performance of the estimators as well as the impact of ignoring the measurement error of covariates. As an illustration we apply the proposed methods to analyze a data set arising from the Busselton Health Study (Knuiman et al., 1994).