Sieve estimation in semiparametric modeling of longitudinal data with informative observation times.

Analyzing irregularly spaced longitudinal data often involves modeling possibly correlated response and observation processes. In this article, we propose a new class of semiparametric mean models that allows for the interaction between the observation history and covariates, leaving patterns of the observation process to be arbitrary. For inference on the regression parameters and the baseline mean function, a spline-based least squares estimation approach is proposed. The consistency, rate of convergence, and asymptotic normality of the proposed estimators are established. Our new approach is different from the usual approaches relying on the model specification of the observation scheme, and it can be easily used for predicting the longitudinal response. Simulation studies demonstrate that the proposed inference procedure performs well and is more robust. The analyses of bladder tumor data and medical cost data are presented to illustrate the proposed method.

Methods for a longitudinal quantitative outcome with a multivariate Gaussian distribution multi-dimensionally censored by therapeutic intervention.

In longitudinal studies, a quantitative outcome (such as blood pressure) may be altered during follow-up by the administration of a non-randomized, non-trial intervention (such as anti-hypertensive medication) that may seriously bias the study results. Current methods mainly address this issue for cross-sectional studies. For longitudinal data, the current methods are either restricted to a specific longitudinal data structure or are valid only under special circumstances. We propose two new methods for estimation of covariate effects on the underlying (untreated) general longitudinal outcomes: a single imputation method employing a modified expectation-maximization (EM)-type algorithm and a multiple imputation (MI) method utilizing a modified Monte Carlo EM-MI algorithm. Each method can be implemented as one-step, two-step, and full-iteration algorithms. They combine the advantages of the current statistical methods while reducing their restrictive assumptions and generalizing them to realistic scenarios. The proposed methods replace intractable numerical integration of a multi-dimensionally censored MVN posterior distribution with a simplified, sufficiently accurate approximation. It is particularly attractive when outcomes reach a plateau after intervention due to various reasons. Methods are studied via simulation and applied to data from the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications study of treatment for type 1 diabetes. Methods proved to be robust to high dimensions, large amounts of censored data, low within-subject correlation, and when subjects receive non-trial intervention to treat the underlying condition only (with high Y), or for treatment in the majority of subjects (with high Y) in combination with prevention for a small fraction of subjects (with normal Y).

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time.

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow-up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random-effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in 'BUGS' language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD.

A rapid questionnaire assessment of environmental exposures to pregnant women in the INTERGROWTH-21st Project.

Impaired fetal growth and preterm birth are the leading causes of neonatal and infant mortality worldwide and there is a growing scientific literature suggesting that environmental exposures during pregnancy may play a causal role in these outcomes. Our purpose was to assess the environmental exposure of the Fetal Growth Longitudinal Study (FGLS) participants in the multinational INTERGROWTH-21(st) Project. First, we developed a tool that could be used internationally to screen pregnant women for such exposures and administered it in eight countries on a subsample (n = 987) of the FGLS participants. The FGLS is a study of fetal growth among healthy pregnant women living in relatively affluent areas, at low risk of adverse pregnancy outcomes and environmental exposures. We confirmed that most women were not exposed to major environmental hazards that could affect pregnancy outcomes according to the protocol's entry criteria. However, the instrument was able to identify some women that reported various environmental concerns in their homes such as peeling paint, high residential density (>1 person per room), presence of rodents or cockroaches (hence the use of pesticides), noise pollution and safety concerns. This screening tool was therefore useful for the purposes of the project and can be used to ascertain environmental exposures in studies in which the primary aim is not focused on environmental exposures. The instrument can be used to identify subpopulations for more in-depth assessment, (e.g. environmental and biological laboratory markers) to pinpoint areas requiring education, intervention or policy change.

Longitudinal methods to investigate the role of health determinants in the dynamics of income-related health inequality.

The usual starting point for understanding changes in income-related health inequality (IRHI) over time has been regression-based decomposition procedures for the health concentration index. However the reliance on repeated cross-sectional analysis for this purpose prevents both the appropriate specification of the health function as a dynamic model and the identification of important determinants of the transition processes underlying IRHI changes such as those relating to mortality. This paper overcomes these limitations by developing alternative longitudinal procedures to analyse the role of health determinants in driving changes in IRHI through both morbidity changes and mortality, with our dynamic modelling framework also serving to identify their contribution to long-run or structural IRHI. The approach is illustrated by an empirical analysis of the causes of the increase in IRHI in Great Britain between 1999 and 2004.

Robust Bayesian inference for multivariate longitudinal data by using normal/independent distributions.

Many randomized clinical trials collect multivariate longitudinal measurements in different scales, for example, binary, ordinal, and continuous. Multilevel item response models are used to evaluate the global treatment effects across multiple outcomes while accounting for all sources of correlation. Continuous measurements are often assumed to be normally distributed. But the model inference is not robust when the normality assumption is violated because of heavy tails and outliers. In this article, we develop a Bayesian method for multilevel item response models replacing the normal distributions with symmetric heavy-tailed normal/independent distributions. The inference is conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in BUGS language. Our proposed method is evaluated by simulation studies and is applied to Earlier versus Later Levodopa Therapy in Parkinson's Disease study, a motivating clinical trial assessing the effect of Levodopa therapy on the Parkinson's disease progression rate.

Combining hidden Markov models for comparing the dynamics of multiple sleep electroencephalograms.

In this manuscript, we consider methods for the analysis of populations of electroencephalogram signals during sleep for the study of sleep disorders using hidden Markov models (HMMs). Notably, we propose an easily implemented method for simultaneously modeling multiple time series that involve large amounts of data. We apply these methods to study sleep-disordered breathing (SDB) in the Sleep Heart Health Study (SHHS), a landmark study of SDB and cardiovascular consequences. We use the entire, longitudinally collected, SHHS cohort to develop HMM population parameters, which we then apply to obtain subject-specific Markovian predictions. From these predictions, we create several indices of interest, such as transition frequencies between latent states. Our HMM analysis of electroencephalogram signals uncovers interesting findings regarding differences in brain activity during sleep between those with and without SDB. These findings include stability of the percent time spent in HMM latent states across matched diseased and non-diseased groups and differences in the rate of transitioning.

How representative is the ACTIVE sample? A statistical comparison of the ACTIVE sample and the HRS sample.

OBJECTIVE: This research is designed to examine demographic differences between the ACTIVE sample and the larger, nationally representative Health and Retirement Study (HRS) sample. METHOD: After describing some relevant demographics (age, education, sex, and race/ethnicity), we use three statistical methods to determine sample differences--logistic regression modeling (LRM), decision tree analysis (DTA), and post-stratification and raking methods. When some differences are found, we create sample weights that other researchers can use to adjust these differences. RESULTS: The ACTIVE sample is younger, more likely to be female, Black, and more highly educated than the HRS sample. Sample weights were created. DISCUSSION: By using the resulting sample weights, all results of ACTIVE analyses can be said to be nationally representative based on HRS demographics.

A general implementation of TMLE for longitudinal data applied to causal inference in survival analysis.

In many randomized controlled trials the outcome of interest is a time to event, and one measures on each subject baseline covariates and time-dependent covariates until the subject either drops-out, the time to event is observed, or the end of study is reached. The goal of such a study is to assess the causal effect of the treatment on the survival curve. We present a targeted maximum likelihood estimator of the causal effect of treatment on survival fully utilizing all the available covariate information, resulting in a double robust locally efficient substitution estimator that will be consistent and asymptotically linear if either the censoring mechanism is consistently estimated, or if the maximum likelihood based estimator is already consistent. In particular, under the independent censoring assumption assumed by current methods, this TMLE is always consistent and asymptotically linear so that it provides valid confidence intervals and tests. Furthermore, we show that when both the censoring mechanism and the initial maximum likelihood based estimator are mis-specified, and thus inconsistent, the TMLE exhibits stability when inverse probability weighted estimators and double robust estimating equation based methods break down The TMLE is used to analyze the Tshepo study, a study designed to evaluate the efficacy, tolerability, and development of drug resistance of six different first-line antiretroviral therapies. Most importantly this paper presents a general algorithm that may be used to create targeted maximum likelihood estimators of a large class of parameters of interest for general longitudinal data structures.

Using the linear mixed model to analyze nonnormal data distributions in longitudinal designs.

Using a Monte Carlo simulation and the Kenward-Roger (KR) correction for degrees of freedom, in this article we analyzed the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential, and log-normal. This showed that, with homogeneous between-groups covariance and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix. However, with heterogeneous between-groups covariance and when the pairing between covariance matrices and group sizes was null, the best fit was shown by the between-subjects heterogeneous unstructured population matrix, which was the case for all of the distributions analyzed. By contrast, with positive or negative pairings, the within-subjects and between-subjects heterogeneous first-order autoregressive structure produced the best fit. In the second stage of the study, the robustness of the LMM was tested. This showed that the KR method provided adequate control of Type I error rates for the time effect with normally distributed data. However, as skewness increased-as occurs, for example, in the log-normal distribution-the robustness of KR was null, especially when the assumption of sphericity was violated. As regards the influence of kurtosis, the analysis showed that the degree of robustness increased in line with the amount of kurtosis.

Predictors of post-release research retention and subsequent reenrollment for women recruited while incarcerated.

Correctional facilities are prime targets for nursing interventions to decrease health disparities, but challenges to post-release follow-up limit use of the longitudinal research designs needed to fully examine intervention effects. Using an adapted version of the Behavioral Model for Vulnerable Populations, we determined predictors of 1-year post-release study retention and subsequent reenrollment an average of 3 years later in 88 mother and child dyads recruited from a state prison nursery. Predisposing characteristics and enabling factors emerged as strong predictors of loss to follow-up. Female research participants can be successfully retained years after release from a correctional facility. Understanding the barriers and facilitators to post-release follow-up supports the creation of theoretically informed strategies to retain formerly incarcerated populations.

Intelligent Systems For Assessing Aging Changes: home-based, unobtrusive, and continuous assessment of aging.

OBJECTIVES: To describe a longitudinal community cohort study, Intelligent Systems for Assessing Aging Changes, that has deployed an unobtrusive home-based assessment platform in many seniors homes in the existing community. METHODS: Several types of sensors have been installed in the homes of 265 elderly persons for an average of 33 months. Metrics assessed by the sensors include total daily activity, time out of home, and walking speed. Participants were given a computer as well as training, and computer usage was monitored. Participants are assessed annually with health and function questionnaires, physical examinations, and neuropsychological testing. RESULTS: Mean age was 83.3 years, mean years of education was 15.5, and 73% of cohort were women. During a 4-week snapshot, participants left their home twice a day on average for a total of 208 min per day. Mean in-home walking speed was 61.0 cm/s. Participants spent 43% of days on the computer averaging 76 min per day. DISCUSSION: These results demonstrate for the first time the feasibility of engaging seniors in a large-scale deployment of in-home activity assessment technology and the successful collection of these activity metrics. We plan to use this platform to determine if continuous unobtrusive monitoring may detect incident cognitive decline.

A cautionary note on modeling growth trends in longitudinal data.

Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a process, at least partially, contains a stochastic trend, then random coefficient regression results are likely to be spurious. This problem is demonstrated via a data example, previous research on simple regression models, and Monte Carlo simulations. A data analytic strategy is proposed to help researchers avoid making inaccurate inferences when observed trends may be due to stochastic processes.

Informative dropout modeling of longitudinal ordered categorical data and model validation: application to exposure-response modeling of physician's global assessment score for ustekinumab in patients with psoriasis.

The physician's global assessment (PGA) score is a 6-point measure of psoriasis severity that is widely used in clinical trials to assess response to psoriasis treatment. The objective of this study was to perform exposure-response modeling using the PGA score as a pharmacodynamic endpoint following treatment with ustekinumab in patients with moderate-to-severe psoriasis who participated in two Phase 3 studies (PHOENIX 1 and PHOENIX 2). Patients were randomly assigned to receive ustekinumab 45 or 90 mg or placebo, followed by active treatment or placebo crossover to ustekinumab, dose intensification or randomized withdrawal and long-term extension periods. A novel joint longitudinal-dropout model was developed from serum ustekinumab concentrations, PGA scores, and patient dropout information. The exposure-response component employed a semi-mechanistic drug model, integrated with disease progression and placebo effect under the mixed-effect logistic regression framework. This allowed potential tolerance to be investigated with a mechanistic approach. The dropout component of the joint model allowed the examination of its potential influence on the exposure-response relationship. The flexible Weibull dropout hazard function was used. Visual predictive check of the joint longitudinal-dropout model required special handling, and a conditional approach was proposed. The conditional approach was extended to external model validation. Finally, appropriate interpretation of model validation is discussed. This longitudinal-dropout model can serve as a basis to support future alternative dosing regimens for ustekinumab in patients with moderate-to-severe plaque psoriasis.

Recruitment and retention strategies in longitudinal clinical studies with low-income populations.

BACKGROUND: Conducting longitudinal research studies with low-income and/or minority participants present a unique set of challenges and opportunities. PURPOSE: To outline the specific strategies employed to successfully recruit and retain participants in a longitudinal study of nutritional anticipatory guidance during early childhood, conducted with a low-income, ethnically diverse, urban population of mothers. METHODS: We describe recruitment and retention efforts made by the research team for the 'MOMS' Study (Making Our Mealtimes Special). The 'multilayered' approach for recruitment and retention included commitment of research leadership, piloting procedures, frequent team reporting, emphasis on participant convenience, incentives, frequent contact with participants, expanded budget, clinical staff buy-in, a dedicated phone line, and the use of research project branding and logos. RESULTS: Barriers to enrollment were not encountered in this project, despite recruiting from a low-income population with a large proportion of African-American families. Process evaluation with clinic staff demonstrated the perception of the MOMS staff was very positive. Participant retention rate was 75% and 64% at 6 months and 12 months post-recruitment, respectively. We attribute retention success largely to a coordinated effort between the research team and the infrastructure support at the clinical sites, as well as project branding and a dedicated phone line. CONCLUSIONS: Successful participant recruitment and retention approaches need to be specific and consistent with clinical staff buy in throughout the project.

Regression analysis of longitudinal data with informative observation times and application to medical cost data.

Longitudinal data analysis is one of the most discussed and applied areas in statistics and a great deal of literature has been developed for it. However, most of the existing literature focus on the situation where observation times are fixed or can be treated as fixed constants. This paper considers the situation where these observation times may be random variables and more importantly, they may be related to the underlying longitudinal variable or process of interest. Furthermore, covariate effects may be time-varying. For the analysis, a joint modeling approach is proposed and in particular, for estimation of time-varying regression parameters, an estimating equation-based procedure is developed. Both asymptotic and finite sample properties of the proposed estimates are established. The methodology is applied to an acute myeloid leukemia trial that motivated this study.

Joint modeling of survival time and longitudinal data with subject-specific changepoints in the covariates.

Joint models are frequently used in survival analysis to assess the relationship between time-to-event data and time-dependent covariates, which are measured longitudinally but often with errors. Routinely, a linear mixed-effects model is used to describe the longitudinal data process, while the survival times are assumed to follow the proportional hazards model. However, in some practical situations, individual covariate profiles may contain changepoints. In this article, we assume a two-phase polynomial random effects with subject-specific changepoint model for the longitudinal data process and the proportional hazards model for the survival times. Our main interest is in the estimation of the parameter in the hazards model. We incorporate a smooth transition function into the changepoint model for the longitudinal data and develop the corrected score and conditional score estimators, which do not require any assumption regarding the underlying distribution of the random effects or that of the changepoints. The estimators are shown to be asymptotically equivalent and their finite-sample performance is examined via simulations. The methods are applied to AIDS clinical trial data.

A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects.

This article studies a general joint model for longitudinal measurements and competing risks survival data. The model consists of a linear mixed effects sub-model for the longitudinal outcome, a proportional cause-specific hazards frailty sub-model for the competing risks survival data, and a regression sub-model for the variance-covariance matrix of the multivariate latent random effects based on a modified Cholesky decomposition. The model provides a useful approach to adjust for non-ignorable missing data due to dropout for the longitudinal outcome, enables analysis of the survival outcome with informative censoring and intermittently measured time-dependent covariates, as well as joint analysis of the longitudinal and survival outcomes. Unlike previously studied joint models, our model allows for heterogeneous random covariance matrices. It also offers a framework to assess the homogeneous covariance assumption of existing joint models. A Bayesian MCMC procedure is developed for parameter estimation and inference. Its performances and frequentist properties are investigated using simulations. A real data example is used to illustrate the usefulness of the approach.