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Panel count data arise when study subjects who may experience certain recurrent events are only observed intermittently at discrete examination times. In addition to the underlying recurrent event process of interest, there usually exist two other nuisance processes, namely the observation and follow-up processes, which may be correlated with the recurrent event process of interest. We propose a general class of random-effects monotonic index models for regression analysis of such panel count data. In order to estimate the regression parameters, we develop a weighted rank (WR) estimation procedure and and establish the consistency and asymptotic normality of the resulting WR estimator. A numerical study and an application of the proposed methodology show that it works well in practice.

Background Longitudinal data can be used to study disease progression and are often collected at irregular intervals. When the assessment times are informative about the severity of the disease, regression analyses of the outcome trajectory over time based on Generalized Estimating Equations (GEEs) result in biased estimates of regression coefficients. Inverse-intensity weighted GEEs (IIW-GEEs) are a popular approach to account for informative assessment times and yield unbiased estimates of outcome model coefficients when the assessment times and outcomes are conditionally independent given previously observed data. However, a consequence of irregular assessment times is that some patients may have no follow-up assessments at all, and it is common practice to omit these patients from analyses when studying the outcome trajectory over time. Methods We show mathematically that IIW-GEEs yield biased estimates of regression coefficients when patients with no follow-up assessments are excluded from analyses. We design a simulation study to evaluate how the bias varies with sample size, assessment frequency, follow-up time, and the informativeness of the assessment time process. Using the STAR*D trial of treatments for major depressive disorder, we examine the extent of bias in practice. Results Our simulation results showed the bias incurred by omitting patients with no follow-up visits increased as visit frequency decreased and as the duration of follow-up decreased. In the STAR*D trial, omitting patients with no follow-up visits led to over-estimation of the rate of improvement in depressive symptoms. Conclusions Studies should be designed to ensure patients with no follow-up are included in the data. This can be achieved by a) creating inception cohorts; b) when taking sub-samples of existing cohorts, ensuring that patients without follow-up assessments are included; c) dropping exclusion criteria based on availability of follow-up visits.

In many longitudinal studies, repeated response and predictors are not directly observed, but can be treated as distorted by unknown functions of a common confounding covariate. Moreover, longitudinal data involve an observation process which may be informative with a longitudinal response process in practice. To deal with such complex data, we propose a class of flexible semiparametric covariate-adjusted joint models. The new models not only allow for the longitudinal response to be correlated with observation times through latent variables and completely unspecified link functions, but they also characterize distorted longitudinal response and predictors by unknown multiplicative factors depending on time and a confounding covariate. For estimation of regression parameters in the proposed models, we develop a novel covariate-adjusted estimating equation approach which does not rely on forms of link functions and distributions of frailties. The asymptotic properties of resulting parameter estimators are established and examined by simulation studies. A longitudinal data example containing calcium absorption and intake measurements is provided for illustration. Supplementary materials for this article are available online.

We consider the proportional hazards model with time-dependent covariates measured with error at informative observation times under shared random effects models. Although various approaches have been proposed to deal with measurement error for time-dependent covariates, very limited research has been done when the observation times are informative. We propose a new corrected score estimator that allows the observation times to depend on the survival time, the random effects, or other covariates. Compared to existing conditional score and corrected score approaches, it relaxes the requirement on non-informative observation times, may substantially improve the efficiency, and is much more robust to deviations from normality of the error. The performance of the estimator is evaluated via simulation studies and by application to data from an HIV clinical trial.

We consider the semiparametric regression of panel count data occurring in longitudinal follow-up studies that concern occurrence rate of certain recurrent events. The analysis of panel count data involves two processes, i.e, a recurrent event process of interest and an observation process controlling observation times. However, the model assumptions of existing methods, such as independent censoring time and Poisson assumption, are restrictive and questionable. In this paper, we propose new joint models for panel count data by considering both informative observation times and censoring times. The asymptotic normality of the proposed estimators are established. Numerical results from simulation studies and a real data example show the advantage of the proposed method.

In this paper, we consider the joint modelling of survival and longitudinal data with informative observation time points. The survival model and the longitudinal model are linked via random effects, for which no distribution assumption is required under our estimation approach. The estimator is shown to be consistent and asymptotically normal. The proposed estimator and its estimated covariance matrix can be easily calculated. Simulation studies and an application to a primary biliary cirrhosis study are also provided.

In many longitudinal studies, longitudinal responses are subject to left-censoring and may be correlated with observation times. In this article, we propose a Tobit quantile regression model for the analysis of left-censored longitudinal data with informative observation times and with the longitudinal responses allowed to depend on the past observation history. Estimating equation approaches are developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. A modified Majorize-Minimize algorithm is proposed to compute the proposed estimators. Simulation studies show that the proposed estimators perform well. An application to a data set from an AIDS clinical trial study is provided.

Multistate models are used to characterize individuals’ natural histories through diseases with discrete states. Observational data resources based on electronic medical records pose new opportunities for studying such diseases. However, these data consist of observations of the process at discrete sampling times, which may either be pre‐scheduled and non‐informative, or symptom‐driven and informative about an individual's underlying disease status. We have developed a novel joint observation and disease transition model for this setting. The disease process is modeled according to a latent continuous‐time Markov chain; and the observation process, according to a Markov‐modulated Poisson process with observation rates that depend on the individual's underlying disease status. The disease process is observed at a combination of informative and non‐informative sampling times, with possible misclassification error. We demonstrate that the model is computationally tractable and devise an expectation‐maximization algorithm for parameter estimation. Using simulated data, we show how estimates from our joint observation and disease transition model lead to less biased and more precise estimates of the disease rate parameters. We apply the model to a study of secondary breast cancer events, utilizing mammography and biopsy records from a sample of women with a history of primary breast cancer.

In many longitudinal studies, the response process is correlated with observation times and dropout. We propose a joint modeling for analysis of longitudinal data with informative observation times and dropout. We specify a semiparametric linear regression model for the longitudinal process, and accelerated time models for the observation and the dropout processes, while leaving the distributional form and dependent structure unspecified. Estimating equation approaches are developed for parameter estimation, and the resulting estimators are shown to be consistent and asymptotically normal. In addition, some numerical procedures are provided for model checking. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is provided.

Longitudinal data frequently occur in many studies, such as longitudinal follow-up studies. To develop statistical methods and theory for the analysis of these data, independent or noninformative observation and censoring times are typically assumed, which naturally leads to inference procedures conditional on observation and censoring times. But in many situations this may not be true or realistic; that is, longitudinal responses may be correlated with observation times as well as censoring times. This article considers the analysis of longitudinal data where these correlations may exist and proposes a joint modeling approach that uses some latent variables to characterize the correlations. For inference about regression parameters, estimating equation approaches are developed and both large-sample and final-sample properties of the proposed estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The methodology is applied to a bladder cancer study that motivated this investigation.