Project description:This article presents semiparametric joint models to analyze longitudinal data with recurrent event (e.g. multiple tumors, repeated hospital admissions) and terminal event such as death. A broad class of transformation models for the cumulative intensity of the recurrent events and the cumulative hazard of the terminal event is considered, which includes the proportional hazards model and the proportional odds model as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we evaluate the performance of the method through extensive simulation studies and a real-data application.
Project description:Joint modeling of longitudinal and time-to-event data, particularly through shared parameter models (SPMs), is a common approach for handling longitudinal marker data with an informative terminal event. A critical but often neglected assumption in this context is that the visiting/observation process is noninformative, depending solely on past marker values and visit times. When this assumption fails, the visiting process becomes informative, resulting potentially to biased SPM estimates. Existing methods generally rely on a conditional independence assumption, positing that the marker model, visiting process, and time-to-event model are independent given shared or correlated random effects. Moreover, they are typically built on an intensity-based visiting process using calendar time. This study introduces a unified approach for jointly modeling a normally distributed marker, the visiting process, and time-to-event data in the form of competing risks. Our model conditions on the history of observed marker values, prior visit times, the marker's random effects, and possibly a frailty term independent of the random effects. While our approach aligns with the shared-parameter framework, it does not presume conditional independence between the processes. Additionally, the visiting process can be defined on either a gap time scale, via proportional hazard models, or a calendar time scale, via proportional intensity models. Through extensive simulation studies, we assess the performance of our proposed methodology. We demonstrate that disregarding an informative visiting process can yield significantly biased marker estimates. However, misspecification of the visiting process can also lead to biased estimates. The gap time formulation exhibits greater robustness compared to the intensity-based model when the visiting process is misspecified. In general, enriching the visiting process with prior visit history enhances performance. We further apply our methodology to real longitudinal data from HIV, where visit frequency varies substantially among individuals.
Project description:Recurrent event data arise frequently in many longitudinal follow-up studies. Hence, evaluating covariate effects on the rates of occurrence of such events is commonly of interest. Examples include repeated hospitalizations, recurrent infections of HIV, and tumor recurrences. In this article, we consider semiparametric regression methods for the occurrence rate function of recurrent events when the covariates may be measured with errors. In contrast to the existing works, in our case the conventional assumption of independent censoring is violated since the recurrent event process is interrupted by some correlated events, which is called informative drop-out. Further, some covariates may be measured with errors. To accommodate for both informative censoring and measurement error, the occurrence of recurrent events is modelled through an unspecified frailty distribution and accompanied with a classical measurement error model. We propose two corrected approaches based on different ideas, and we show that they are numerically identical when estimating the regression parameters. The asymptotic properties of the proposed estimators are established, and the finite sample performance is examined via simulations. The proposed methods are applied to the Nutritional Prevention of Cancer trial for assessing the effect of the plasma selenium treatment on the recurrence of squamous cell carcinoma.
Project description:Electrical brain activity related to external stimulation and internal mental events can be measured at the scalp as tiny time-varying electric potential waveforms (electroencephalogram; EEG), typically a few tens of microvolts peak to peak (Berger, 1930). Even tinier brain responses, too small to be seen by naked eye in the EEG, can be detected by repeating the stimulation, aligning the EEG recordings to the triggering event and averaging them at each time point (Dawson, 1951, 1954). Under assumptions that the brain response (signal) is the same in each recording and the ongoing background EEG (noise) varies randomly, averaging improves the estimate of the "true" brain response at each time point as the random variation cancels. The average event-related brain potential (ERP) and its counterpart for event-related magnetic fields (ERFs) are cornerstones of experimental brain research in human sensation, perception, and cognition (Luck & Kappenman, 2013). Smith and Kutas pointed out that the average ERP at each time t is mathematically identical to the estimated constant β^0(t) for the regression model y(t) = β 0(t) + ε(t), fit by minimizing squared error (Smith & Kutas, 2015a). The average ERP can be viewed as a time series of model parameter estimates. Generalizing to more complex models such as multiple regression y = β 0 + β 1 X 1 + … + β pXp + ε, likewise produces time series of estimates for the constant and each regressor coefficient, the β^0(t),β^1(t),…,β^p(t) dubbed regression ERP (rERP) waveforms (see Smith & Kutas, 2015a, 2015b for discussion of related approaches). This holds for straight-line fits ("slope" rERPs) as well as models of curvilinear relationships such as spline regression (Smith & Kutas, 2015b). Besides the estimated coefficient rERPs, the approach also produces time series for all the basic and derived quantities of the fitted model: coefficient standard errors, residuals, likelihood, Akaike information criterion (AIC), and so forth. With the shift from averaging to regression modeling, however, comes a new problem: fitting, diagnosing, comparing, evaluating and interpreting large numbers of regression models.
Project description:Recurrent events could be stopped by a terminal event, which commonly occurs in biomedical and clinical studies. In this situation, dependent censoring is encountered because of potential dependence between these two event processes, leading to invalid inference if analyzing recurrent events alone. The joint frailty model is one of the widely used approaches to jointly model these two processes by sharing the same frailty term. One important assumption is that recurrent and terminal event processes are conditionally independent given the subject-level frailty; however, this could be violated when the dependency may also depend on time-varying covariates across recurrences. Furthermore, marginal correlation between two event processes based on traditional frailty modeling has no closed form solution for estimation with vague interpretation. In order to fill these gaps, we propose a novel joint frailty-copula approach to model recurrent events and a terminal event with relaxed assumptions. Metropolis-Hastings within the Gibbs Sampler algorithm is used for parameter estimation. Extensive simulation studies are conducted to evaluate the efficiency, robustness, and predictive performance of our proposal. The simulation results show that compared with the joint frailty model, the bias and mean squared error of the proposal is smaller when the conditional independence assumption is violated. Finally, we apply our method into a real example extracted from the MarketScan database to study the association between recurrent strokes and mortality.
Project description:Recurrent event data are commonly encountered in clinical and epidemiological studies. A major complication arises when recurrent events are terminated by death. To assess the overall effects of covariates on the two types of events, we define a weighted composite endpoint as the cumulative number of recurrent and terminal events properly weighted by the relative severity of each event. We propose a semiparametric proportional rates model which specifies that the (possibly time-varying) covariates have multiplicative effects on the rate function of the weighted composite endpoint while leaving the form of the rate function and the dependence among recurrent and terminal events completely unspecified. We construct appropriate estimators for the regression parameters and the cumulative frequency function. We show that the estimators are consistent and asymptotically normal with variances that can be consistently estimated. We also develop graphical and numerical procedures for checking the adequacy of the model. We then demonstrate the usefulness of the proposed methods in simulation studies. Finally, we provide an application to a major cardiovascular clinical trial.
Project description:Repeated measures are often collected in longitudinal follow-up from clinical trials and observational studies. In many situations, these measures are adherent to some specific event and are only available when it occurs; an example is serum creatinine from laboratory tests for hospitalized acute kidney injuries. The frequency of event recurrences is potentially correlated with overall health condition and hence may influence the distribution of the outcome measure of interest, leading to informative cluster size. In particular, there may be a large portion of subjects without any events, thus no longitudinal measures are available, which may be due to insusceptibility to such events or censoring before any events, and this zero-inflation nature of the data needs to be taken into account. On the other hand, there often exists a terminal event that may be correlated with the recurrent events. Previous work in this area suffered from the limitation that not all these issues were handled simultaneously. To address this deficiency, we propose a novel joint modeling approach for longitudinal data adjusting for zero-inflated and informative cluster size as well as a terminal event. A three-stage semiparametric likelihood-based approach is applied for parameter estimation and inference. Extensive simulations are conducted to evaluate the performance of our proposal. Finally, we utilize the Assessment, Serial Evaluation, and Subsequent Sequelae of Acute Kidney Injury (ASSESS-AKI) study for illustration.
Project description:Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same event. Most regression models with recurrent events tacitly assume constant effects of covariates over time, which may not be realistic in practice. To address time-varying effects, we develop a dynamic regression model to target the mean frequency of recurrent events. We propose an estimation procedure which fully exploits observed data. Consistency and weak convergence of the proposed estimator are established. Simulation studies demonstrate that the proposed method works well, and two real data analyses are presented for illustration.
Project description:Recurrent events are common in clinical studies and are often subject to terminal events. In pragmatic trials, participants are often nested in clinics and can be susceptible or structurally unsusceptible to the recurrent events. We develop a Bayesian shared random effects model to accommodate this complex data structure. To achieve robustness, we consider the Dirichlet processes to model the residual of the accelerated failure time model for the survival process as well as the cluster-specific shared frailty distribution, along with an efficient sampling algorithm for posterior inference. Our method is applied to a recent cluster randomized trial on fall injury prevention.
Project description:Two major challenges arise in regression analyses of recurrent event data: first, popular existing models, such as the Cox proportional rates model, may not fully capture the covariate effects on the underlying recurrent event process; second, the censoring time remains informative about the risk of experiencing recurrent events after accounting for covariates. We tackle both challenges by a general class of semiparametric scale-change models that allow a scale-change covariate effect as well as a multiplicative covariate effect. The proposed model is flexible and includes several existing models as special cases, such as the popular proportional rates model, the accelerated mean model, and the accelerated rate model. Moreover, it accommodates informative censoring through a subject-level latent frailty whose distribution is left unspecified. A robust estimation procedure which requires neither a parametric assumption on the distribution of the frailty nor a Poisson assumption on the recurrent event process is proposed to estimate the model parameters. The asymptotic properties of the resulting estimator are established, with the asymptotic variance estimated from a novel resampling approach. As a byproduct, the structure of the model provides a model selection approach among the submodels via hypothesis testing of model parameters. Numerical studies show that the proposed estimator and the model selection procedure perform well under both noninformative and informative censoring scenarios. The methods are applied to data from two transplant cohorts to study the risk of infections after transplantation.