Semiparametric estimation of the accelerated mean model with panel count data under informative examination times.
ABSTRACT: Panel count data arise when the number of recurrent events experienced by each subject is observed intermittently at discrete examination times. The examination time process can be informative about the underlying recurrent event process even after conditioning on covariates. We consider a semiparametric accelerated mean model for the recurrent event process and allow the two processes to be correlated through a shared frailty. The regression parameters have a simple marginal interpretation of modifying the time scale of the cumulative mean function of the event process. A novel estimation procedure for the regression parameters and the baseline rate function is proposed based on a conditioning technique. In contrast to existing methods, the proposed method is robust in the sense that it requires neither the strong Poisson-type assumption for the underlying recurrent event process nor a parametric assumption on the distribution of the unobserved frailty. Moreover, the distribution of the examination time process is left unspecified, allowing for arbitrary dependence between the two processes. Asymptotic consistency of the estimator is established, and the variance of the estimator is estimated by a model-based smoothed bootstrap procedure. Numerical studies demonstrated that the proposed point estimator and variance estimator perform well with practical sample sizes. The methods are applied to data from a skin cancer chemoprevention trial.
Project description:In this article we propose an accelerated intensity frailty (AIF) model for recurrent events data and derive a test for the variance of frailty. In addition, we develop a kernel-smoothing-based EM algorithm for estimating regression coefficients and the baseline intensity function. The variance of the resulting estimator for regression parameters is obtained by a numerical differentiation method. Simulation studies are conducted to evaluate the finite sample performance of the proposed estimator under practical settings and demonstrate the efficiency gain over the Gehan rank estimator based on the AFT model for counting process (Lin et al., 1998). Our method is further illustrated with an application to a bladder tumor recurrence data.
Project description:Recurrent event data arise frequently in various fields such as biomedical sciences, public health, engineering, and social sciences. In many instances, the observation of the recurrent event process can be stopped by the occurrence of a correlated failure event, such as treatment failure and death. In this article, we propose a joint scale-change model for the recurrent event process and the failure time, where a shared frailty variable is used to model the association between the two types of outcomes. In contrast to the popular Cox-type joint modeling approaches, the regression parameters in the proposed joint scale-change model have marginal interpretations. The proposed approach is robust in the sense that no parametric assumption is imposed on the distribution of the unobserved frailty and that we do not need the strong Poisson-type assumption for the recurrent event process. We establish consistency and asymptotic normality of the proposed semiparametric estimators under suitable regularity conditions. To estimate the corresponding variances of the estimators, we develop a computationally efficient resampling-based procedure. Simulation studies and an analysis of hospitalization data from the Danish Psychiatric Central Register illustrate the performance of the proposed method.
Project description:This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method.
Project description:In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non-parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non-parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson-type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma.
Project description:In clinical and observational studies, the event of interest can often recur on the same subject. In a more complicated situation, there exists a terminal event (e.g., death) which stops the recurrent event process. In many such instances, the terminal event is strongly correlated with the recurrent event process. We consider the recurrent/terminal event setting and model the dependence through a shared gamma frailty that is included in both the recurrent event rate and terminal event hazard functions. Conditional on the frailty, a model is specified only for the marginal recurrent event process, hence avoiding the strong Poisson-type assumptions traditionally used. Analysis is based on estimating functions that allow for estimation of covariate effects on the recurrent event rate and terminal event hazard. The method also permits estimation of the degree of association between the two processes. Closed-form asymptotic variance estimators are proposed. The proposed method is evaluated through simulations to assess the applicability of the asymptotic results in finite samples and the sensitivity of the method to its underlying assumptions. The methods can be extended in straightforward ways to accommodate multiple types of recurrent and terminal events. Finally, the methods are illustrated in an analysis of hospitalization data for patients in an international multi-center study of outcomes among dialysis patients.
Project description:Recurrent adverse events, once occur often continue for some duration of time in clinical trials; and the number of events along with their durations is clinically considered as a measure of severity of a disease under study. While there are methods available for analyzing recurrent events or durations or for analyzing both side by side, no effort has been made so far to combine them and present as a single measure. However, this single-valued combined measure may help clinicians assess the wholesome effect of recurrence of incident comprising events and durations. Non-parametric approach is adapted here to develop an estimator for estimating the combined rate of both, the recurrence of events as well as the event-continuation, that is the duration per event. The proposed estimator produces a single numerical value, the interpretation and meaningfulness of which are discussed through the analysis of a real-life clinical dataset. The algebraic expression of variance is derived, asymptotic normality of the estimator is noted, and demonstration is provided on how the estimator can be used in the setup of testing of statistical hypothesis. Further possible development of the estimator is also noted, to adjust for the dependence of event occurrences on the history of the process generating recurrent events through covariates and for the case of dependent censoring.
Project description:Panel-count data arise when each study subject is observed only at discrete time points in a recurrent event study, and only the numbers of the event of interest between observation time points are recorded (Sun and Zhao, 2013). However, sometimes the exact number of events between some observation times is unknown and what we know is only whether the event of interest has occurred. In this article, we will refer this type of data to as mixed panel-count data and propose a likelihood-based semiparametric regression method for their analysis by using the nonhomogeneous Poisson process assumption. However, we establish the asymptotic properties of the resulting estimator by employing the empirical process theory and without using the Poisson assumption. Also, we conduct an extensive simulation study, which suggests that the proposed method works well in practice. Finally, the method is applied to a Childhood Cancer Survivor Study that motivated this study.
Project description:The process by which patients experience a series of recurrent events, such as hospitalizations, may be subject to death. In cohort studies, one strategy for analyzing such data is to fit a joint frailty model for the intensities of the recurrent event and death, which estimates covariate effects on the two event types while accounting for their dependence. When certain covariates are difficult to obtain, however, researchers may only have the resources to subsample patients on whom to collect complete data: one way is using the nested case-control (NCC) design, in which risk set sampling is performed based on a single outcome. We develop a general framework for the design of NCC studies in the presence of recurrent and terminal events and propose estimation and inference for a joint frailty model for recurrence and death using data arising from such studies. We propose a maximum weighted penalized likelihood approach using flexible spline models for the baseline intensity functions. Two standard error estimators are proposed: a sandwich estimator and a perturbation resampling procedure. We investigate operating characteristics of our estimators as well as design considerations via a simulation study and illustrate our methods using two studies: one on recurrent cardiac hospitalizations in patients with heart failure and the other on local recurrence and metastasis in patients with breast cancer.
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.