Semiparametric additive marginal regression models for multiple type recurrent events

Regression analysis of multivariate recurrent event data allowing time-varying dependence with application to stroke registry data

In multivariate recurrent event data, each patient may repeatedly experience more than one type of event. Analysis of such data gets further complicated by the time-varying dependence structure among different types of recurrent events. The available literature regarding the joint modeling of multivariate recurrent events assumes a constant dependency over time, which is strict and often violated in practice. To close the knowledge gap, we propose a class of flexible shared random effects models for multivariate recurrent event data that allow for time-varying dependence to adequately capture complex correlation structures among different types of recurrent events. We developed an expectation-maximization algorithm for stable and efficient model fitting. Extensive simulation studies demonstrated that the estimators of the proposed approach have satisfactory finite sample performance. We applied the proposed model and the estimating method to data from a cohort of stroke patients identified in the University of Texas Houston Stroke Registry and evaluated the effects of risk factors and the dependence structure of different types of post-stroke readmission events.

Multistate modeling and structure selection for multitype recurrent events and terminal event data

In cardiovascular disease studies, a large number of risk factors are measured but it often remains unknown whether all of them are relevant variables and whether the impact of these variables is changing with time or remains constant. In addition, more than one kind of cardiovascular disease events can be observed in the same patient and events of different types are possibly correlated. It is expected that different kinds of events are associated with different covariates and the forms of covariate effects also vary between event types. To tackle these problems, we proposed a multistate modeling framework for the joint analysis of multitype recurrent events and terminal event. Model structure selection is performed to identify covariates with time-varying coefficients, time-independent coefficients, and null effects. This helps in understanding the disease process as it can detect relevant covariates and identify the temporal dynamics of the covariate effects. It also provides a more parsimonious model to achieve better risk prediction. The performance of the proposed model and selection method is evaluated in numerical studies and illustrated on a real dataset from the Atherosclerosis Risk in Communities study.

Augmented weighting estimators for the additive rates model under multivariate recurrent event data with missing event type

Multivariate recurrent event data are frequently encountered in biomedical and epidemiological studies when subjects experience multiple types of recurrent events. In practice, the event type information may be missing due to a variety of reasons. In this article, we consider a semiparametric additive rates model for multivariate recurrent event data with missing event types. We develop the augmented inverse probability weighting technique to handle event types that are missing at random. The nonparametric kernel-assisted proposals for the missing mechanisms are studied. The resulting estimator is shown to be consistent and asymptotically normal. Extensive simulation studies and a real data application are provided to illustrate the validity and practical utility of the proposed method.

An additive hazards frailty model with semi-varying coefficients

Proportional hazards frailty models have been extensively investigated and used to analyze clustered and recurrent failure times data. However, the proportional hazards assumption in the models may not always hold in practice. In this paper, we propose an additive hazards frailty model with semi-varying coefficients, which allows some covariate effects to be time-invariant while other covariate effects to be time-varying. The time-varying and time-invariant regression coefficients are estimated by a set of estimating equations, whereas the frailty parameter is estimated by the moment method. The large sample properties of the proposed estimators are established. The finite sample performance of the estimators is examined by simulation studies. The proposed model and estimation are illustrated with an analysis of data from a rehospitalization study of colorectal cancer patients.

Semiparametric estimation of the proportional rates model for recurrent events data with missing event category

Proportional rates models are frequently used for the analysis of recurrent event data with multiple event categories. When some of the event categories are missing, a conventional approach is to either exclude the missing data for a complete-case analysis or employ a parametric model for the missing event type. It is well known that the complete-case analysis is inconsistent when the missingness depends on covariates, and the parametric approach may incur bias when the model is misspecified. In this paper, we aim to provide a more robust approach using a rate proportion method for the imputation of missing event types. We show that the log-odds of the event type can be written as a semiparametric generalized linear model, facilitating a theoretically justified estimation framework. Comprehensive simulation studies were conducted demonstrating the improved performance of the semiparametric method over parametric procedures. Multiple types of Pseudomonas aeruginosa infections of young cystic fibrosis patients were analyzed to demonstrate the feasibility of our proposed approach.

Functional modeling of recurrent events on time-to-event processes

In clinical practice, it is often the case where the association between the occurrence of events and time-to-event outcomes is of interest; thus, it can be modeled within the framework of recurrent events. The purpose of our study is to enrich the information available for modeling survival with relevant dynamic features, properly taking into account their possibly time-varying nature, as well as to provide a new setting for quantifying the association between time-varying processes and time-to-event outcomes. We propose an innovative methodology to model information carried out by time-varying processes by means of functional data, modeling each time-varying variable as the compensator of marked point process the recurrent events are supposed to derive from. By means of Functional Principal Component Analysis, a suitable dimensional reduction of these objects is carried out in order to plug them into a Cox-type functional regression model for overall survival. We applied our methodology to data retrieved from the administrative databases of Lombardy Region (Italy), related to patients hospitalized for Heart Failure (HF) between 2000 and 2012. We focused on time-varying processes of HF hospitalizations and multiple drugs consumption and we studied how they influence patients' overall survival. This novel way to account for time-varying variables allowed to model self-exciting behaviors, for which the occurrence of events in the past increases the probability of a new event, and to quantify the effect of personal behaviors and therapeutic patterns on survival, giving new insights into the direction of personalized treatment.

Inverse probability weighted estimation for recurrent events data with missing category

Modeling recurrent event data with multiple event types has drawn interest in recent biomedical studies due to its flexibility for understanding different risk factors for multiple recurrent event processes. However, in such data type, missing event type appears frequently because of various reasons such as recording ignorance or resource limitation. In this study, we aim to propose an inverse probability weighted estimation that is commonly used in the missing data literature to correct possibly biased estimation by a complete-case analysis. This approach is not limited to a specific form of the recurrent event model. We derive the large sample theory in a general form. We demonstrate that our approach can be applied to either multiplicative or additive rates model with practical sample size via comprehensive simulations. Nonmucoid and mucoid Pseudomonas aeruginosa infections of 14 888 patients in 2016 Cystic Fibrosis Foundation Patient Registry data are analyzed to show that, without including 12% events with missing event type in the analysis, several factors may be misidentified as risk factors for the nonmucoid type of infections.

A semiparametric additive rates model for the weighted composite endpoint of recurrent and terminal events

Recurrent event data with a terminal event commonly arise in longitudinal follow-up studies. We use a weighted composite endpoint of all recurrent and terminal events to assess the overall effects of covariates on the two types of events. A semiparametric additive rates model is proposed to analyze the weighted composite event process and the dependence structure among recurrent and terminal events is left unspecified. An estimating equation approach is developed for inference, and the asymptotic properties of the resulting estimators are established. The finite-sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is illustrated.

Dependence modeling for multi-type recurrent events via copulas

When several types of recurrent events may arise, interest often lies in marginal modeling and studying the nature of the dependence structure. In this paper, we propose a multivariate mixed-Poisson model with the dependence between events accommodated by type-specific random effects which are associated through use of a Gaussian copula. Such models retain marginal features with a simple interpretation, reflect the heterogeneity in risk for each type of event, and provide insight into the dependence between the different types of events. Semiparametric inference is proposed based on composite likelihood to avoid high dimensional integration. An application to a study of nutritional supplements in malnourished children is given in which the goal is to evaluate the reduction in the rate of several different kinds of infection.

Frailty modelling for multitype recurrent events in clinical trials

Recurrent event outcomes are ubiquitous among clinical trial data which encourages a conventional approach to analysis. Yet a common feature of these data has received less attention, that is, survival times often comprise multiple types of events that may imply a disparity in cost and disease severity. Typically, we neglect this feature of the data by combining event-types or analyzing each type separately, thus ignoring any interdependence among them. This practice may reflect a dearth of readily available methods and software that more appropriately acknowledge the true data structure. We provide a review of the literature on multitype recurrent events and frailty modelling which reflects a renewed interest in the topic over the past decade and the emergence of software for estimation. Thus, a review of available methods seems timely, if not overdue.