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In follow-up studies, utility marker measurements are usually collected upon the occurrence of recurrent events until a terminal event such as death takes place. In this article, we define the recurrent marker process to characterize utility accumulation over time. For example, with medical cost and repeated hospitalizations being treated as marker and recurrent events, respectively, the recurrent marker process is the trajectory of cumulative cost, which stops to increase after death. In many applications, competing risks arise as subjects are at risk of more than one mutually exclusive terminal event, such as death from different causes, and modeling the recurrent marker process for each failure type is often of interest. However, censoring creates challenges in the methodological development, because for censored subjects, both failure type and recurrent marker process after censoring are unobserved. To circumvent this problem, we propose a nonparametric framework for the recurrent marker process with competing terminal events. In the presence of competing risks, we start with an estimator by using marker information from uncensored subjects. As a result, the estimator can be inefficient under heavy censoring. To improve efficiency, we propose a second estimator by combining the first estimator with auxiliary information from the estimate under noncompeting risks model. The large sample properties and optimality of the second estimator are established. Simulation studies and an application to the SEER-Medicare linked data are presented to illustrate the proposed methods. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Benefit–risk assessment is a crucial step in medical decision process. In many biomedical studies, both longitudinal marker measurements and time to a terminal event serve as important endpoints for benefit–risk assessment. The effect of an intervention or a treatment on the longitudinal marker process, however, can be in conflict with its effect on the time to the terminal event. Thus, questions arise on how to evaluate treatment effects based on the two endpoints, for the purpose of deciding on which treatment is most likely to benefit the patients. In this article, we present a unified framework for benefit–risk assessment using the observed longitudinal markers and time to event data. We propose a cumulative weighted marker process to synthesize information from the two endpoints, and use its mean function at a prespecified time point as a benefit–risk summary measure. We consider nonparametric estimation of the summary measure under two scenarios: (i) the longitudinal marker is measured intermittently during the study period, and (ii) the value of the longitudinal marker is observed throughout the entire follow-up period. The large-sample properties of the estimators are derived and compared. Simulation studies and data examples exhibit that the proposed methods are easy to implement and reliable for practical use. Supplemental materials for this article are available online. [ABSTRACT FROM PUBLISHER]

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. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Recurrent event processes with marker measurements are mostly and largely studied with forward time models starting from an initial event. Interestingly, the processes could exhibit important terminal behavior during a time period before occurrence of the failure event. A natural and direct way to study recurrent events prior to a failure event is to align the processes using the failure event as the time origin and to examine the terminal behavior by a backward time model. This article studies regression models for backward recurrent marker processes by counting time backward from the failure event. A three-level semiparametric regression model is proposed for jointly modeling the time to a failure event, the backward recurrent event process, and the marker observed at the time of each backward recurrent event. The first level is a proportional hazards model for the failure time, the second level is a proportional rate model for the recurrent events occurring before the failure event, and the third level is a proportional mean model for the marker given the occurrence of a recurrent event backward in time. By jointly modeling the three components, estimating equations can be constructed for marked counting processes to estimate the target parameters in the three-level regression models. Large sample properties of the proposed estimators are studied and established. The proposed models and methods are illustrated by a community-based AIDS clinical trial to examine the terminal behavior of frequencies and severities of opportunistic infections among HIV-infected individuals in the last 6 months of life. [ABSTRACT FROM AUTHOR]

We consider a specific situation of correlated data where multiple outcomes are repeatedly measured on each member of a couple. Such multivariate longitudinal data from couples may exhibit multi-faceted correlations that can be further complicated if there are polygamous partnerships. An example is data from cohort studies on human papillomavirus (HPV) transmission dynamics in heterosexual couples. HPV is a common sexually transmitted disease with 14 known oncogenic types causing anogenital cancers. The binary outcomes on the multiple types measured in couples over time may introduce inter-type, intra-couple, and temporal correlations. Simple analysis using generalized estimating equations or random effects models lacks interpretability and cannot fully use the available information. We developed a hybrid modeling strategy using Markov transition models together with pairwise composite likelihood for analyzing such data. The method can be used to identify risk factors associated with HPV transmission and persistence, estimate difference in risks between male-to-female and female-to-male HPV transmission, compare type-specific transmission risks within couples, and characterize the inter-type and intra-couple associations. Applying the method to HPV couple data collected in a Ugandan male circumcision (MC) trial, we assessed the effect of MC and the role of gender on risks of HPV transmission and persistence. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The APOE ε4 allele increases the risk of developing Alzheimer’s disease, whereas the APOE ε2 allele reduces risk. We examined whether cognitive reserve (CR), as measured by an index consisting of education, reading, and vocabulary, modifies these associations. CR was measured at baseline in 257 cognitively normal individuals (mean age 57.2 years) who have been followed for up to 17 years (mean follow-up = 9.2 years). Cox regression models showed that CR and APOE ε4 independently affected the risk of progressing from normal cognition to onset of clinical symptoms: CR reduced risk by about 50% in both ε4 carriers and non-carriers, while ε4 increased risk by about 150%. In contrast, APOE ε2 interacted with CR, such that CR was more protective in ε2 carriers than non-carriers. This suggests that individuals with an ε2 genotype may disproportionately benefit from lifetime experiences that enhance cognition. [ABSTRACT FROM AUTHOR]

Recurrent events arise in many longitudinal medical studies where time to a terminal event or failure is the primary endpoint. With incomplete follow-up data, the analysis of recurrent events is a challenge owing to their association with the failure. One specific quantity of interest rarely addressed in the statistical literature is the recurrence frequency at the failure time: an example is hospitalization frequency, which is often used as a rough measure of lifetime medical cost. In this article we show that a marginal model (e.g., the log-linear model) of the recurrence frequency, although desirable, is typically not identifiable. For this reason, we advocate modeling the recurrent events and the failure time jointly, and propose an approach to forming semiparametric joint models from prespecified marginal ones. We suggest two conceptually simple and nested regression models aiming at the recurrence frequency as a mark of the failure and at the process of recurrent events. We formulate monotone estimating functions and propose novel interval-estimation procedures to accommodate nonsmooth estimating functions. The resulting estimators are consistent and asymptotically normal. Simulation studies and the application to an AIDS clinical trial exhibit that these proposals are easy to implement and reliable for practical use. Finally, we generalize our proposals to marked recurrent events, and also devise a global inference procedure for recurrent events of multiple types. [ABSTRACT FROM AUTHOR]

The proportional hazards model for survival time data usually assumes that the covariates of interest take constant effects proportionally on an unspecified baseline hazard function. However, it may not be applicable when the assumption of constant proportionality is violated. In a two-arm randomized clinical trial, for example, the treatment is often expected to be fully effective only after a certain lag period. Some alternatives, such as the accelerated failure time model, have been developed in statistical literature. This article introduces an accelerated hazards model when there is a scale change relationship between the hazard functions. An estimating equation is proposed to estimate the parameter semiparametrically. The methodology is demonstrated within a two-sample framework. Several extensions of the model are also considered. Real clinical trial data are used to investigate the model's practical use. [ABSTRACT FROM AUTHOR]

Suppose the progress of a disease consists of two chronologically ordered events, termed the starting event and the failure event. In retrospective sampling, the sampling scheme under which observations in the data set are identified retrospectively, individuals who experienced the starting event but not the failure event are excluded and thus arc truncated from the data set, and only those who experienced both the starting event and the failure event before a given time are observed, The problem of reporting delays arises when some of the failure events are not reported before the given time and thus the corresponding cases also are excluded from the data set. In survival studies failure time data sometimes are collected under the retrospective sampling scheme subject to reporting delays. This article explores nonparametric and semiparametric methods of dealing with this type of data. The results generalize some existing nonparametric and semiparametric methods for analyzing tight-truncated data when reporting delays are absent. Estimation of the expected number of events is studied in detail, interpretation of the proposed estimates is discussed. and an analysis of the blood transfusion data from the Centers for Disease Control is presented. [ABSTRACT FROM AUTHOR]

Considers a product-limit estimate for estimating S and characterize the nonparametric maximum likelihood estimate (NPMLE) of H under an additional constraint. Background of the stationarity assumption and comparison between product-limit estimate and Vardi's estimate (1988); Brief description of NPMLE for G; Several asymptotic properties of G; Overview of nonparametric estimation of H; Concluding remarks.