Design and analysis of nested case-control studies for recurrent events subject to a terminal event.
ABSTRACT: 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 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: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:AIMS:Recurrent hospitalizations are a major part of the disease burden in heart failure (HF), but conventional analyses consider only the first event. We compared the effect of sacubitril/valsartan vs. enalapril on recurrent events, incorporating all HF hospitalizations and cardiovascular (CV) deaths in PARADIGM-HF, using a variety of statistical approaches advocated for this type of analysis. METHODS AND RESULTS:In PARADIGM-HF, a total of 8399 patients were randomized and followed for a median of 27?months. We applied various recurrent event analyses, including a negative binomial model, the Wei, Lin and Weissfeld (WLW), and Lin, Wei, Ying and Yang (LWYY) methods, and a joint frailty model, all adjusted for treatment and region. Among a total of 3181 primary endpoint events (including 1251 CV deaths) during the trial, only 2031 (63.8%) were first events (836 CV deaths). Among a total of 1195 patients with at least one HF hospitalization, 410 (34%) had at least one further HF hospitalization. Sacubitril/valsartan compared with enalapril reduced the risk of recurrent HF hospitalization using the negative binomial model [rate ratio (RR) 0.77, 95% confidence interval (CI) 0.67-0.89], the WLW method [hazard ratio (HR) 0.79, 95% CI 0.71-0.89], the LWYY method (RR 0.78, 95% CI 0.68-0.90), and the joint frailty model (HR 0.75, 95% CI 0.66-0.86) (all P <?0.001). The effect of sacubitril/valsartan vs. enalapril on recurrent HF hospitalizations/CV death was similar. CONCLUSIONS:In PARADIGM-HF, approximately one third of patients with a primary endpoint (time-to-first) experienced a further event. Compared with enalapril, sacubitril/valsartan reduced both first and recurrent events. The treatment effect size was similar, regardless of the statistical approach applied.
Project description:Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length-of-stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance-covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end-stage renal disease patients.
Project description:Little attention has been given to the design of efficient studies to evaluate longitudinal biomarkers. Measuring longitudinal markers on an entire cohort is cost prohibitive and, especially for rare outcomes such as cancer, may be infeasible. Thus, methods for evaluation of longitudinal biomarkers using efficient and cost-effective study designs are needed. Case cohort (CCH) and nested case-control (NCC) studies allow investigators to evaluate biomarkers rigorously and at reduced cost, with only a small loss in precision. In this article, we develop estimators of several measures to evaluate the accuracy and discrimination of predicted risk under CCH and NCC study designs. We use double inverse probability weighting (DIPW) to account for censoring and sampling bias in estimation and inference procedures. We study the asymptotic properties of the proposed estimators. To facilitate inference using two-phase longitudinal data, we develop valid resampling-based variance estimation procedures under CCH and NCC. We evaluate the performance of our estimators under CCH and NCC using simulation studies and illustrate them on a NCC study within the hepatitis C antiviral long-term treatment against cirrhosis (HALT-C) clinical trial. Our estimators and inference procedures perform well under CCH and NCC, provided that the sample size at the time of prediction (effective sample size) is reasonable. These methods are widely applicable, efficient, and cost-effective and can be easily adapted to other study designs used to evaluate prediction rules in a longitudinal setting.
Project description:OBJECTIVES:To investigate the association between recurrent AIDS-defining events and a semicompeting risk of death in patients with advanced, multidrug-resistant human immunodeficiency virus infection and to identify individuals at increased risk for these events using a joint frailty model. STUDY DESIGN AND SETTING:Three hundred sixty-eight patients with antiretroviral treatment failure in the Options in Management of Antiretrovirals Trial randomized to two antiretroviral treatment strategies using a 2 × 2 factorial design, intensive vs. standard and interruption vs. continuation, and followed for development of AIDS-defining events and death. RESULTS:Participants were heterogeneous for risk of AIDS-defining events and death (P < 0.001), and AIDS-defining events were strongly associated with death (P < 0.001), irrespective of treatment. The frailty model was used to classify individuals into high- and low-risk groups based on unobserved heterogeneity. Low-risk individuals were unlikely to die (0%) or have an AIDS-defining event (<4%), whereas high-risk individuals had event rates approaching 70%. About one-third of high-risk individuals had accelerated mortality, all who died before experiencing an AIDS-defining event. High-risk was associated with being immunocompromised and higher predicted 5-year mortality. CONCLUSION:The joint frailty model permits classification of individuals into risk groups based on unobserved heterogeneity that may be identifiable based on observed covariates, providing advantages over the traditional Cox model.
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: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: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:Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster-specific random effect. Such models are often incorporated in more complicated joint models in survival analysis. If the random effect distribution has finite expectation, then the conditional proportional hazards assumption does not carry over to the marginal models. It has been shown that, for univariate data, this makes it impossible to distinguish between the presence of unobserved heterogeneity (eg, due to missing covariates) and marginal nonproportional hazards. We show that time-dependent covariate effects may falsely appear as evidence in favor of a frailty model also in the case of clustered failures or recurrent events data, when the cluster size or number of recurrent events is small. When true unobserved heterogeneity is present, the presence of nonproportional hazards leads to overestimating the frailty effect. We show that this phenomenon is somewhat mitigated as the cluster size grows. We carry out a simulation study to assess the behavior of test statistics and estimators for frailty models in such contexts. The gamma, inverse Gaussian, and positive stable shared frailty models are contrasted using a novel software implementation for estimating semiparametric shared frailty models. Two main questions are addressed in the contexts of clustered failures and recurrent events: whether covariates with a time-dependent effect may appear as indication of unobserved heterogeneity and whether the additional presence of unobserved heterogeneity can be detected in this case. Finally, the practical implications are illustrated in a real-world data analysis example.