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

Lifetime Data Analysis - 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...     

A varying-coefficient model for gap times between recurrent events

Lifetime Data Analysis - Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events...     

A semiparametric additive rates model for recurrent event data

Recurrent event data often arise in biomedical studies, with examples including hospitalizations, infections, and treatment failures. In observational studies, it is often of interest to estimate the effects of covariates on the marginal recurrent event rate. The majority of existing rate regression methods assume multiplicative covariate effects. We propose a semiparametric model for the marginal recurrent event rate, wherein the covariates are assumed to add to the unspecified baseline rate. Covariate effects are summarized by rate differences, meaning that the absolute effect on the rate function can be determined from the regression coefficient alone. We describe modifications of the proposed method to accommodate a terminating event (e.g., death). Proposed estimators of the regression parameters and baseline rate are shown to be consistent and asymptotically Gaussian. Simulation studies demonstrate that the asymptotic approximations are accurate in finite samples. The proposed methods are applied to a state-wide kidney transplant data set.     

Additive risk model with case-cohort sampled current status data

Two-phase stratified sampling has been extensively used in large epidemiologic studies as a way of reducing costs associated with assembling covariate histories and enlarging relative sample sizes of the most informative subgroups. In this article, we investigate case-cohort sampled current status data under the additive risk model assumption. We describe a class of estimating equations, each depending on a different prevalence ratio estimate. Asymptotic properties of the proposed estimators and inference based on the “m out of n” nonparametric bootstrap are investigated. A small simulation study is employed to evaluate the finite sample performance and relative efficiency of the proposed estimators.     

Modeling marginal features in studies of recurrent events in the presence of a terminal event

We study models for recurrent events with special emphasis on the situation where a terminal event acts as a competing risk for the recurrent events process and where there may be gaps between periods during which subjects are at risk for the recurrent event. We focus on marginal analysis of the expected number of events and show that an Aalen–Johansen type estimator proposed by Cook and Lawless is applicable in this situation. A motivating example deals with psychiatric hospital admissions where we supplement with analyses of the marginal distribution of time to the competing event and the marginal distribution of the time spent in hospital. Pseudo-observations are used for the latter purpose.

     

Partial sufficient dimension reduction on joint model of recurrent and terminal events

Joint modeling of recurrent and terminal events has attracted considerable interest and extensive investigations by many authors. The assumption of low-dimensional covariates has been usually applied in the existing studies, which is however inapplicable in many practical situations. In this paper, we consider a partial sufficient dimension reduction approach for a joint model with high-dimensional covariates. Some simulations as well as three real data applications are presented to confirm and assess the performance of the proposed model and approach.     

Statistical inference for generalized case-cohort design under the proportional hazards model with parameter constraints

ABSTRACT

The generalized case-cohort design is widely used in large cohort studies to reduce the cost and improve the efficiency. Taking prior information of parameters into consideration in modeling process can further raise the inference efficiency. In this paper, we consider fitting proportional hazards model with constraints for generalized case-cohort studies. We establish a working likelihood function for the estimation of model parameters. The asymptotic properties of the proposed estimator are derived via the Karush-Kuhn-Tucker conditions, and their finite properties are assessed by simulation studies. A modified minorization-maximization algorithm is developed for the numerical calculation of the constrained estimator. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice.     

A regularized variable selection procedure in additive hazards model with stratified case-cohort design

Case-cohort designs are commonly used in large epidemiological studies to reduce the cost associated with covariate measurement. In many such studies the number of covariates is very large. An efficient variable selection method is needed for case-cohort studies where the covariates are only observed in a subset of the sample. Current literature on this topic has been focused on the proportional hazards model. However, in many studies the additive hazards model is preferred over the proportional hazards model either because the proportional hazards assumption is violated or the additive hazards model provides more relevent information to the research question. Motivated by one such study, the Atherosclerosis Risk in Communities (ARIC) study, we investigate the properties of a regularized variable selection procedure in stratified case-cohort design under an additive hazards model with a diverging number of parameters. We establish the consistency and asymptotic normality of the penalized estimator and prove its oracle property. Simulation studies are conducted to assess the finite sample performance of the proposed method with a modified cross-validation tuning parameter selection methods. We apply the variable selection procedure to the ARIC study to demonstrate its practical use.     

Asymptotic results for fitting marginal hazards models from stratified case-cohort studies with multiple disease outcomes

In stratified case-cohort designs, samplings of case-cohort samples are conducted via a stratified random sampling based on covariate information available on the entire cohort members. In this paper, we extended the work of Kang & Cai (2009) to a generalized stratified case-cohort study design for failure time data with multiple disease outcomes. Under this study design, we developed weighted estimating procedures for model parameters in marginal multiplicative intensity models and for the cumulative baseline hazard function. The asymptotic properties of the estimators are studied using martingales, modern empirical process theory, and results for finite population sampling.     

Event dependent sampling of recurrent events

The effect of event-dependent sampling of processes consisting of recurrent events is investigated when analyzing whether the risk of recurrence increases with event count. We study the situation where processes are selected for study if an event occurs in a certain selection interval. Motivation comes from psychiatric epidemiology where repeated hospital admissions are studied for patients with affective disease, as seen in Kessing et al. (Acta Psychiatr Scand 109:339–344, 2004b). For the selected processes, either only disease course from selection and onwards is used in the analysis, or, both retrospective and prospective disease course histories are used. We examine two methods to correct for the selection depending on which data are used in the analysis. In the first case, the conditional distribution of the process given the pre-selection history is determined. In the second case, an inverse-probability-of-selection weighting scheme is suggested. The ability of the methods to correct for the bias due to selection is investigated with simulations. Furthermore, the methods are applied to affective disease data from a register-based study (Kessing et al. Br J Psychiatry 185:372–377, 2004a) and from a long-term clinical study (Kessing et al. Acta Psychiatr Scand 109:339–344, 2004b).     

Semiparametric inference for a general class of models for recurrent events

Procedures for estimating the parameters of the general class of semiparametric models for recurrent events proposed by Peña and Hollander [(2004). Models for recurrent events in reliability and survival analysis. In: Soyer R., Mazzuchi T., Singpurwalla N. (Eds.), Mathematical Reliability: An Expository Perspective. Kluwer Academic Publishers, Dordrecht, pp. 105–123 (Chapter 6)] are developed. This class of models incorporates an effective age function encoding the effect of changes after each event occurrence such as the impact of an intervention, it models the impact of accumulating event occurrences on the unit, it admits a link function in which the effect of possibly time-dependent covariates are incorporated, and it allows the incorporation of unobservable frailty components which induce dependencies among the inter-event times for each unit. The estimation procedures are semiparametric in that a baseline hazard function is nonparametrically specified. The sampling distribution properties of the estimators are examined through a simulation study, and the consequences of mis-specifying the model are analyzed. The results indicate that the flexibility of this general class of models provides a safeguard for analyzing recurrent event data, even data possibly arising from a frailty-less mechanism. The estimation procedures are applied to real data sets arising in the biomedical and public health settings, as well as from reliability and engineering situations. In particular, the procedures are applied to a data set pertaining to times to recurrence of bladder cancer and the results of the analysis are compared to those obtained using three methods of analyzing recurrent event data.     

Semiparametric additive marginal regression models for multiple type recurrent events

Recurrent event data are often encountered in biomedical research, for example, recurrent infections or recurrent hospitalizations for patients after renal transplant. In many studies, there are more than one type of events of interest. Cai and Schaube (Lifetime Data Anal 10:121-138, 2004) advocated a proportional marginal rate model for multiple type recurrent event data. In this paper, we propose a general additive marginal rate regression model. Estimating equations approach is used to obtain the estimators of regression coefficients and baseline rate function. We prove the consistency and asymptotic normality of the proposed estimators. The finite sample properties of our estimators are demonstrated by simulations. The proposed methods are applied to the India renal transplant study to examine risk factors for bacterial, fungal and viral infections.     

Case-cohort analysis of clusters of recurrent events

The case-cohort sampling, first proposed in Prentice (Biometrika 73:1–11, 1986), is one of the most effective cohort designs for analysis of event occurrence, with the regression model being the typical Cox proportional hazards model. This paper extends to consider the case-cohort design for recurrent events with certain specific clustering feature, which is captured by a properly modified Cox-type self-exciting intensity model. We discuss the advantage of using this model and validate the pseudo-likelihood method. Simulation studies are presented in support of the theory. Application is illustrated with analysis of a bladder cancer data.     

Fast accelerated failure time modeling for case-cohort data

Semiparametric accelerated failure time (AFT) models directly relate the expected failure times to covariates and are a useful alternative to models that work on the hazard function or the survival function. For case-cohort data, much less development has been done with AFT models. In addition to the missing covariates outside of the sub-cohort in controls, challenges from AFT model inferences with full cohort are retained. The regression parameter estimator is hard to compute because the most widely used rank-based estimating equations are not smooth. Further, its variance depends on the unspecified error distribution, and most methods rely on computationally intensive bootstrap to estimate it. We propose fast rank-based inference procedures for AFT models, applying recent methodological advances to the context of case-cohort data. Parameters are estimated with an induced smoothing approach that smooths the estimating functions and facilitates the numerical solution. Variance estimators are obtained through efficient resampling methods for nonsmooth estimating functions that avoids full blown bootstrap. Simulation studies suggest that the recommended procedure provides fast and valid inferences among several competing procedures. Application to a tumor study demonstrates the utility of the proposed method in routine data analysis.     

Models and estimation for systems with recurrent events and usage processes

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to implement maximum likelihood estimation in such cases. Random effects models with linear usage processes and gamma usage processes are considered in some detail. Data on automobile warranty claims are used to illustrate the proposed models and estimation methodology.     

Semiparametric regression for the mean and rate functions of recurrent events

The counting process with the Cox-type intensity function has been commonly used to analyse recurrent event data. This model essentially assumes that the underlying counting process is a time-transformed Poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process. Recently, Pepe and Cai, and Lawless and co-workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the Poisson-type assumption. In this paper, we provide a rigorous justification of such robust procedures through modern empirical process theory. Furthermore, we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean–rate model. The advantages of the robust procedures are demonstrated through simulation studies. An illustration with multiple-infection data taken from a clinical study on chronic granulomatous disease is also provided.     

Quantile regression for competing risks analysis under case-cohort design

The case-cohort design brings cost reduction in large cohort studies. In this paper, we consider a nonlinear quantile regression model for censored competing risks under the case-cohort design. Two different estimation equations are constructed with or without the covariates information of other risks included, respectively. The large sample properties of the estimators are obtained. The asymptotic covariances are estimated by using a fast resampling method, which is useful to consider further inferences. The finite sample performance of the proposed estimators is assessed by simulation studies. Also a real example is used to demonstrate the application of the proposed methods.     

Mixed model for analyzing geographic variability in mortality rates

"A mixed model is proposed for the analysis of geographic variability in mortality rates. In addition to demographic parameters and random geographic parameters, the model includes additional random-effects parameters to adjust for extra-Poisson variability. The model uses a gamma-Poisson distribution with a random scale parameter having an inverse gamma prior. An empirical Bayes approach is used to estimate relative risks for geographic regions and annual rates for demographic groups within each region. Lung cancer in Missouri is used to motivate and illustrate the procedure."     

Joint covariate-adjusted score test statistics for recurrent events and a terminal event

Recurrent events data are frequently encountered and could be stopped by a terminal event in clinical trials. It is of interest to assess the treatment efficacy simultaneously with respect to both the recurrent events and the terminal event in many applications. In this paper we propose joint covariate-adjusted score test statistics based on joint models of recurrent events and a terminal event. No assumptions on the functional form of the covariates are needed. Simulation results show that the proposed tests can improve the efficiency over tests based on covariate unadjusted model. The proposed tests are applied to the SOLVD data for illustration.