General single-index survival regression models for incident and prevalent covariate data and prevalent data without follow-up.

This article mainly focuses on analyzing covariate data from incident and prevalent cohort studies and a prevalent sample with only baseline covariates of interest and truncation times. Our major task in both research streams is to identify the effects of covariates on a failure time through very general single-index survival regression models without observing survival outcomes. With a strict increase of the survival function in the linear predictor, the ratio of incident and prevalent covariate densities is shown to be a non-degenerate and monotonic function of the linear predictor under covariate-independent truncation. Without such a structural assumption, the conditional density of a truncation time in a prevalent cohort is ensured to be a non-degenerate function of the linear predictor. In light of these features, some innovative approaches, which are based on the maximum rank correlation estimation or the pseudo least integrated squares estimation, are developed to estimate the coefficients of covariates up to a scale factor. Existing theoretical results are further used to establish the n -consistency and asymptotic normality of the proposed estimators. Moreover, extensive simulations are conducted to assess and compare the finite-sample performance of various estimators. To illustrate the methodological ideas, we also analyze data from the Worcester Heart Attack Study and the National Comorbidity Survey Replication.

Bias and variance reduction in nonparametric estimation of time-dependent accuracy measures.

A new nonparametric approach is developed to estimate the time-dependent accuracy measure curves, which are defined on the cumulative cases and dynamic controls, for censored survival data. Based on an estimable survival process, the main intention of this study is to reduce the finite-sample biases of nearest neighbor estimators. The asymptotic variances of some retrospective accuracy measure estimators are further reduced by applying a smoothing technique to the underlying process of a marker. Meanwhile, practically feasible and theoretically valid procedures are proposed for bandwidth selection in the presented estimators. In addition, the proposed methodology can be reasonably extended to accommodate stratified survival data and survival data with multiple markers. As shown in the simulations, our new estimators outperform the nearest neighbor and inverse censoring weighted estimators. Data from the AIDS Clinical Trials Group study 175 and an angiographic coronary artery disease study are also used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

Foot-and-mouth disease entrance assessment model through air passenger violations.

This article aims to construct a risk model for the prediction of foot-and-mouth disease (FMD) entrance caused by passengers who illegally carry meat products of cloven-hoofed animals through international airports into a country. The risk that meat contaminated with the FMD virus is formulated as the probabilities of FMD factor events (the prevalence of FMD), the commodity factor event (the transportation, storage, and distribution (TSD) factor event), and the passenger event. Data used for analysis were records of illegal meat product carriers from areas A and B intercepted at an international airport in Taiwan. A risk model was proposed to simulate the probability distributions in disease prevalence, probability of FMD virus existing in the meat products after meat processing, and estimation of survival of virus and time period for TSD. The probability of the passenger event was hypothesized with the odds of intercepted passengers and estimated via logistic regression. The results showed that the odds of passengers being intercepted by beagles were higher than those intercepted by Customs. By conducting Monte Carlo simulations, the probability of FMD virus risk caused by FMD factors from area A was 149 times lower than that from area B. The probability of FMD virus risk caused by the passenger event from area A was four times lower than the corresponding probability from area B. The model provides a contribution to FMD prevention and can be a reference for developing models of other diseases.

Estimation for the optimal combination of markers without modeling the censoring distribution.

In the time-dependent receiver operating characteristic curve analysis with several baseline markers, research interest focuses on seeking appropriate composite markers to enhance the accuracy in predicting the vital status of individuals over time. Based on censored survival data, we proposed a more flexible estimation procedure for the optimal combination of markers under the validity of a time-varying coefficient generalized linear model for the event time without restrictive assumptions on the censoring pattern. The consistency of the proposed estimators is also established in this article. In contrast, the inverse probability weighting (IPW) approach might introduce a bias when the selection probabilities are misspecified in the estimating equations. The performance of both estimation procedures are examined and compared through a class of simulations. It is found from the simulation study that the proposed estimators are far superior to the IPW ones. Applying these methods to an angiography cohort, our estimation procedure is shown to be useful in predicting the time to all-cause and coronary artery disease related death.

Random weighted bootstrap method for recurrent events with informative censoring.

Using the data from the AIDS Link to Intravenous Experiences cohort study as an example, an informative censoring model was used to characterize the repeated hospitalization process of a group of patients. Under the informative censoring assumption, the estimators of the baseline rate function and the regression parameters were shown to be related to a latent variable. Hence, it becomes impractical to directly estimate the unknown quantities in the moments of the estimators for the bandwidth selection of a smoothing estimator and the construction of confidence intervals, which are respectively based on the asymptotic mean squared errors and the asymptotic distributions of the estimators. To overcome these difficulties, we develop a random weighted bootstrap procedure to select appropriate bandwidths and to construct approximated confidence intervals. One can see that our method is simple and faster to implement from a practical point of view, and is at least as accurate as other bootstrap methods. In this article, it is shown that the proposed method is useful through the performance of a Monte Carlo simulation. An application of our procedure is also illustrated by a recurrent event sample of intravenous drug users for inpatient cares over time.

Kernel Estimation of Rate Function for Recurrent Event Data.

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce a curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Non-parametric methods for recurrent event data with informative and non-informative censorings.

Recurrent event data are commonly encountered in health-related longitudinal studies. In this paper time-to-events models for recurrent event data are studied with non-informative and informative censorings. In statistical literature, the risk set methods have been confirmed to serve as an appropriate and efficient approach for analysing recurrent event data when censoring is non-informative. This approach produces biased results, however, when censoring is informative for the time-to-events outcome data. We compare the risk set methods with alternative non-parametric approaches which are robust subject to informative censoring. In particular, non-parametric procedures for the estimation of the cumulative occurrence rate function (CORF) and the occurrence rate function (ORF) are discussed in detail. Simulation and an analysis of data from the AIDS Link to Intravenous Experiences Cohort Study is presented.

Analyzing Recurrent Event Data With Informative Censoring.

Recurrent event data are frequently encountered in longitudinal follow-up studies. In statistical literature, noninformative censoring is typically assumed when statistical methods and theory are developed for analyzing recurrent event data. In many applications, however, the observation of recurrent events could be terminated by informative dropouts or failure events, and it is unrealistic to assume that the censoring mechanism is independent of the recurrent event process. In this article we consider recurrent events of the same type and allow the censoring mechanism to be possibly informative. The occurrence of recurrent events is modeled by a subject-specific nonstationary Poisson process via a latent variable. A multiplicative intensity model is used as the underlying model for nonparametric estimation of the cumulative rate function. The multiplicative intensity model is also extended to a regression model by taking the covariate information into account. Statistical methods and theory are developed for estimation of the cumulative rate function and regression parameters. As a major feature of this article, we treat the distributions of both the censoring and latent variables as nuisance parameters. We avoid modeling and estimating the nuisance parameters by proper procedures. An analysis of the AIDS Link to Intravenous Experiences cohort data is presented to illustrate the proposed methods.