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ABSTRACT: To assess the classification accuracy of a continuous diagnostic result, the
receiver operating characteristic (ROC) curve is commonly used in applications.
The partial area under the ROC curve (pAUC) is one of widely accepted summary
measures due to its generality and ease of probability interpretation. In the
field of life science, a direct extension of the pAUC into the time-to-event
setting can be used to measure the usefulness of a biomarker for disease
detection over time. Without using a trapezoidal rule, we propose nonparametric
estimators, which are easily computed and have closed-form expressions, for the
time-dependent pAUC. The asymptotic Gaussian processes of the estimators are
established and the estimated variance-covariance functions are provided, which
are essential in the construction of confidence intervals. The finite sample
performance of the proposed inference procedures are investigated through a
series of simulations. Our method is further applied to evaluate the
classification ability of CD4 cell counts on patient's survival time in the
AIDS Clinical Trials Group (ACTG) 175 study. In addition, the inferences can be
generalized to compare the time-dependent pAUCs between patients received the
prior antiretroviral therapy and those without it.
03/2011;
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ABSTRACT: The performance of clinical tests for disease screening is often evaluated using the area under the receiver-operating characteristic (ROC) curve (AUC). Recent developments have extended the traditional setting to the AUC with binary time-varying failure status. Without considering covariates, our first theme is to propose a simple and easily computed nonparametric estimator for the time-dependent AUC. Moreover, we use generalized linear models with time-varying coefficients to characterize the time-dependent AUC as a function of covariate values. The corresponding estimation procedures are proposed to estimate the parameter functions of interest. The derived limiting Gaussian processes and the estimated asymptotic variances enable us to construct the approximated confidence regions for the AUCs. The finite sample properties of our proposed estimators and inference procedures are examined through extensive simulations. An analysis of the AIDS Clinical Trials Group (ACTG) 175 data is further presented to show the applicability of the proposed methods. The Canadian Journal of Statistics 38:8–26; 2010 © 2009 Statistical Society of CanadaLa performance des tests cliniques pour le dépistage de maladie est souvent évaluée en utilisant l'aire sous la courbe caractéristique de fonctionnements du récepteur (≪ ROC ≫ ), notée ≪ AUC ≫ . Des développements récents ont généralisé le cadre traditionnel à l'AUC avec un statut de panne binaire variant dans le temps. Sans considérer les covariables, nous commençons par proposer un estimateur non paramétrique pour l'AUC simple et facile à calculer. De plus, nous utilisons des modèles linéaires généralisés avec des coefficients dépendant du temps pour caractériser les AUC, dépendant du temps, comme fonction des covariables. Les procédures d'estimation asociées correspondantes sont proposées afin d'estimer les fonctions paramètres d'intérêt. Les processus gaussiens limites sont obtenus ainsi que les variances asymptotiques estimées afin de construire des régions de confiance approximatives pour les AUC. À l'aide de nombreuses simulations, les propriétés pour de petits échantillons des estimateurs proposés et des procédures d'inférence sont étudiées. Une analyse du groupe d'essais cliniques sur le sida 175 (ACTG 175) est aussi présentée afin de montrer l'applicabilité des méthodes proposées. La revue canadienne de statistique 38: 8–26; 2010 © 2009 Société statistique du Canada
Canadian Journal of Statistics 02/2010; 38(1):8 - 26. · 0.67 Impact Factor
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Annals of the Institute of Statistical Mathematics 02/2009; 61(1):197-213. · 0.86 Impact Factor
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ABSTRACT: 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.
Risk Analysis 02/2009; 29(4):601-11. · 2.37 Impact Factor
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ABSTRACT: 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.
Biometrics 05/2008; 65(1):152-8. · 1.83 Impact Factor
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ABSTRACT: 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.
Lifetime Data Analysis 01/2006; 11(4):489-509. · 0.92 Impact Factor
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Chin-Tsang Chiang
Annals of the Institute of Statistical Mathematics 02/2005; 57(4):637-653. · 0.86 Impact Factor
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ABSTRACT: 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. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..
Scandinavian Journal of Statistics 01/2005; 32(1):77-91. · 1.12 Impact Factor
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Annals of the Institute of Statistical Mathematics 02/2004; 56(1):87-100. · 0.86 Impact Factor
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ABSTRACT: 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.
Statistics in Medicine 03/2002; 21(3):445-56. · 1.88 Impact Factor
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ABSTRACT: Datasets involving repeated measurements over time are common in medical trials and epidemiological cohort studies. The outcomes and covariates are usually observed from randomly selected subjects, each at a set of possibly unequally spaced time design points. One useful approach for evaluating the effects of covariates is to consider linear models at a specific time, but the coefficients are smooth curves over time. We show that kernel estimators of the coefficients that are based on ordinary local least squares may be subject to large biases when the covariates are time-dependent. As a modification, we propose a two-step kernel method that first centers the covariates and then estimates the curves based on some local least squares criteria and the centered covariates. The practical superiority of the two-step kernel method over the ordinary least squares kernel method is shown through a fetal growth study and simulations. Theoretical properties of both the two-step and ordinary least squares kernel estimators are developed through their large sample mean squared risks.
Annals of the Institute of Statistical Mathematics 08/2000; 52(3):519-543. · 0.86 Impact Factor
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Annals of the Institute of Statistical Mathematics 02/2000; 52(3):519-543. · 0.86 Impact Factor
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ABSTRACT: This paper considers a nonparametric varying coefficient regression model with longitudinal dependent variable and cross-sectional covariates. The relation-ship between the dependent variable and the covariates is assumed to be linear at a specific time point, but the coefficients are allowed to change over time. Two kernel estimators based on componentwise local least squares criteria are proposed to esti-mate the time varying coefficients. A cross-validation criterion and a bootstrap pro-cedure are used for selecting data-driven bandwidths and constructing confidence intervals, respectively. The theoretical properties of our estimators are developed through their asymptotic mean squared errors and mean integrated squared errors. The finite sample properties of our procedures are investigated through a simulation study. Applications of our procedures are illustrated through an epidemiological example of predicting the effects of cigarette smoking, pre-HIV infection CD4 cell percentage and age at HIV infection on the depletion of CD4 cell percentage among HIV infected persons.
Statistica Sinica 01/2000; 10:433-456. · 1.02 Impact Factor
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ABSTRACT: A confidence region for the time-dependent area under the receiver op-erating characteristic curve (AUC) can be constructed based on the asymptotic normality of a non-parametric estimator. In numerical studies, it was found that the performance of the normal approximated confidence interval is dramatically affected by small sample size and high censoring rate. To improve the accuracy of coverage probabilities as well as interval estimators, the random weighted bootstrap distribution and the Edgeworth expansion with remainder term o(n −1/2) are pro-posed to approximate the sampling distribution of the estimator. The asymptotic properties of random weighted bootstrap analogue and the one-term Edgeworth expansion are developed in this article. The usefulness of the proposed procedures are confirmed by a class of simulations with different sample sizes and censoring rates. Moreover, our methods are demonstrated using the ACTG 175 data.
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ABSTRACT: The area under the receiver operating characteristic (ROC) curve (AUC) is one of the commonly used measure to evaluate or compare the predictive ability of markers to the disease status. Motivated by an angiographic coronary artery disease (CAD) study, our objective is mainly to evaluate and compare the performance of several baseline plasma levels in the prediction of CAD-related vital status over time. Based on censored survival data, the non-parametric estimators are proposed for the time-dependent AUC. The limiting Gaussian processes of the estimators and the estimated asymptotic variance–covariance functions enable us to further construct confidence bands and develop testing procedures. Applications and finite sample properties of the proposed estimation methods and inference procedures are demonstrated through the CAD-related death data from the British Columbia Vital Statistics Agency and Monte Carlo simulations.
Journal of Statistical Planning and Inference.
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ABSTRACT: To increase the predictive abilities of several plasma biomarkers on the coronary artery disease (CAD)-related vital statuses over time, our research interest mainly focuses on seeking combinations of these biomarkers with the highest time-dependent receiver operating characteristic curves. An extended generalized linear model (EGLM) with time-varying coefficients and an unknown bivariate link function is used to characterize the conditional distribution of time to CAD-related death. Based on censored survival data, two non-parametric procedures are proposed to estimate the optimal composite markers, linear predictors in the EGLM model. Estimation methods for the classification accuracies of the optimal composite markers are also proposed. In the article we establish theoretical results of the estimators and examine the corresponding finite-sample properties through a series of simulations with different sample sizes, censoring rates and censoring mechanisms. Our optimization procedures and estimators are further shown to be useful through an application to a prospective cohort study of patients undergoing angiography. Copyright (c) 2010 Board of the Foundation of the Scandinavian Journal of Statistics.
Scandinavian Journal of Statistics 37(4):664-679. · 1.12 Impact Factor
