Time-dependent AUC with right-censored data: a survey study <s> Incident static estimators with longitudinal marker <s> Early diagnosis of disease has potential to reduce morbidity and mortality. Biomarkers may be useful for detecting disease at early stages before it becomes clinically apparent. Prostate-specific antigen (PSA) is one such marker for prostate cancer. This article is concerned with modeling receiver operating characteristic (ROC) curves associated with biomarkers at various times prior to the time at which the disease is detected clinically, by two methods. The first models the biomarkers statistically using mixed-effects regression models, and uses parameter estimates from these models to estimate the time-specific ROC curves. The second directly models the ROC curves as a function of time prior to diagnosis and may be implemented using software packages with binary regression or generalized linear model routines. The approaches are applied to data from 71 prostate cancer cases and 71 controls who participated in a lung cancer prevention trial. Two biomarkers for prostate cancer were considered: total serum PSA and the ratio of free to total PSA. Not surprisingly, both markers performed better as the interval between PSA measurement and clinical diagnosis decreased. Although the two markers performed similarly eight years prior to diagnosis, it appears that total PSA performed better than the ratio measure at times closer to diagnosis. The area under the ROC curve was consistently greater for total PSA than for the ratio four and two years prior to diagnosis and at the time of diagnosis. <s> BIB001 </s> Time-dependent AUC with right-censored data: a survey study <s> Incident static estimators with longitudinal marker <s> We consider the analysis of serial biomarkers to screen and monitor individuals in a given population for onset of a specific disease of interest. The biomarker readings are subject to error. We survey some of the existing literature and concentrate on two recently proposed models. The first is a fully Bayesian hierarchical structure for a mixed effects segmented regression model. Posterior estimates of the changepoint (onset time) distribution are obtained by Gibbs sampling. The second is a hidden changepoint model in which the onset time distribution is estimated by maximum likelihood using the EM algorithm. Both methods lead to a dynamic index that represents a strength of evidence that onset has occurred by the current time in an individual subject. The methods are applied to some large data sets concerning prostate specific antigen (PSA) as a serial marker for prostate cancer. Rules based on the indices are compared to standard diagnostic criteria through the use of ROC curves adapted for longitudinal data. <s> BIB002 </s> Time-dependent AUC with right-censored data: a survey study <s> Incident static estimators with longitudinal marker <s> ∗Harvard University, tcai@hsph.harvard.edu †University of Washington, mspepe@u.washington.edu ‡University of Washington, tlumley@u.washington.edu ∗∗Fred Hutchinson Cancer Research Center, yzheng@fhcrc.org ††University of Vermont, Nancy.Jenny@uvm.edu This working paper is hosted by The Berkeley Electronic Press (bepress) and may not be commercially reproduced without the permission of the copyright holder. <s> BIB003 </s> Time-dependent AUC with right-censored data: a survey study <s> Incident static estimators with longitudinal marker <s> Receiver operating characteristic (ROC) curves play a central role in the evaluation of biomarkers and tests for disease diagnosis. Predictors for event time outcomes can also be evaluated with ROC curves, but the time lag between marker measurement and event time must be acknowledged. We discuss different definitions of time-dependent ROC curves in the context of real applications. Several approaches have been proposed for estimation. We contrast retrospective versus prospective methods in regards to assumptions and flexibility, including their capacities to incorporate censored data, competing risks and different sampling schemes. Applications to two datasets are presented. <s> BIB004 </s> Time-dependent AUC with right-censored data: a survey study <s> Incident static estimators with longitudinal marker <s> OBJECTIVE ::: To assess the time-dependent accuracy of a continuous longitudinal biomarker used as a test for early diagnosis or prognosis. ::: ::: ::: METHODS ::: A method for accuracy assessment is proposed taking into account the marker measurement time and the delay between marker measurement and outcome. It dealt with markers having interval-censored measurements and a detection threshold. The threshold crossing times were assessed by a Bayesian method. A numerical study was conducted to test the procedures that were later applied to PCR measurements for prediction of cytomegalovirus disease after renal transplantation. ::: ::: ::: RESULTS ::: The Bayesian method corrected the bias induced by interval-censored measurements on sensitivity estimates, with corrections from 0.07 to 0.3. In the application to cytomegalovirus disease, the Bayesian method estimated the area under the ROC curve to be over 75% during the first 20 days after graft and within five days between marker measurement and disease onset. However, the accuracy decreased quickly as that delay increased and late after graft. ::: ::: ::: CONCLUSIONS ::: The proposed Bayesian method is easy to implement for assessing the time-dependent accuracy of a longitudinal biomarker and gives unbiased results under some conditions. <s> BIB005
Several authors consider the incident/static definition of AUC BIB002 BIB001 BIB003 BIB005 . However, censored data are only accounted for by Cai et al. BIB003 who proposed to model where g D and g τ are specified inverse link functions and h(·) and d(·) are unspecified baseline functions of threshold c. The dependence in time is parametrically modeled by η α (t, s) = α T η(t, s) and ξ a (s) = a T ξ (s) where η(t, s) and ξ (s) are vectors of polynomial or spline basis functions. These models are semiparametric with respect to the marker distribution in cases and nonparametric in regards to controls. As pointed out in BIB004 , this model is very flexible as it does not specify any distributional form for the distribution of the marker given the event-time, but only model the effect of time-to-event on the marker distribution with a parametric form. Model estimation is performed by solving some estimating equations and large sample theory was established allowing a resampling method to construct confidence bands and make inference BIB003 . Interestingly, the authors of BIB003 also showed that covariates can easily be included in TPR I and FPR S , enabling to directly quantify how performances of the marker vary with these covariates.