Time-dependent AUC with right-censored data: a survey study <s> Time-dependent ROC curve and AUCs with longitudinal marker <s> One approach to evaluating the strength of association between a longitudinal marker process and a key clinical event time is through predictive regression methods such as a time-dependent covariate hazard model. For example, a time-varying covariate Cox model specifies the instantaneous risk of the event as a function of the time-varying marker and additional covariates. In this manuscript we explore a second complementary approach which characterizes the distribution of the marker as a function of both the measurement time and the ultimate event time. Our goal is to flexibly extend the standard diagnostic accuracy concepts of sensitivity and specificity to explicitly recognize both the timing of the marker measurement and the timing of disease. The accuracy of a longitudinal marker can be fully characterized using time-dependent receiver operating characteristic (ROC) curves. We detail a semiparametric estimation method for time-dependent ROC curves that adopts a regression quantile approach for longitudinal data introduced by Heagerty and Pepe (1999}. We extend the work of Heagerty and Pepe (1999} by developing asymptotic distribution theory for the ROC estimators where the distributional shape for the marker is allowed to depend on covariates. To illustrate our method, we analyze pulmonary function measurements among cystic fibrosis subjects to assemble a case-control study and estimate ROC curves that assess how well the pulmonary function measurement can distinguish subjects that progress to death from subjects that remain alive. Comparing the results from our semiparametric analysis to a fully parametric method discussed by Etzioni and Pepe (1999} suggests that the ability to relax distributional assumptions may be important in practice. <s> BIB001 </s> Time-dependent AUC with right-censored data: a survey study <s> Time-dependent ROC curve and AUCs with longitudinal marker <s> In this article we focus on appropriate statistical methods for characterizing the prognostic value of a longitudinal clinical marker. Frequently it is possible to obtain repeated measurements. If the measurement has the ability to signify a pending change in the clinical status of a patient then the marker has the potential to guide key medical decisions. Heagerty, Lumley, and Pepe (2000, Biometrics 56, 337-344) proposed characterizing the diagnostic accuracy of a marker measured at baseline by calculating receiver operating characteristic curves for cumulative disease or death incidence by time t. They considered disease status as a function of time, D(t) = 1(T<or=t), for a clinical event time T. In this article we aim to address the question of how well Y(s), a diagnostic marker measured at time s(s>or= 0, after the baseline time) can discriminate between people who become diseased and those who do not in a subsequent time interval [s, t]. We assume the disease status is derived from an observed event time T and thus interest is in individuals who transition from disease free to diseased. We seek methods that also allow the inclusion of prognostic covariates that permit patient-specific decision guidelines when forecasting a future change in health status. Our proposal is to use flexible semiparametric models to characterize the bivariate distribution of the event time and marker values at an arbitrary time s. We illustrate the new methods by analyzing a well-known data set from HIV research, the Multicenter AIDS Cohort Study data. <s> BIB002
In this section, we review extensions of the above estimators for longitudinally collected subject measurements. For instance some authors would assess the discrimination performance of CD4 counts repeatedly measured every week on time from seroconvertion to progression to AIDS BIB002 . Therefore, time-dependent sensitivities and specificities have been extended to deal with the fact that (i) the time at which marker X is measured can vary and (ii) marker can be repeatedly measured on the same subject. Let s denote the timing of marker measurement and X(s) the marker value at time s. For t ≥ s, Zheng and Heagerty BIB002 extended cumulative/dynamic definitions For a fixed time τ ≥ s, Zheng and Heagerty BIB001 extended incident/static definitions: Although others approaches have been proposed to estimate these quantities, we only review estimators that deal with censored data here. We should also mention that in this longitudinal context, estimators of the AUC are obtained by numerically integrating estimators of the ROC curve.