Time-dependent AUC with right-censored data: a survey study <s> Cumulative dynamic estimators with longitudinal marker <s> The appropriate interpretation of measurements often requires standardization for concomitant factors. For example, standardization of weight for both height and age is important in obesity research and in failure‐to‐thrive research in children. Regression quantiles from a reference population afford one intuitive and popular approach to standardization. Current methods for the estimation of regression quantiles can be classified as nonparametric with respect to distributional assumptions or as fully parametric. We propose a semiparametric method where we model the mean and variance as flexible regression spline functions and allow the unspecified distribution to vary smoothly as a function of covariates. Similarly to Cole and Green, our approach provides separate estimates and summaries for location, scale and distribution. However, similarly to Koenker and Bassett, we do not assume any parametric form for the distribution. Estimation for either cross‐sectional or longitudinal samples is obtained by using estimating equations for the location and scale functions and through local kernel smoothing of the empirical distribution function for standardized residuals. Using this technique with data on weight, height and age for females under 3 years of age, we find that there is a close relationship between quantiles of weight for height and age and quantiles of body mass index (BMI=weight/height2) for age in this cohort. <s> BIB001 </s> Time-dependent AUC with right-censored data: a survey study <s> Cumulative dynamic estimators with longitudinal marker <s> It is common in longitudinal studies to collect information on the time until a key clinical event, such as death, and to measure markers of patient health at multiple follow-up times. One approach to the joint analysis of survival and repeated measures data adopts a time-varying covariate regression model for the event time hazard. Using this standard approach, the instantaneous risk of death at time t is specified as a possibly semi-parametric function of covariate information that has accrued through time t. In this manuscript, we decouple the time scale for modeling the hazard from the time scale for accrual of available longitudinal covariate information. Specifically, we propose a class of models that condition on the covariate information through time s and then specifies the conditional hazard for times t, where t > s. Our approach parallels the "partly conditional" models proposed by Pepe and Couper (1997, Journal of the American Statistical Association 92, 991-998) for pure repeated measures applications. Estimation is based on the use of estimating equations applied to clusters of data formed through the creation of derived survival times that measure the time from measurement of covariates to the end of follow-up. Patient follow-up may be terminated either by the occurrence of the event or by censoring. The proposed methods allow a flexible characterization of the association between a longitudinal covariate process and a survival time, and facilitate the direct prediction of survival probabilities in the time-varying covariate setting. <s> BIB002 </s> Time-dependent AUC with right-censored data: a survey study <s> Cumulative dynamic estimators 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> BIB003 </s> Time-dependent AUC with right-censored data: a survey study <s> Cumulative dynamic estimators with longitudinal marker <s> In longitudinal studies it is often of interest to investigate how a marker that is repeatedly measured in time is associated with a time to an event of interest. This type of research question has given rise to a rapidly developing field of biostatistics research that deals with the joint modeling of longitudinal and time-to-event data. In this article, we consider this modeling framework and focus particularly on the assessment of the predictive ability of the longitudinal marker for the time-to-event outcome. In particular, we start by presenting how survival probabilities can be estimated for future subjects based on their available longitudinal measurements and a fitted joint model. Following we derive accuracy measures under the joint modeling framework and assess how well the marker is capable of discriminating between subjects who experience the event within a medically meaningful time frame from subjects who do not. We illustrate our proposals on a real data set on human immunodeficiency virus infected patients for which we are interested in predicting the time-to-death using their longitudinal CD4 cell count measurements. <s> BIB004
Rizopoulos BIB004 recently proposed a joint modeling approach. The marker trajectory is modeled by usual linear mixed model for longitudinal data, and a parametric pro-portional hazard is used to model the time-to-event given the marker trajectory. The two submodels are linked with shared random effects to capture the intra-subject correlation. Standard maximum likelihood estimation is used to fit the joint model. Then, TPR C and FPR D are computed from the estimated parameters and Monte Carlo simulations are used to make inference. As this approach is fully parametric, its main advantage is its efficiency. This approach also allows censoring to depend on the marker  . The counterpart is that the parametric model must be carefully chosen, and checking model fit is not straightforward. A more flexible methodology was proposed in BIB003 , with fewer parametric assumptions. Setting T * = T − s, the "residual failure time", and t * = t − s, they rewrote with F X|s (c) = IP(X(s) < c|s, T * > 0) the conditional distribution of marker given measurement time, S(t * |s) = IP(T * > t * |s, T * > 0) the survival probability for individuals who survived beyond s and S(c,t * |s) = IP(X(s) > c, T * > t * |s, T * > 0). They proposed to estimate F X|s (c) with the semiparametric estimator proposed by Heagerty and Pepe BIB001 . Therefore, only the location and scale of the conditional distribution of marker given measurement time are parametrized. To estimate the survival terms S(c,t * |s) and S(t * |s), they proposed the use of a "partly conditional" hazard function to model the residual failure time T * = T − s. For subject i at measurement time s ik , this function is modeled by where f (s) are vectors of spline basis functions evaluated at measurement time s, and λ 0 (t * ) is left unspecified. Estimators of β (·) and α have been previously proposed BIB002 . As this approach is semiparametric, its main advantage is its flexibility. However, by contrast to the approach of Rizopoulos BIB004 , this one is less efficient and does not allow marker-dependent censoring.