Xiao Song

The receiver operating characteristic curve is a popular tool to characterize the capabilities of diagnostic tests with continuous or ordinal responses. One common design for assessing the accuracy of diagnostic tests involves multiple readers and multiple tests, in which all readers read all test results from the same patients. This design is most commonly used in a radiology setting, where the results of diagnostic tests depend on a radiologist's subjective interpretation. The most widely used approach for analyzing data from such a study is the Dorfman–Berbaum–Metz (DBM) method (Dorfman et al., 1992) which utilizes a standard analysis of variance (ANOVA) model for the jackknife pseudovalues of the area under the ROC curves (AUCs). Although the DBM method has performed well in published simulation studies, there is no clear theoretical basis for this approach. In this paper, focusing on continuous outcomes, we investigate its theoretical basis. Our result indicates that the DBM method does not satisfy the regular assumptions for standard ANOVA models, and thus might lead to erroneous inference. We then propose a marginal model approach based on the AUCs which can adjust for covariates as well. Consistent and asymptotically normal estimators are derived for regression coefficients. We compare our approach with the DBM method via simulation and by an application to data from a breast cancer study. The simulation results show that both our method and the DBM method perform well when the accuracy of tests under the study is the same and that our method outperforms the DBM method for inference on individual AUCs when the accuracy of tests is not the same. The marginal model approach can be easily extended to ordinal outcomes.

Summary. Joint models for a time‐to‐event (e.g., survival) and a longitudinal response have generated considerable recent interest. The longitudinal data are assumed to follow a mixed effects model, and a proportional hazards model depending on the longitudinal random effects and other covariates is assumed for the survival endpoint. Interest may focus on inference on the longitudinal data process, which is informatively censored, or on the hazard relationship. Several methods for fitting such models have been proposed, most requiring a parametric distributional assumption (normality) on the random effects. A natural concern is sensitivity to violation of this assumption; moreover, a restrictive distributional assumption may obscure key features in the data. We investigate these issues through our proposal of a likelihood‐based approach that requires only the assumption that the random effects have a smooth density. Implementation via the EM algorithm is described, and performance and the benefits for uncovering noteworthy features are illustrated by application to data from an HIV clinical trial and by simulation.

In many longitudinal studies, it is of interest to characterize the relationship between a time‐to‐event (e.g. survival) and several time‐dependent and time‐independent covariates. Time‐dependent covariates are generally observed intermittently and with error. For a single time‐dependent covariate, a popular approach is to assume a joint longitudinal data–survival model, where the time‐dependent covariate follows a linear mixed effects model and the hazard of failure depends on random effects and time‐independent covariates via a proportional hazards relationship. Regression calibration and likelihood or Bayesian methods have been advocated for implementation; however, generalization to more than one time‐dependent covariate may become prohibitive. For a single time‐dependent covariate, Tsiatis and Davidian (2001) have proposed an approach that is easily implemented and does not require an assumption on the distribution of the random effects. This technique may be generalized to multiple, possibly correlated, time‐dependent covariates, as we demonstrate. We illustrate the approach via simulation and by application to data from an HIV clinical trial.