Modelling the association between biomarkers and clinical outcome: An introduction to nonlinear joint models

The area under the time-dependent ROC curve (AUC) may be used to quantify the ability of a marker to predict the onset of a clinical outcome in the future. For survival analysis with competing risks, two alternative definitions of the specificity may be proposed depending of the way to deal with subjects who undergo the competing events. In this work, we propose nonparametric inverse probability of censoring weighting estimators of the AUC corresponding to these two definitions, and we study their asymptotic properties. We derive confidence intervals and test statistics for the equality of the AUCs obtained with two markers measured on the same subjects. A simulation study is performed to investigate the finite sample behaviour of the test and the confidence intervals. The method is applied to the French cohort PAQUID to compare the abilities of two psychometric tests to predict dementia onset in the elderly accounting for death without dementia competing risk. The 'timeROC' R package is provided to make the methodology easily usable. Copyright © 2013 John Wiley & Sons, Ltd.

Informative diagnostic tools are vital to the development of useful mixed-effects models. The Visual Predictive Check (VPC) is a popular tool for evaluating the performance of population PK and PKPD models. Ideally, a VPC will diagnose both the fixed and random effects in a mixed-effects model. In many cases, this can be done by comparing different percentiles of the observed data to percentiles of simulated data, generally grouped together within bins of an independent variable. However, the diagnostic value of a VPC can be hampered by binning across a large variability in dose and/or influential covariates. VPCs can also be misleading if applied to data following adaptive designs such as dose adjustments. The prediction-corrected VPC (pcVPC) offers a solution to these problems while retaining the visual interpretation of the traditional VPC. In a pcVPC, the variability coming from binning across independent variables is removed by normalizing the observed and simulated dependent variable based on the typical population prediction for the median independent variable in the bin. The principal benefit with the pcVPC has been explored by application to both simulated and real examples of PK and PKPD models. The investigated examples demonstrate that pcVPCs have an enhanced ability to diagnose model misspecification especially with respect to random effects models in a range of situations. The pcVPC was in contrast to traditional VPCs shown to be readily applicable to data from studies with a priori and/or a posteriori dose adaptations.