Landmarking 2.0: Bridging the gap between joint models and landmarking
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The problem of dynamic prediction with time-dependent covariates, given by biomarkers, repeatedly measured over time, has received much attention over the last decades. Two contrasting approaches have become in widespread use. The first is joint modelling, which attempts to jointly model the longitudinal markers and the event time. The second is landmarking, a more pragmatic approach that avoids modelling the marker process. Landmarking has been shown to be less efficient than correctly specified joint models in simulation studies, when data are generated from the joint model. When the mean model is misspecified, however, simulation has shown that joint models may be inferior to landmarking. The objective of this paper is to develop methods that improve the predictive accuracy of landmarking, while retaining its relative simplicity and robustness. We start by fitting a working longitudinal model for the biomarker, including a temporal correlation structure. Based on that model, we derive a predictable time-dependent process representing the expected value of the biomarker after the landmark time, and we fit a time-dependent Cox model based on the predictable time-dependent covariate. Dynamic predictions based on this approach for new patients can be obtained by first deriving the expected values of the biomarker, given the measured values before the landmark time point, and then calculating the predicted probabilities based on the time-dependent Cox model. We illustrate the approach in predicting overall survival in liver cirrhosis patients based on prothrombin index.
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