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Abstract:
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Dynamic prediction incorporates time-dependent marker information accrued during follow-up to improve personalized survival prediction probabilities. At any follow-up (landmark) time, the residual time distribution for an individual, conditional on their updated marker values, can be used to produce a dynamic prediction. To satisfy a consistency condition that links dynamic predictions at different time points, the residual time distribution must follow from a prediction function that models the joint distribution of the marker process and time to failure, such as a joint model. To circumvent modeling the marker process, the approximate method landmarking is used, which fits a Cox model at a sequence of landmark times. Considering an illness-death model, we derive the residual time distribution and demonstrate that the structure of the Cox model baseline hazard and covariate effects under a landmark approach do not have a simple form. We suggest extensions to the landmark model to provide a good enough approximation. We compare the performance of landmark models with a multi-state model using simulation studies and a public health application.
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