Dynamic Prediction Using Landmark Historical Functional Cox Regression

Dynamic prediction of survival data in the presence of time-varying covariates is an area of active research. Two common analytic approaches for this type of data are joint modeling of the longitudinal and survival processes and landmarking. However, there has been little work dedicated to densely measured time-varying covariates using either approach. Moreover, the software for joint modeling is slow, especially for large datasets, and rather limited for landmarking. We propose a landmark approach for dynamic prediction of survival outcomes using densely measured longitudinal predictors, which treats the past of the time-varying covariate at each landmark point as a functional predictor. This approach is orders of magnitude faster than existing software for simpler joint models. Our extensive comparative simulation study required 8.4 computation-years, over 99% of which was devoted to fitting and predicting from two joint models. Our landmark approach performs similarly to joint modeling when the joint model is correctly specified and substantially out-performs it when it is not. Methods are motivated by an application predicting time to recovery of Multiple Sclerosis lesions in a large neuroimaging dataset. Supplementary materials for this article are available online.