Risk prediction models for survival outcomes are widely applied in medical research to predict future risk for the occurrence of the event. In many clinical studies, the biomarker data are measured repeatedly over time. To facilitate timely disease prognosis and decision making, many dynamic prediction models have been developed and generate predictions on a real-time basis. As a dynamic prediction model updates an individual's risk prediction over time based on new measurements, it is often important to examine how well the model performs at different measurement times and prediction times. In this article, we propose a two-dimensional area under curve (AUC) measure for dynamic prediction models and develop associated estimation and inference procedures. The estimation procedures are discussed under two types of biomarker measurement schedules: regular visits and irregular visits. The model parameters are estimated effectively by maximizing a pseudo-partial likelihood function. We apply the proposed method to a renal transplantation study to evaluate the discrimination performance of dynamic prediction models based on longitudinal biomarkers for graft failure.
Accelerometers are widely used for tracking human movement and provide minute-level (or even 30 Hz level) physical activity (PA) records for detailed analysis. Instead of using day-level summary statistics to assess these densely sampled inputs, we implement functional principal component analysis (FPCA) approaches to study the temporal patterns of PA data from 245 overweight/obese women at three visits over a 1-year period. We apply longitudinal FPCA to decompose PA inputs, incorporating subject-specific variability, and then test the association between these patterns and obesity-related health outcomes by multiple mixed effect regression models. With the proposed methods, the longitudinal patterns in both densely sampled inputs and scalar outcomes are investigated and connected. The results show that the health outcomes are strongly associated with PA variation, in both subject and visit-level. In addition, we reveal that timing of PA during the day can impact changes in outcomes, a finding that would not be possible with day-level PA summaries. Thus, our findings imply that the use of longitudinal FPCA can elucidate temporal patterns of multiple levels of PA inputs. Furthermore, the exploration of the relationship between PA patterns and health outcomes can be useful for establishing weight-loss guidelines.
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