Andrew Potter of the Department of Biostatistics defends his dissertation “Multiscale Multivariate Functional Principal Component Analysis with an Application to Multivariate Longitudinal Cardiac Signals”
Graduate faculty of the University and all other interested parties are invited to attend.
Circadian cycles in humans are an important health indicator in cardiovascular disease. With recent developments in Ventricular Assist Devices (VADs), continuous recording of cardiac circadian cycles in cohorts of heart failure patients is now possible for the entire life of the implant. Specifically, VADs continuously record multivariate data on blood flow and device status providing a unique longitudinal view of circadian cycles in these cohorts.
Our statistical challenge is to simultaneously model the cohort average pump output (PO) and pulsatility (PI) circadian cycle measurements and patient specific longitudinal evolution of his/her circadian cycle. While functional principal components analysis (FPCA) methods exist for the analysis of univariate longitudinal functional data with this structure, these techniques don’t address bivariate functional data.
We first divide time into two time scales: “fast” (circadian) and “slow” (longitudinal). We assume that the data are generated by smooth functions of time and extend FPCA to include both time scales. We propose a partial likelihood based technique that separates the estimation and inference for the two time scales.
On the circadian time scale, we use wavelet based FPCA to estimate the cohort mean cycle and subject specific cycles. Confidence bands for the cohort mean and other estimates are calculated with a bootstrap. On the longitudinal time scale, a second FPCA step captures the subject specific longitudinal evolution.
We outline theoretical properties of our new model such as pointwise convergence of estimates on both the fast and slow time scales. Furthermore, using data from VAD patients, we use our method to characterize the population circadian cycle and identify regions of high between-subject variability in both the fast and slow time scales.
Our model provides a novel approach for analyzing multivariate circadian cycles. This work opens new avenues to understand the relationship between circadian cycles in simultaneously recorded cardiovascular measurements. The public health significance is that care can be improved with better understanding of the longitudinal course of these patients.