Functional Data Analysis in The Era of Digital Health

The advent of wearable and sensor technologies now leads to functional predictors which are intrinsically infinite dimensional. While the existing approaches for functional data and survival outcomes lean on the well-established Cox model, the proportional hazard (PH) assumption might not always be suitable in real-world applications. Motivated by physiological signals encountered in digital medicine, we develop a more general and flexible functional time-transformation model for estimating the conditional survival function with both functional and scalar covariates. A partially functional regression model is used to directly model the survival time on the covariates through an unknown monotone transformation and a known error distribution. We use Bernstein polynomials to model the monotone transformation function and the smooth functional coefficients. A sieve method of maximum likelihood is employed for estimation. Numerical simulations illustrate a satisfactory performance of the proposed method in estimation and inference. We demonstrate the application of the proposed model through two case studies involving wearable data i) Understanding the association between diurnal physical activity pattern and all-cause mortality based on accelerometer data from the National Health and Nutrition Examination Survey (NHANES) 2011-2014 and ii) Modelling Time-to-Hypoglycemia events in a cohort of diabetic patients based on distributional representation of continuous glucose monitoring (CGM) data. The results provide important epidemiological insights into the direct association between survival times and the physiological signals and also exhibit superior predictive performance compared to traditional summary based biomarkers in the CGM study. 

Histology imaging is the cornerstone for confirming and understanding cancer. Current practice for examination and interpretation of histopathology images requires highly trained anatomic pathologists. The identification of cancerous image patches is time-consuming, suffers from large inter- and intra- pathologist variation; there is an increasing interest in automatizing this part of cancer screening. We propose an automatic approach to classify the image patches into cancerous and non-cancerous, when multiple image patches are taken per subject. Our methodology comprises two main steps. First we summarize the image patches using a set of spatially indexed vector-valued functions which are modeled to extract the main features that capture the image patch - specific functional and the spatial variation. Second, these features are then used in a classification approach to identify cancerous image patches. We illustrate the performance of the method through simulations and present the results on a data set containing cancerous and non-cancerous HE stained patches collected from whole slide images of prostate tissue for many patients. 

We develop a novel survival on image regression model with partially functional distributional predictors. Technological advancements in wearables and medical imaging leads to high-dimensional physiological signals in the forms of images. The existing approaches for functional data and survival outcomes have been primarily developed for uni-dimensional functional predictors. Recent developments in distributional data analysis enables us to model temporally varying distributional representation of physical activity (PA) as a partially functional predictor and investigate its association with survival using a semiparametric Cox model. We use tensor product splines to model the smooth bivariate functional coefficients. A penalized partial likelihood is employed for estimation. Numerical analysis through simulations illustrates a satisfactory finite sample performance of the proposed method in estimation. The application of the proposed method is demonstrated in understanding the association between temporally varying distributional representation of physical activity and all-cause mortality based on the National Health and Nutrition Examination Survey (NHANES) 2011-2014. The results provide important insights for developing time-of-day and intensity specific PA interventions.