Additive Functional Cox Model

NHANES 2011-2014: Objective Physical Activity Is the Strongest Predictor of All-Cause Mortality

INTRODUCTION

Objectively measured physical activity (PA) is a modifiable risk factor for mortality. Understanding the predictive performance of PA is essential to establish potential targets for early intervention to reduce mortality among older adults.

METHODS

The study used a subset of the National Health and Nutrition Examination Survey (NHANES) 2011-2014 data consisting of participants 50 to 80 yr old ( n = 3653, 24297.5 person-years of follow-up, 416 deaths). Eight accelerometry-derived features and 14 traditional predictors of all-cause mortality were compared and ranked in terms of their individual and combined predictive performance using the 10-fold cross-validated concordance (C) from Cox regression.

RESULTS

The top 3 predictors of mortality in univariate analysis were PA related: average Monitor-Independent Movement Summary (MIMS) in the 10 most active hours (C = 0.697), total MIMS per day (C = 0.686), and average log-transformed MIMS in the most 10 active hours of the day (C = 0.684), outperforming age (C = 0.676) and other traditional predictors of mortality. In multivariate regression, adding objectively measured PA to the top performing model without PA variables increased concordance from C = 0.776 to C = 0.790 ( P < 0.001).

CONCLUSIONS

These findings highlight the importance of PA as a risk marker of mortality and are consistent with prior studies, confirming the importance of accelerometer-derived activity measures beyond total volume.

SpaceANOVA: Spatial Co-occurrence Analysis of Cell Types in Multiplex Imaging Data Using Point Process and Functional ANOVA

Multiplex imaging platforms have enabled the identification of the spatial organization of different types of cells in complex tissue or the tumor microenvironment. Exploring the potential variations in the spatial co-occurrence or colocalization of different cell types across distinct tissue or disease classes can provide significant pathological insights, paving the way for intervention strategies. However, the existing methods in this context either rely on stringent statistical assumptions or suffer from a lack of generalizability. We present a highly powerful method to study differential spatial co-occurrence of cell types across multiple tissue or disease groups, based on the theories of the Poisson point process and functional analysis of variance. Notably, the method accommodates multiple images per subject and addresses the problem of missing tissue regions, commonly encountered due to data-collection complexities. We demonstrate the superior statistical power and robustness of the method in comparison with existing approaches through realistic simulation studies. Furthermore, we apply the method to three real data sets on different diseases collected using different imaging platforms. In particular, one of these data sets reveals novel insights into the spatial characteristics of various types of colorectal adenoma.

Recurrent event analysis in the presence of real-time high frequency data via random subsampling

Digital monitoring studies collect real-time high frequency data via mobile sensors in the subjects' natural environment. This data can be used to model the impact of changes in physiology on recurrent event outcomes such as smoking, drug use, alcohol use, or self-identified moments of suicide ideation. Likelihood calculations for the recurrent event analysis, however, become computationally prohibitive in this setting. Motivated by this, a random subsampling framework is proposed for computationally efficient, approximate likelihood-based estimation. A subsampling-unbiased estimator for the derivative of the cumulative hazard enters into an approximation of log-likelihood. The estimator has two sources of variation: the first due to the recurrent event model and the second due to subsampling. The latter can be reduced by increasing the sampling rate; however, this leads to increased computational costs. The approximate score equations are equivalent to logistic regression score equations, allowing for standard, "off-the-shelf" software to be used in fitting these models. Simulations demonstrate the method and efficiency-computation trade-off. We end by illustrating our approach using data from a digital monitoring study of suicidal ideation.

Quantifying the Association between Objectively Measured Physical Activity and Multiple Sclerosis in the UK Biobank

INTRODUCTION

Objectively measured physical activity (PA) data were collected in the accelerometry substudy of the UK Biobank. UK Biobank also contains information about multiple sclerosis (MS) diagnosis at the time of and after PA collection. This study aimed to 1) quantify the difference in PA between prevalent MS cases and matched healthy controls, and 2) evaluate the predictive performance of objective PA measures for incident MS cases.

METHODS

The first analysis compared eight accelerometer-derived PA summaries between MS patients ( N = 316) and matched controls (30 controls for each MS case). The second analysis focused on predicting time to MS diagnosis among participants who were not diagnosed with MS. A total of 19 predictors including eight measures of objective PA were compared using Cox proportional hazards models (number of events = 47; 585,900 person-years of follow-up).

RESULTS

In the prevalent MS study, the difference between MS cases and matched controls was statistically significant for all PA summaries ( P < 0.001). In the incident MS study, the most predictive variable of progression to MS in univariate Cox regression models was lower age ( C = 0.604), and the most predictive PA variable was lower relative amplitude (RA, C = 0.594). A two-stage forward selection using Cox regression resulted in a model with concordance C = 0.693 and four predictors: age ( P = 0.015), stroke ( P = 0.009), Townsend deprivation index ( P = 0.874), and RA ( P = 0.004). A model including age, stroke, and RA had a concordance of C = 0.691.

CONCLUSIONS

Objective PA summaries were significantly different and consistent with lower activity among study participants who had MS at the time of the accelerometry study. Among individuals who did not have MS, younger age, stroke history, and lower RA were significantly associated with a higher risk of a future MS diagnosis.

Functional proportional hazards mixture cure model with applications in cancer mortality in NHANES and post ICU recovery

We develop a functional proportional hazards mixture cure model with scalar and functional covariates measured at the baseline. The mixture cure model, useful in studying populations with a cure fraction of a particular event of interest is extended to functional data. We employ the expectation-maximization algorithm and develop a semiparametric penalized spline-based approach to estimate the dynamic functional coefficients of the incidence and the latency part. The proposed method is computationally efficient and simultaneously incorporates smoothness in the estimated functional coefficients via roughness penalty. Simulation studies illustrate a satisfactory performance of the proposed method in accurately estimating the model parameters and the baseline survival function. Finally, the clinical potential of the model is demonstrated in two real data examples that incorporate rich high-dimensional biomedical signals as functional covariates measured at the baseline and constitute novel domains to apply cure survival models in contemporary medical situations. In particular, we analyze (i) minute-by-minute physical activity data from the National Health And Nutrition Examination Survey 2003-2006 to study the association between diurnal patterns of physical activity at baseline and all cancer mortality through 2019 while adjusting for other biological factors; (ii) the impact of daily functional measures of disease severity collected in the intensive care unit on post intensive care unit recovery and mortality event. Our findings provide novel epidemiological insights into the association between daily patterns of physical activity and cancer mortality. Software implementation and illustration of the proposed estimation method are provided in R.

Quantile Index Biomarkers Based on Single-Cell Expression Data

Current histocytometry methods enable single-cell quantification of biomolecules in tumor tissue sections by multiple detection technologies, including multiplex fluorescence-based immunohistochemistry or in situ hybridization. Quantitative pathology platforms can provide distributions of cellular signal intensity (CSI) levels of biomolecules across the entire cell populations of interest within the sampled tumor tissue. However, the heterogeneity of CSI levels is usually ignored, and the simple mean signal intensity value is considered a cancer biomarker. Here we consider the entire distribution of CSI expression levels of a given biomolecule in the cancer cell population as a predictor of clinical outcome. The proposed quantile index (QI) biomarker is defined as the weighted average of CSI distribution quantiles in individual tumors. The weight for each quantile is determined by fitting a functional regression model for a clinical outcome. That is, the weights are optimized so that the resulting QI has the highest power to predict a relevant clinical outcome. The proposed QI biomarkers were derived for proteins expressed in cancer cells of malignant breast tumors and demonstrated improved prognostic value compared with the standard mean signal intensity predictors. The R package Qindex implementing QI biomarkers has been developed. The proposed approach is not limited to immunohistochemistry data and can be based on any cell-level expressions of proteins or nucleic acids.

SpaceANOVA: Spatial co-occurrence analysis of cell types in multiplex imaging data using point process and functional ANOVA

Motivation

Multiplex imaging platforms have enabled the identification of the spatial organization of different types of cells in complex tissue or tumor microenvironment (TME). Exploring the potential variations in the spatial co-occurrence or co-localization of different cell types across distinct tissue or disease classes can provide significant pathological insights, paving the way for intervention strategies. However, the existing methods in this context either rely on stringent statistical assumptions or suffer from a lack of generalizability.

Results

We present a highly powerful method to study differential spatial co-occurrence of cell types across multiple tissue or disease groups, based on the theories of the Poisson point process (PPP) and functional analysis of variance (FANOVA). Notably, the method accommodates multiple images per subject and addresses the problem of missing tissue regions, commonly encountered in such a context due to the complex nature of the data-collection procedure. We demonstrate the superior statistical power and robustness of the method in comparison to existing approaches through realistic simulation studies. Furthermore, we apply the method to three real datasets on different diseases collected using different imaging platforms. In particular, one of these datasets reveals novel insights into the spatial characteristics of various types of precursor lesions associated with colorectal cancer.

Availability

The associated R package can be found here, https://github.com/sealx017/SpaceANOVA.

Statistical Analysis of Multiplex Immunofluorescence and Immunohistochemistry Imaging Data

Advances in multiplexed single-cell immunofluorescence (mIF) and multiplex immunohistochemistry (mIHC) imaging technologies have enabled the analysis of cell-to-cell spatial relationships that promise to revolutionize our understanding of tissue-based diseases and autoimmune disorders. Multiplex images are collected as multichannel TIFF files; then denoised, segmented to identify cells and nuclei, normalized across slides with protein markers to correct for batch effects, and phenotyped; and then tissue composition and spatial context at the cellular level are analyzed. This chapter discusses methods and software infrastructure for image processing and statistical analysis of mIF/mIHC data.

Fast Multilevel Functional Principal Component Analysis

We introduce fast multilevel functional principal component analysis (fast MFPCA), which scales up to high dimensional functional data measured at multiple visits. The new approach is orders of magnitude faster than and achieves comparable estimation accuracy with the original MFPCA (Di et al., 2009). Methods are motivated by the National Health and Nutritional Examination Survey (NHANES), which contains minute-level physical activity information of more than 10000 participants over multiple days and 1440 observations per day. While MFPCA takes more than five days to analyze these data, fast MFPCA takes less than five minutes. A theoretical study of the proposed method is also provided. The associated function mfpca.face() is available in the R package refund.

Fixed-effects inference and tests of correlation for longitudinal functional data

We propose an inferential framework for fixed effects in longitudinal functional models and introduce tests for the correlation structures induced by the longitudinal sampling procedure. The framework provides a natural extension of standard longitudinal correlation models for scalar observations to functional observations. Using simulation studies, we compare fixed effects estimation under correctly and incorrectly specified correlation structures and also test the longitudinal correlation structure. Finally, we apply the proposed methods to a longitudinal functional dataset on physical activity. The computer code for the proposed method is available at https://github.com/rli20ST758/FILF.

Scalar on time-by-distribution regression and its application for modelling associations between daily-living physical activity and cognitive functions in Alzheimer's Disease

Wearable data is a rich source of information that can provide a deeper understanding of links between human behaviors and human health. Existing modelling approaches use wearable data summarized at subject level via scalar summaries in regression, temporal (time-of-day) curves in functional data analysis (FDA), and distributions in distributional data analysis (DDA). We propose to capture temporally local distributional information in wearable data using subject-specific time-by-distribution (TD) data objects. Specifically, we develop scalar on time-by-distribution regression (SOTDR) to model associations between scalar response of interest such as health outcomes or disease status and TD predictors. Additionally, we show that TD data objects can be parsimoniously represented via a collection of time-varying L-moments that capture distributional changes over the time-of-day. The proposed method is applied to the accelerometry study of mild Alzheimer's disease (AD). We found that mild AD is significantly associated with reduced upper quantile levels of physical activity, particularly during morning hours. In-sample cross validation demonstrated that TD predictors attain much stronger associations with clinical cognitive scales of attention, verbal memory, and executive function when compared to predictors summarized via scalar total activity counts, temporal functional curves, and quantile functions. Taken together, the present results suggest that SOTDR analysis provides novel insights into cognitive function and AD.

A semiparametric risk score for physical activity

We develop a generalized partially additive model to build a single semiparametric risk scoring system for physical activity across multiple populations. A score comprised of distinct and objective physical activity measures is a new concept that offers challenges due to the nonlinear relationship between physical behaviors and various health outcomes. We overcome these challenges by modeling each score component as a smooth term, an extension of generalized partially linear single-index models. We use penalized splines and propose two inferential methods, one using profile likelihood and a nonparametric bootstrap, the other using a full Bayesian model, to solve additional computational problems. Both methods exhibit similar and accurate performance in simulations. These models are applied to the National Health and Nutrition Examination Survey and quantify nonlinear and interpretable shapes of score components for all-cause mortality.

Fast Univariate Inference for Longitudinal Functional Models

We propose fast univariate inferential approaches for longitudinal Gaussian and non-Gaussian functional data. The approach consists of three steps: (1) fit massively univariate pointwise mixed effects models; (2) apply any smoother along the functional domain; and (3) obtain joint confidence bands using analytic approaches for Gaussian data or a bootstrap of study participants for non-Gaussian data. Methods are motivated by two applications: (1) Diffusion Tensor Imaging (DTI) measured at multiple visits along the corpus callosum of multiple sclerosis (MS) patients; and (2) physical activity data measured by body-worn accelerometers for multiple days. An extensive simulation study indicates that model fitting and inference are accurate and much faster than existing approaches. Moreover, the proposed approach was the only one that was computationally feasible for the physical activity data application. Methods are accompanied by R software, though the method is "read-and-use", as it can be implemented by any analyst who is familiar with mixed effects model software.

Diurnal Physical Activity Patterns across Ages in a Large UK Based Cohort: The UK Biobank Study

The ability of individuals to engage in physical activity is a critical component of overall health and quality of life. However, there is a natural decline in physical activity associated with the aging process. Establishing normative trends of physical activity in aging populations is essential to developing public health guidelines and informing clinical perspectives regarding individuals' levels of physical activity. Beyond overall quantity of physical activity, patterns regarding the timing of activity provide additional insights into latent health status. Wearable accelerometers, paired with statistical methods from functional data analysis, provide the means to estimate diurnal patterns in physical activity. To date, these methods have been only applied to study aging trends in populations based in the United States. Here, we apply curve registration and functional regression to 24 h activity profiles for 88,793 men (N = 39,255) and women (N = 49,538) ages 42-78 from the UK Biobank accelerometer study to understand how physical activity patterns vary across ages and by gender. Our analysis finds that daily patterns in both the volume of physical activity and probability of being active change with age, and that there are marked gender differences in these trends. This work represents the largest-ever population analyzed using tools of this kind, and suggest that aging trends in physical activity are reproducible in different populations across countries.