Time-varying functional regression for predicting remaining lifetime distributions from longitudinal trajectories

Daily activity profiles over the lifespan of female medflies as biomarkers of aging and longevity

The relationship between the early-age activity of Mediterranean fruit flies (medflies) or other fruit flies and their lifespan has not been much studied, in contrast to the connections between lifespan and diet, sexual signaling, and reproduction. The objective of this study is to assess intra-day and day-to-day activity profiles of female Mediterranean fruit flies and their role as biomarker of longevity as well as to explore the relationships between these activity profiles, diet, and age-at-death throughout the lifespan. We use advanced statistical methods from functional data analysis (FDA). Three distinct patterns of activity variations in early-age activity profiles can be distinguished. A low-caloric diet is associated with a delayed activity peak, while a high-caloric diet is linked with an earlier activity peak. We find that age-at-death of individual medflies is connected to their activity profiles in early life. An increased risk of mortality is associated with increased activity in early age, as well as with a higher contrast between daytime and nighttime activity. Conversely, medflies are more likely to have a longer lifespan when they are fed a medium-caloric diet and when their daily activity is more evenly distributed across the early-age span and between daytime and nighttime. The before-death activity profile of medflies displays two characteristic before-death patterns, where one pattern is characterized by slowly declining daily activity and the other by a sudden decline in activity that is followed by death.

Daily Activity Profiles over the Lifespan of Female Medflies as Biomarkers of Aging and Longevity

The relationship between the early age activity of Mediterranean fruit flies or other fruit flies and their lifespan has not been much studied, in contrast to the connections between lifespan and diet, sexual signaling and reproduction. The objective of this study is to assess intraday and day-to-day activity profiles of female Mediterranean fruit flies and their role as biomarker of longevity as well as to explore the relationships between these activity profiles, diet and age-at-death throughout the lifespan. Three distinct patterns of activity variations in early age activity profiles can be distinguished. A low-caloric diet is associated with a delayed activity peak, while a high-caloric diet is linked with an earlier activity peak. We find that age-at-death of individual medflies is connected to their activity profiles in early life. An increased risk of mortality is associated with increased activity in early age, as well as with a higher contrast between daytime and nighttime activity. Conversely, medflies are more likely to have a longer lifespan when they are fed a medium caloric diet and when their daily activity is more evenly distributed across the early age span and between daytime and nighttime. The before-death activity profile of medflies displays two characteristic before-death patterns, where one pattern is characterized by slowly declining daily activity and the other by a sudden decline in activity that is followed by death.

Conditional Kaplan–Meier Estimator with Functional Covariates for Time-to-Event Data

Due to the wide availability of functional data from multiple disciplines, the studies of functional data analysis have become popular in the recent literature. However, the related development in censored survival data has been relatively sparse. In this work, we consider the problem of analyzing time-to-event data in the presence of functional predictors. We develop a conditional generalized Kaplan–Meier (KM) estimator that incorporates functional predictors using kernel weights and rigorously establishes its asymptotic properties. In addition, we propose to select the optimal bandwidth based on a time-dependent Brier score. We then carry out extensive numerical studies to examine the finite sample performance of the proposed functional KM estimator and bandwidth selector. We also illustrated the practical usage of our proposed method by using a data set from Alzheimer’s Disease Neuroimaging Initiative data.

Birthweight, time-varying adiposity growth and early menarche in girls: A Mendelian randomisation and mediation analysis

OBJECTIVE

To explore the causal effect of time-varying z-BMI growth on early menarche using Mendelian randomisation (MR); to identify critical adiposity predictors of early menarche; to compare the effects of birthweight and time-varying z-BMI growth as mediators of the path from genes to early menarche using mediation analysis.

METHODS

We used data from the Taiwan Children Health Study with 21 obesity-related single-nucleotide polymorphisms (SNPs) to yield genetic (instrumental variable)IVs for adiposity. Children with available data on genotyping, birthweight, adiposity, and menarcheal age were included.

RESULTS

In MR analyses, results based on the time-varying z-BMI growth show more statistical power and capture more information of adiposity growth (p=0.01) than those based on single point z-BMI (p=0.02). Among adiposity measures, critical predictors of early menarche are fat free mass (RR=1.33, 95% CI 1.07-1.65) and waist/height ratio (RR=1.27, 95% CI 1.03-1.56). Other potential predictors of early menarche are sum of skinfold (RR=1.24, 95% CI 1.03-1.48) and total body fat (RR=1.20, 95% CI 1.05-1.38). In both one-mediation and multi-mediation analyses, time-varying z-BMI growth in the prepubertal years plays a crucial mediator in the pathway from the genes to early menarche.

CONCLUSIONS

This study discovered that greater prepubertal adiposity growth is a crucial mediator in the path from genes to early menarche. For girls with genes positively associated with obesity; and/or of lower birthweight, a strategy to prevent childhood adiposity should be implemented in order to avoid early menarche development.

Cox Regression Models with Functional Covariates for Survival Data

We extend the Cox proportional hazards model to cases when the exposure is a densely sampled functional process, measured at baseline. The fundamental idea is to combine penalized signal regression with methods developed for mixed effects proportional hazards models. The model is fit by maximizing the penalized partial likelihood, with smoothing parameters estimated by a likelihood-based criterion such as AIC or EPIC. The model may be extended to allow for multiple functional predictors, time varying coefficients, and missing or unequally-spaced data. Methods were inspired by and applied to a study of the association between time to death after hospital discharge and daily measures of disease severity collected in the intensive care unit, among survivors of acute respiratory distress syndrome.

ANALYSIS ON CENSORED QUANTILE RESIDUAL LIFE MODEL VIA SPLINE SMOOTHING

We propose a general class of quantile residual life models, where a specific quantile of the residual life time, conditional on an individual has survived up to time t, is a function of certain covariates with their coefficients varying over time. The varying coefficients are assumed to be smooth unspecified functions of t. We propose to estimate the coefficient functions using spline approximation. Incorporating the spline representation directly into a set of unbiased estimating equations, we obtain a one-step estimation procedure, and we show that this leads to a uniformly consistent estimator. To obtain further computational simplification, we propose a two-step estimation approach in which we estimate the coefficients on a series of time points first, and follow this with spline smoothing. We compare the two methods in terms of their asymptotic efficiency and computational complexity. We further develop inference tools to test the significance of the covariate effect on residual life. The finite sample performance of the estimation and testing procedures are further illustrated through numerical experiments. We also apply the methods to a data set from a neurological study.

Functional mixture regression

In functional linear models (FLMs), the relationship between the scalar response and the functional predictor process is often assumed to be identical for all subjects. Motivated by both practical and methodological considerations, we relax this assumption and propose a new class of functional regression models that allow the regression structure to vary for different groups of subjects. By projecting the predictor process onto its eigenspace, the new functional regression model is simplified to a framework that is similar to classical mixture regression models. This leads to the proposed approach named as functional mixture regression (FMR). The estimation of FMR can be readily carried out using existing software implemented for functional principal component analysis and mixture regression. The practical necessity and performance of FMR are illustrated through applications to a longevity analysis of female medflies and a human growth study. Theoretical investigations concerning the consistent estimation and prediction properties of FMR along with simulation experiments illustrating its empirical properties are presented in the supplementary material available at Biostatistics online. Corresponding results demonstrate that the proposed approach could potentially achieve substantial gains over traditional FLMs.

Longitudinal functional principal component analysis

We introduce models for the analysis of functional data observed at multiple time points. The dynamic behavior of functional data is decomposed into a time-dependent population average, baseline (or static) subject-specific variability, longitudinal (or dynamic) subject-specific variability, subject-visit-specific variability and measurement error. The model can be viewed as the functional analog of the classical longitudinal mixed effects model where random effects are replaced by random processes. Methods have wide applicability and are computationally feasible for moderate and large data sets. Computational feasibility is assured by using principal component bases for the functional processes. The methodology is motivated by and applied to a diffusion tensor imaging (DTI) study designed to analyze differences and changes in brain connectivity in healthy volunteers and multiple sclerosis (MS) patients. An R implementation is provided.87.

Forecasting pollen concentration by a two-step functional model

A functional regression model to forecast the cypress pollen concentration during a given time interval, considering the air temperature in a previous interval as the input, is derived by means of a two-step procedure. This estimation is carried out by functional principal component (FPC) analysis and the residual noise is also modeled by FPC regression, taking as the explicative process the pollen concentration during the earlier interval. The prediction performance is then tested on pollen data series recorded in Granada (Spain) over a period of 10 years.

Nutrients in fruit increase fertility in wild-caught females of large and long-lived Euphaedra species (Lepidoptera, Nymphalidae)

Fruit-feeding butterflies can experience a more nutrient rich adult diet than nectar-feeding species, and can be expected to use these nutrients for egg production. Here we compare life span, and reproduction parameters of wild-caught females of large and long-lived species on either a sucrose or a mashed banana diet. With small sample sizes per species, but rich longitudinal data for each individual, we examined the longitudinal reproduction pattern, egg size and hatchability of these butterflies in captivity. Diet significantly affected mortality in captivity in a time-dependent manner. On average, we found that butterflies fed mashed banana laid 1.855 times more eggs than those fed sugar. They laid significantly more eggs when they laid and conserved egg size with age while butterflies fed sucrose showed significantly declining egg sizes. Egg hatchability was not significantly affected by diet. Long pre-oviposition periods, significantly smaller first eggs, and absence of age at capture effects on intensity of reproduction indicate low reproduction rates in the field that are due to low food availability. With our small sample sizes, we did not detect significant differences between the species in their response to the diet treatments.

Hypothesis testing in comparative and experimental studies of function-valued traits

Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.

Behavioral trajectories as predictors in event history analysis: male calling behavior forecasts medfly longevity

A recent study on wild male Mediterranean fruit flies [Papadopoulos, N.T., Katsoyannos, B.I., Kouloussis, N.A., Carey, J.R., Müller, H.-G., Zhang, Y., 2004. High sexual signalling rates of young individuals predict extended life span in male Mediterranean fruit flies. Oecologia 138, 127-134] provided evidence that intense sexual signalling (calling behavior) is associated with longer life span. We demonstrate here an approach based on functional data analysis methodology for predicting individual remaining longevity and the distribution of remaining lifetime from individual behavioral trajectories. A key methodological concept is the time evolution of mean functions and eigenfunctions. This methodology is applied to the event history of calling behavior of male medflies. The results demonstrate complex relationships between male calling behavior and subsequent longevity that complement previous biodemographic analyses of these data. A high level of recent calling activity is found to be associated with increased remaining lifetime for an individual male fly, while calling activity at early ages plays no role for remaining longevity.