FLCRM: Functional linear cox regression model

Summary

We consider a functional linear Cox regression model for characterizing the association between time‐to‐event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high‐dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time‐to‐event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high‐dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer's disease. Data used in the preparation of this article were obtained from the ADNI database ( adni.loni.usc.edu ).     

空间独立成分分析实现fMRI信号的盲分离

独立成分分析（ICA）在功能核磁共振成像（fMRI)技术中的应用是近年来人们关注的一个热点。简要介绍了空间独立成分分析（SICA）的模型和方法,将fMRI信号分析看作是一种盲源分离问题,用快速算法实现fMRI信号的盲源分离。对fMRI信号的研究大多是在假定已知事件相关时间过程曲线的情况下,利用相关性分析得到脑的激活区域。在不清楚有哪几种因素对fMRI信号有贡献、也不清楚其时间过程曲线的情况下,用SICA可以对fMRI信号进行盲源分离,提取不同独立成分得到任务相关成分、头动成分、瞬时任务相关成分、噪声干扰、以及其它产生fMRI信号的多种源信号。     

Comparison of discrete-point vs. dimensionality-reduction techniques for describing performance-related aspects of maximal vertical jumping

The aim of this study was to assess and compare the ability of discrete point analysis (DPA), functional principal component analysis (fPCA) and analysis of characterizing phases (ACP) to describe a dependent variable (jump height) using vertical ground reaction force curves captured during the propulsion phase of a countermovement jump. FPCA and ACP are continuous data analysis techniques that reduce the dimensionality of a data set by identifying phases of variation (key phases), which are used to generate subject scores that describe a subject?s behavior. A stepwise multiple regression analysis was used to measure the ability to describe jump height of each data analysis technique. Findings indicated that the order of effectiveness (high to low) across the examined techniques was: ACP (99%), fPCA (78%) and DPA (21%). DPA was outperformed by fPCA and ACP because it can inadvertently compare unrelated features, does not analyze the whole data set and cannot examine important features that occur solely as a phase. ACP outperformed fPCA because it utilizes information within the combined magnitude-time domain, and identifies and examines key phases separately without the deleterious interaction of other key phases.     

新的独立成分分析算法实现功能磁共振成像信号的盲分离

采用独立成分分析(independent component analysis,ICA)的一种新的牛顿型算法来提取功能磁共振成像(functional magnetic rasonance imaging,fMRI)信号中的各种独立成分(包括与实验设计相关的成分以及各种噪声)。与fastICA相比,该算法减少了运算量,提高了运算速度,而且能够很好地分离出各个独立成分。结果表明该算法是一种有效的fMRI信号分析手段。     

Understanding relationship between sequence and functional evolution in yeast proteins

The underlying relationship between functional variables and sequence evolutionary rates is often assessed by partial correlation analysis. However, this strategy is impeded by the difficulty of conducting meaningful statistical analysis using noisy biological data. A recent study suggested that the partial correlation analysis is misleading when data is noisy and that the principal component regression analysis is a better tool to analyze biological data. In this paper, we evaluate how these two statistical tools (partial correlation and principal component regression) perform when data are noisy. Contrary to the earlier conclusion, we found that these two tools perform comparably in most cases. Furthermore, when there is more than one ‘true’ independent variable, partial correlation analysis delivers a better representation of the data. Employing both tools may provide a more complete and complementary representation of the real data. In this light, and with new analyses, we suggest that protein length and gene dispensability play significant, independent roles in yeast protein evolution. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

Exploring spatial and temporal variations of cadmium concentrations in pacific oysters from british columbia

Oysters from the Pacific Northwest coast of British Columbia, Canada, contain high levels of cadmium, in some cases exceeding some international food safety guidelines. A primary goal of this article is the investigation of the spatial and temporal variation in cadmium concentrations for oysters sampled from coastal British Columbia. Such information is important so that recommendations can be made as to where and when oysters can be cultured such that accumulation of cadmium within these oysters is minimized. Some modern statistical methods are applied to achieve this goal, including monotone spline smoothing, functional principal component analysis, and semi-parametric additive modeling. Oyster growth rates are estimated as the first derivatives of the monotone smoothing growth curves. Some important patterns in cadmium accumulation by oysters are observed. For example, most inland regions tend to have a higher level of cadmium concentration than most coastal regions, so more caution needs to be taken for shellfish aquaculture practices occurring in the inland regions. The semi-parametric additive modeling shows that oyster cadmium concentration decreases with oyster length, and oysters sampled at 7 m have higher average cadmium concentration than those sampled at 1 m.     

Joint modelling of paired sparse functional data using principal components

We propose a modelling framework to study the relationship betweentwo paired longitudinally observed variables. The data for eachvariable are viewed as smooth curves measured at discrete time-pointsplus random errors. While the curves for each variable are summarizedusing a few important principal components, the associationof the two longitudinal variables is modelled through the associationof the principal component scores. We use penalized splinesto model the mean curves and the principal component curves,and cast the proposed model into a mixed-effects model frameworkfor model fitting, prediction and inference. The proposed methodcan be applied in the difficult case in which the measurementtimes are irregular and sparse and may differ widely acrossindividuals. Use of functional principal components enhancesmodel interpretation and improves statistical and numericalstability of the parameter estimates.     

Functional Generalized Linear Models with Images as Predictors

Summary .  Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this article, we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high-resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify brain regions that are associated with a clinical outcome. A new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function. The performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors.     

Functional diversity in nematode communities across terrestrial ecosystems

Functional diversity can be defined as the distribution of trait values within a community. Hence, functional diversity can be an indicator of habitat filtering and a reliable environmental predictor of ecosystem functioning. However, there is a serious lack of studies that test how functional diversity indices change depending on the environmental conditions. The aim of this study is to provide such evidence by analyzing the distribution and variation of continuous body-mass values (i.e. functional diversity) and related shifts in body length and width in a nematode community.We used a large online dataset on nematode traits to analyze: (i) the distribution of body mass using three functional diversity indices, i.e. functional richness, functional divergence and functional evenness; (ii) the shifts in body-size traits (length and width); and (iii) the body-mass distributions of five trophic groups and of the entire nematode community.Managed grasslands exhibited the widest range of body-mass values while body-mass distribution in arable fields covered the greatest area in comparison to the other ecosystem types. The shift in body size revealed environmental filters that could not have been identified by the study of functional diversity indices per se. We found low values of functional evenness to be associated with high values of functional richness. We provide novel empirical evidence that body-mass distribution within a trophic group mirrors the effects of habitat filtering more than the distribution in the community as a whole. Hence, our trait-based approach, more than functional diversity itself, disclosed soil food-web structure and identified community responses.     

基于时间聚类分析和独立成分分析的癫痫fMRI盲分析方法

提出了一种基于时间聚类分析和独立成分分析的癫痫fMRI数据盲分析方法,并将两种方法有效联合,提取发作间期的癫痫fMRI激活时空信息.该方法首先由时间聚类分析得到与激活相关的时间峰度特征曲线,以此特征作为时间参考信息;再由空间独立成分分析分解fMRI信号得到空间独立成分;最后将每个独立成分所对应的时间曲线与参考曲线做相关分析提取相应脑激活图.提出的方法无需任何关于癫痫fMRI的先验假设信息,有效解决了独立成分的排序问题,实现了对数据的盲分析.仿真试验结果阐明了这一方法的有效性及可靠性,对癫痫数据的试验结果显示空间定位准确性优于统计参数图方法.     

Functional diversity analysis helps to identify filters affecting community assembly after fen restoration by top-soil removal and hay transfer

Top-soil removal followed by species introduction through hay transfer has appeared as a method to restore drained fens. This method addresses abiotic constraints by restoring hydrology and nutrient status, and biotic constraints by removing an unwanted seed bank and counteracting dispersal-limitation. Restoration works by altering environmental filters. Knowledge about the restoration actions effect on functional traits is necessary to understand which types of species may establish. In this study we analyse which factors in top-soil removal followed by hay transfer influence selection and composition of functional traits. Top-soil removal followed by hay transfer from reference sites was conducted at two sites in the Całowanie fen, 33 km SE of Warsaw, Poland. Species and abundance data were recorded for three consecutive years. These data, combined with data on functional traits were used to analyse the effect of the restoration actions on four functional diversity-indices and the community weighted mean of functional traits. Our results reveal a strong habitat filter in the restoration site that follows an elevation gradient. At low elevation this filter selects low values of autochory and specific leaf area and high values of clonal lateral spread, Ellenberg moisture values, and dispersal through hydrochory. The transferred hay differs in trait characteristics compared to the reference site vegetation by having species of higher specific leaf area, lower Ellenberg moisture value and lower dispersal by autochory and hydrochory. The result presented here has three important implications for fen restoration. First, the difference in trait-characteristics between the transferred hay and the reference site it was harvested from limits the restoration potential. Second, since for several fen species important functional traits are filtered along an elevation-gradient, careful planning regarding depth of top-soil removal is needed. Finally the results illustrate how a functional analysis can be used to detect environmental filters acting during ecological restoration.     

Functional regularity: a neglected aspect of functional diversity

Functional diversity has been identified as a key to understanding ecosystem and community functioning. However, due to the lack of a sound definition its nature and measurement are still poorly understood. In the same way that species diversity can be split into species richness and species evenness, so functional diversity can be split into functional richness (i.e. the amount of functional trait/character/attribute space filled) and functional evenness (i.e. the evenness of abundance distribution in functional trait space). We propose a functional regularity index (FRO) as a measure of functional evenness for situations where species are represented only by a single functional trait value (e.g. mean, median or mode), and species abundances are known. This new index is based on the Bulla O index of species evenness. When dealing with functional types or categorical functional traits, the Bulla O or any other accepted species evenness index may be used directly to measure functional evenness. The advantage of FRO is that it supplies a measure of functional evenness for continuous trait data. The FRO index presented in this paper fulfils all the a priori criteria required. We demonstrate with two example datasets that a range of FRO values may be obtained for both plant and animal communities. Moreover, FRO was strongly related to ecosystem function as seen in photosynthetic biomass in plant communities, and was able to differentiate sampling stations in a lagoon based on the functional traits of fish. Thus, the FRO index is potentially a highly useful tool for measuring functional diversity in a variety of ecological situations.     

Comparing and predicting between several methods of measurement

In studies designed to compare different methods of measurement where more than two methods are compared or replicate measurements by each method are available, standard statistical approaches such as computation of limits of agreement are not directly applicable. A model is presented for comparing several methods of measurement in the situation where replicate measurements by each method are available. Measurements are viewed as classified by method, subject and replicate. Models assuming exchangeable as well as non-exchangeable replicates are considered. A fitting algorithm is presented that allows the estimation of linear relationships between methods as well as relevant variance components. The algorithm only uses methods already implemented in most statistical software.     

Effects of different components of diversity on productivity in artificial plant communities

In an experiment on artificial plant communities, the effects of three components of plant diversity—plant species diversity, plant functional group diversity and plant functional diversity—on community productivity and soil water content were compared. We found that simple regression analysis showed a positive diversity effect on ecosystem processes (productivity and soil water content). However, when three components of diversity were included in the multiple regression analyses, the results showed that functional group diversity and functional diversity had more important effects on productivity and resource use efficiency. These results suggested that, compared with species number, functional differences among species and the range of functional traits carried by plants are the basis of biodiversity effects on ecosystem functioning. These diversity effects of increasing functional group diversity or functional diversity were likely because species differing greatly in size, life form, phenology and capacity to capture and use resources efficiently in diverse communities realize complementary resource use in temporal, spatial, and biological ways.     

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

A recurring objective in longitudinal studies on aging and longevity has been the investigation of the relationship between age-at-death and current values of a longitudinal covariate trajectory that quantifies reproductive or other behavioral activity. We propose a novel technique for predicting age-at-death distributions for situations where an entire covariate history is included in the predictor. The predictor trajectories up to current time are represented by time-varying functional principal component scores, which are continuously updated as time progresses and are considered to be time-varying predictor variables that are entered into a class of time-varying functional regression models that we propose. We demonstrate for biodemographic data how these methods can be applied to obtain predictions for age-at-death and estimates of remaining lifetime distributions, including estimates of quantiles and of prediction intervals for remaining lifetime. Estimates and predictions are obtained for individual subjects, based on their observed behavioral trajectories, and include a dimension-reduction step that is implemented by projecting on a single index. The proposed techniques are illustrated with data on longitudinal daily egg-laying for female medflies, predicting remaining lifetime and age-at-death distributions from individual event histories observed up to current time.