Assessing alignment between functional markers and ordinal outcomes based on broad sense agreement

Functional markers and their quantitative features (eg, maximum value, time to maximum, area under the curve [AUC], etc) are increasingly being used in clinical studies to diagnose diseases. It is thus of interest to assess the diagnostic utility of functional markers by assessing alignment between their quantitative features and an ordinal gold standard test that reflects the severity of disease. The concept of broad sense agreement (BSA) has recently been introduced for studying the relationship between continuous and ordinal measurements, and provides a promising tool to address such a question. Our strategy is to adopt a general class of summary functionals (SFs), each of which flexibly captures a different quantitative feature of a functional marker, and study its alignment according to an ordinal outcome via BSA. We further illustrate the proposed framework using three special classes of SFs (AUC‐type, magnitude‐specific, and time‐specific) that are widely used in clinical settings. The proposed BSA estimator is proven to be consistent and asymptotically normal given a consistent estimator for the SF. We further provide an inferential framework for comparing a pair of candidate SFs in terms of their importance on the ordinal outcome. Our simulation results demonstrate satisfactory finite‐sample performance of the proposed framework. We demonstrate the application of our methods using a renal study.     

常见寿命数据类型及生命表的编制方法

生命表是描述种群死亡过程的有用工具,介绍了4种常见的寿命数据类型;寿终数据,右删失数据,左删失数据和区间型数据特征及其相应的数据分析处理方法即生命表法,乘积限估计和Turbull估计法,对生命表法和乘积限估计法应用上的特点进行了比较,同时还对特殊的寿命数据类型－－截断数据做了简要介绍。     

Robust functional principal component analysis via a functional pairwise spatial sign operator

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy-tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large-scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women.     

Maximum Likelihood Methods for Fitting the Burr Type XII Distribution to Life Test Data

This paper describes mathematical and computational methodology for estimating the parameters of the Burr Type XII distribution by the method of maximum likelihood. Expressions for the asymptotic variances and covariances of the parameter estimates are given, and the modality of the log-likelihood and conditional log-likelihood functions is analyzed. As a result of this analysis for various a priori known and unknown parameter combinations, conditions are given which guarantee that the parameter estimates obtained will, indeed, be maximum likelihood estimates. An efficient numerical method for maximizing the conditional log-likelihood function is described, and mathematical expressions are given for the various numerical approximations needed to evaluate the expressions given for the asymptotic variances and covariances of the parameter estimates. The methodology discussed is applied in a numerical example to life test data arising in a clinical setting.     

Weighted rank regression for clustered data analysis

Summary .   We consider ranked-based regression models for clustered data analysis. A weighted Wilcoxon rank method is proposed to take account of within-cluster correlations and varying cluster sizes. The asymptotic normality of the resulting estimators is established. A method to estimate covariance of the estimators is also given, which can bypass estimation of the density function. Simulation studies are carried out to compare different estimators for a number of scenarios on the correlation structure, presence/absence of outliers and different correlation values. The proposed methods appear to perform well, in particular, the one incorporating the correlation in the weighting achieves the highest efficiency and robustness against misspecification of correlation structure and outliers. A real example is provided for illustration.     

Personal exposure to mobile communication networks and well‐being in children—A statistical analysis based on a functional approach

The MobilEe‐study was the first cross‐sectional population‐based study to investigate possible health effects of mobile communication networks on children using personal dosimetry. Exposure was assessed every second resulting in 86,400 measurements over 24 h for each participant. Therefore, a functional approach to analyze the exposure data was considered appropriate. The aim was to categorize exposure taking into account the course of the measurements over 24 h. The analyses were based on the 480 maxima of each 3 min time interval. Exposure was classified using a nonparametric functional method. Heterogeneity of a sample of functional data was assessed by comparing the functional mode and mean of the distribution of a functional variable. The partition was built within a descending hierarchical method. The resulting exposure groups were compared with categories derived from a standard method, which used the average exposure over 24 h and set the cut‐off at the 90th percentile. The functional classification resulted in a splitting of the exposure data into two groups. Plots of the mean curves showed that the groups could be interpreted as children with “low exposure” (88%) and “higher exposure” (12%). These groups were comparable with categories of the standard method. No association between the categorized exposure and well‐being was observed in logistic regression models. The functional classification approach yielded a plausible partition of the exposure data. The comparability with the standard approach might be due to the data structure and should not be generalized to other exposures. Bioelectromagnetics 30:261–269, 2009. © 2009 Wiley‐Liss, Inc.     

Maturation and sexual ontogeny in the spangled emperor Lethrinus nebulosus

The reproductive development and sexual ontogeny of spangled emperor Lethrinus nebulosus populations in the Ningaloo Marine Park (NMP) were investigated to obtain an improved understanding of its evolved reproductive strategy and data for fisheries management. Evidence derived from (1) analyses of histological data and sampled sex ratios with size and age, (2) the identification of residual previtellogenic oocytes in immature and mature testes sampled during the spawning season and (3) observed changes in testis internal structure with increasing fish size and age, demonstrated a non‐functional protogynous hermaphroditic strategy (or functional gonochorism). All the smallest and youngest fish sampled were female until they either changed sex to male at a mean 277·5 mm total length (L_T) and 2·3 years old or remained female and matured at a larger mean L_T (392·1 mm) and older age (3·5 years). Gonad masses were similar for males and females over the size range sampled and throughout long reproductive lives (up to a maximum estimated age of c. 31 years), which was another correlate of functional gonochorism. That the mean L_T at sex change and female maturity were below the current minimum legal size (MLS) limit (410 mm) demonstrated that the current MLS limit is effective for preventing recreational fishers in the NMP retaining at least half of the juvenile males and females in their landed catches.     

A penalized spline approach to functional mixed effects model analysis

In this article, we propose penalized spline (P-spline)-based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects, and residual measurement error processes. Using P-splines, we propose nonparametric estimation of the population mean function, varying coefficient, random subject-specific curves, and the associated covariance function that represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Proposed methods offer flexible estimation of both the population- and subject-level curves. In addition, decomposing variability of the outcomes as a between- and within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood-based method to select multiple smoothing parameters. Furthermore, we study the asymptotics of the baseline P-spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between- and within-subject covariance decomposition is illustrated through an analysis of Berkeley growth data, where we identified clearly distinct patterns of the between- and within-subject covariance functions of children's heights. We also apply the proposed methods to estimate the effect of antihypertensive treatment from the Framingham Heart Study data.     

Nonnegative decomposition of functional count data

We present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization. Our decomposition, which we refer to as NARFD (nonnegative and regularized function decomposition), enables the study of patterns in variation across subjects in a highly interpretable manner. Prototypic modes of variation are estimated directly on the observed scale of the data, are local, and are transparently added together to reconstruct observed functions. This contrasts with generalized functional principal component analysis, an alternative approach that estimates functional principal components on a transformed scale, produces components that typically vary across the entire functional domain, and reconstructs observations using complex patterns of cancellation and multiplication of functional principal components. NARFD is implemented using an alternating minimization algorithm, and we evaluate our approach in simulations. We apply NARFD to an accelerometer dataset comprising observations of physical activity for healthy older Americans.     

捕食性昆虫的功能反应方程及其参数的估算

昆虫的功能反应是指每头捕食者在一定时间内的捕食量对猎物密度变化的反应。该文介绍描述这种功能反应的圆盘方程 (Ⅱ型 )的由来及其参数的估测方法 ,简要讨论了影响昆虫功能反应测定的主要因素。     

A novel Bayesian functional spatial partitioning method with application to prostate cancer lesion detection using MRI

Spatial partitioning methods correct for nonstationarity in spatially related data by partitioning the space into regions of local stationarity. Existing spatial partitioning methods can only estimate linear partitioning boundaries. This is inadequate for detecting an arbitrarily shaped anomalous spatial region within a larger area. We propose a novel Bayesian functional spatial partitioning (BFSP) algorithm, which estimates closed curves that act as partitioning boundaries around anomalous regions of data with a distinct distribution or spatial process. Our method utilizes transitions between a fixed Cartesian and moving polar coordinate system to model the smooth boundary curves using functional estimation tools. Using adaptive Metropolis-Hastings, the BFSP algorithm simultaneously estimates the partitioning boundary and the parameters of the spatial distributions within each region. Through simulation we show that our method is robust to shape of the target zone and region-specific spatial processes. We illustrate our method through the detection of prostate cancer lesions using magnetic resonance imaging.     

具有左截断、右删失寿命数据类型的生命表编制方法

左截断数据是一类特殊的寿命数据类型,其定义为一些动物个体并非在初始时间（出生或孵化）而是在某个时间（年龄）延滞之后才进入调查取样范围而收集到的一类寿命数据。传统的乘积限估计法只能处理寿终数据和右删失数据,对左截断数据则无能为力。本文提出一种对乘积限估计法改进方法,此种方法能同时处理寿终数据、右删失数据和左截断数据,从而有效地利用了左截断数据所含有的物种存活信息。     

Functional data analysis for longitudinal data with informative observation times

In functional data analysis for longitudinal data, the observation process is typically assumed to be noninformative, which is often violated in real applications. Thus, methods that fail to account for the dependence between observation times and longitudinal outcomes may result in biased estimation. For longitudinal data with informative observation times, we find that under a general class of shared random effect models, a commonly used functional data method may lead to inconsistent model estimation while another functional data method results in consistent and even rate-optimal estimation. Indeed, we show that the mean function can be estimated appropriately via penalized splines and that the covariance function can be estimated appropriately via penalized tensor-product splines, both with specific choices of parameters. For the proposed method, theoretical results are provided, and simulation studies and a real data analysis are conducted to demonstrate its performance.     

Reproduction is adapted to survival characteristics across geographically isolated medfly populations

We propose the hypothesis that individual longitudinal trajectories of fertility are closely coupled to varying survival schedules across geographically isolated populations of the same species, in such a way that peak reproduction takes place before substantial increases in mortality are observed. This reproductive adaptation hypothesis is investigated for medflies through a statistical analysis of biodemographic data that were obtained for female medflies from six geographically far apart regions. The following results support the hypothesis: (i) both survival and reproductive schedules differ substantially between these populations, where early peaks and subsequently fast declining reproduction are observed for short-lived and protracted reproductive schedules for long-lived flies; (ii) when statistically adjusting reproduction for the observed differences in survival, the differences in reproductive schedules largely vanish, and thus the observed differences in fertility across the populations can be explained by differences in population-specific longevity; and (iii) specific survival patterns of the medflies belonging to a specific population predict the individual reproductive schedule for the flies in this population. The analysis is based on innovative statistical tools from functional data analysis. Our findings are consistent with an adaptive mechanism whereby trajectories of fertility evolve in response to specific constraints inherent in the population survival schedules.