Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).     

Accounting for data errors discovered from an audit in multiple linear regression

A data coordinating team performed onsite audits and discovered discrepancies between the data sent to the coordinating center and that recorded at sites. We present statistical methods for incorporating audit results into analyses. This can be thought of as a measurement error problem, where the distribution of errors is a mixture with a point mass at 0. If the error rate is nonzero, then even if the mean of the discrepancy between the reported and correct values of a predictor is 0, naive estimates of the association between two continuous variables will be biased. We consider scenarios where there are (1) errors in the predictor, (2) errors in the outcome, and (3) possibly correlated errors in the predictor and outcome. We show how to incorporate the error rate and magnitude, estimated from a random subset (the audited records), to compute unbiased estimates of association and proper confidence intervals. We then extend these results to multiple linear regression where multiple covariates may be incorrect in the database and the rate and magnitude of the errors may depend on study site. We study the finite sample properties of our estimators using simulations, discuss some practical considerations, and illustrate our methods with data from 2815 HIV-infected patients in Latin America, of whom 234 had their data audited using a sequential auditing plan.     

Estimating the prevalence of protein sequences adopting functional enzyme folds

Proteins employ a wide variety of folds to perform their biological functions. How are these folds first acquired? An important step toward answering this is to obtain an estimate of the overall prevalence of sequences adopting functional folds. Since tertiary structure is needed for a typical enzyme active site to form, one way to obtain this estimate is to measure the prevalence of sequences supporting a working active site. Although the immense number of sequence combinations makes wholly random sampling unfeasible, two key simplifications may provide a solution. First, given the importance of hydrophobic interactions to protein folding, it seems likely that the sample space can be restricted to sequences carrying the hydropathic signature of a known fold. Second, because folds are stabilized by the cooperative action of many local interactions distributed throughout the structure, the overall problem of fold stabilization may be viewed reasonably as a collection of coupled local problems. This enables the difficulty of the whole problem to be assessed by assessing the difficulty of several smaller problems. Using these simplifications, the difficulty of specifying a working beta-lactamase domain is assessed here. An alignment of homologous domain sequences is used to deduce the pattern of hydropathic constraints along chains that form the domain fold. Starting with a weakly functional sequence carrying this signature, clusters of ten side-chains within the fold are replaced randomly, within the boundaries of the signature, and tested for function. The prevalence of low-level function in four such experiments indicates that roughly one in 10(64) signature-consistent sequences forms a working domain. Combined with the estimated prevalence of plausible hydropathic patterns (for any fold) and of relevant folds for particular functions, this implies the overall prevalence of sequences performing a specific function by any domain-sized fold may be as low as 1 in 10(77), adding to the body of evidence that functional folds require highly extraordinary sequences.     

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.     

木本植物茎叶功能性状及其关系随环境变化的研究进展

植物功能性状反映了植物对生长环境的响应和适应,是植物与环境相互作用的结果。植物功能性状之间的关系决定了植物的生活史对策,进而影响多物种的共存和生物多样性的维持。本文综述了叶大小、比叶面积、叶寿命和木质密度、叶大小-小枝大小、叶内生物量分配和叶大小-数量等随环境变化的研究进展,并简述其变化机理。植物功能性状及其关系的研究已经取得了很多成果,建立起了一套有效的研究方法和理论体系;但在今后的研究中,还需要对植物的地上部分和地下部分植物性状之间的协变关系、当年生末端小枝上功能性状间的关系的普遍性,以及叶大小-数量的等速关系在整个被子植物中的保守程度等几个方面进行深入研究。我国常绿阔叶林物种的植物功能性状及其关系研究较少,有待加强和系统化。     

Support-vector-machine classification of linear functional motifs in proteins

Our algorithm predicts short linear functional motifs in proteins using only sequence information. Statistical models for short linear functional motifs in proteins are built using the database of short sequence fragments taken from proteins in the current release of the Swiss-Prot database. Those segments are confirmed by experiments to have single-residue post-translational modification. The sensitivities of the classification for various types of short linear motifs are in the range of 70%. The query protein sequence is dissected into short overlapping fragments. All segments are represented as vectors. Each vector is then classified by a machine learning algorithm (Support Vector Machine) as potentially modifiable or not. The resulting list of plausible post-translational sites in the query protein is returned to the user. We also present a study of the human protein kinase C family as a biological application of our method.     

南亚热带森林常见种和偶见种的功能多样性特征

群落特征可能取决于物种在功能实体功能特征的独特组合（FE）中的分布。了解这些分布是保护生物多样性和维持生态系统功能的基础。鼎湖山南亚热带常绿阔叶林群落物种丰富,根据物种的多度来区分常见种（每hm²超过一个个体）和偶见种（每hm²少于一个个体）。基于功能实体,分别计算功能实体数量、功能冗余度、功能脆弱度和功能过度冗余度来描述每个样方中常见种和偶见种的功能多样性。采用Wilcoxon检验检测常见种和偶见种功能性状的差异,通过线性回归分析常见种和偶见种的功能多样性与物种数量的关系,采用冗余分析（RDA）影响常见种和偶见种的功能多样性的环境因子。研究结果表明：（1）鼎湖山南亚热带常绿阔叶林群落中功能性状在常见种和偶见种间差异显著。（2）群落中数量较低的偶见种保持着较高比例的功能实体数量。功能实体数量、功能冗余度与常见种和偶见种数量显著正相关,功能过度冗余度与偶见种数量显著正相关,功能脆弱度与常见种和偶见种的物种数量呈显著负相关。（3）海拔是影响常见种功能多样性最关键的地形因子,凹凸度是影响偶见种功能多样性最关键的地形因子。土壤含水量是影响常见种功能多样性最关键的土壤因子,速效钾是影响偶见种功能多样性最关键的环境因子。研究结果表明,尽管物种丰富的热带森林具有较高的功能冗余,但其提供的保险效应不能抵消生态系统的功能脆弱性。减少具有独特功能实体和偶见种的损失是避免热带森林生态系统功能损失的有效和必要的方法。