Proportional Hazards Regression for the Analysis of Clustered Survival Data from Case–Cohort Studies

Summary Case–cohort sampling is a commonly used and efficient method for studying large cohorts. Most existing methods of analysis for case–cohort data have concerned the analysis of univariate failure time data. However, clustered failure time data are commonly encountered in public health studies. For example, patients treated at the same center are unlikely to be independent. In this article, we consider methods based on estimating equations for case–cohort designs for clustered failure time data. We assume a marginal hazards model, with a common baseline hazard and common regression coefficient across clusters. The proposed estimators of the regression parameter and cumulative baseline hazard are shown to be consistent and asymptotically normal, and consistent estimators of the asymptotic covariance matrices are derived. The regression parameter estimator is easily computed using any standard Cox regression software that allows for offset terms. The proposed estimators are investigated in simulation studies, and demonstrated empirically to have increased efficiency relative to some existing methods. The proposed methods are applied to a study of mortality among Canadian dialysis patients.     

Stabilization of telomeres in nonlinear models of proliferating cell lines

We analyse an age-structured model of telomere loss in a proliferating cell population. The cell population is divided into telomere classes, which shorten each round of division. The model consists of a nonlinear system of partial differential equations for the telomere classes. We prove that if the highest telomere class is exempted from mortality, then all the classes stabilize to a nontrivial equilibrium dependent on the initial state of cells in the highest telomere class.     

Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant

The relationship between spatial density and size of plants is an important topic in plant ecology. The self‐thinning rule suggests a ?3/2 power between average biomass and density or a ?1/2 power between stand yield and density. However, the self‐thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log‐linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self‐thinning rule to improve light interception.     

3D Stationary electric current density in a spherical tumor treated with low direct current: an analytical solution

Electrotherapy with direct current delivered through implanted electrodes is used for local control of solid tumors in both preclinical and clinical studies. The aim of this research is to develop a solution method for obtaining a three-dimensional analytical expression for potential and electric current density as functions of direct electric current intensity, differences in conductivities between the tumor and the surrounding healthy tissue, and length, number and polarity of electrodes. The influence of these parameters on electric current density in both media is analyzed. The results show that the electric current density in the tumor is higher than that in the surrounding healthy tissue for any value of these parameters. The conclusion is that the solution method presented in this study is of practical interest because it provides, in a few minutes, a convenient way to visualize in 3D the electric current densities generated by a radial electrode array by means of the adequate selection of direct current intensity, length, number, and polarity of electrodes, and the difference in conductivity between the solid tumor and its surrounding healthy tissue.     

应用结构方程模型解析影响黄连木果实产量 和种子命运的因素

果实(种子)产量和质量是影响植物种群更新的重要因素。为了探明影响黄连木果实产量和种子命运的因素以及这些影响因素之间的相互作用, 作者于2009年对河南省济源市45株黄连木(Pistacia chinensis)结果样树的植株特征、果实特征、果实产量和种子命运等进行了测定, 并用结构方程模型进行综合分析。结果表明: (1)黄连木果实产量与树高、树冠面积和果序大小等特征成正相关, 但与胸径、果实大小相关性不显著; (2)与捕食者饱和假说的预测不一致, 单株果实产量对黄连木广肩小蜂(Eurytoma plotnikovi)的种子捕食率(即虫蛀率)无显著直接负向效应; (3)树高和果实大小对虫蛀率为显著直接正向效应, 胸径对虫蛀率为显著直接负向效应, 显示黄连木广肩小蜂对植株特征和果实特征有一定的选择能力; (4)空壳率与虫蛀率成显著负相关, 空壳果实越多, 越易逃避黄连木广肩小蜂的寄生, 空壳果实的存在对完好种子起到了一定保护作用, 可能是黄连木防御昆虫寄生的重要机制; (5)空壳率和虫蛀率对种子完好率有显著直接负向效应, 而胸径、果序大小和果实产量对完好率为间接正向效应, 树高和果实大小为间接负向效应。可见, 黄连木植株特征和果实特征均不同程度地影响其果实产量和昆虫寄生, 从而影响黄连木的种子质量和种群更新。     

Short-term acclimation of the photosynthetic electron transfer chain to changing light: a mathematical model

Photosynthetic eukaryotes house two photosystems with distinct light absorption spectra. Natural fluctuations in light quality and quantity can lead to unbalanced or excess excitation, compromising photosynthetic efficiency and causing photodamage. Consequently, these organisms have acquired several distinct adaptive mechanisms, collectively referred to as non-photochemical quenching (NPQ) of chlorophyll fluorescence, which modulates the organization and function of the photosynthetic apparatus. The ability to monitor NPQ processes fluorometrically has led to substantial progress in elucidating the underlying molecular mechanisms. However, the relative contribution of distinct NPQ mechanisms to variable light conditions in different photosynthetic eukaryotes remains unclear. Here, we present a mathematical model of the dynamic regulation of eukaryotic photosynthesis using ordinary differential equations. We demonstrate that, for Chlamydomonas, our model recapitulates the basic fluorescence features of short-term light acclimation known as state transitions and discuss how the model can be iteratively refined by comparison with physiological experiments to further our understanding of light acclimation in different species.     

Validation of the Boussinesq equation for use in traction field determination

Cell traction force plays an important role in many biological processes. Several traction force microscopy methods have been developed to determine cell traction forces based on the Boussinesq solution. This approach, however, is rooted in a half-space assumption. The purpose of this study was to determine the error induced in the half-space assumption using a finite element method (FEM). It demonstrates that displacement error between the FEM and the Boussinesq equation can be used to measure the accuracy of the Boussinesq equation, although singularity exists in the loading point. For one concentrated force, significant difference between the FEM and the Boussinesq equation occurs in the whole field; this difference decreases with an increase in the plate thickness. However, in the case of the balanced forces, the offset of the balanced forces decreases the errors in the middle area. Overall, this study demonstrates that increasing the thickness of the polyacrylamide gel is important for reducing the error of the Boussinesq equation when determining the displacement field of the gel under loads.     

避难所对七星瓢虫捕食桃蚜功能反应的影响

自然情况下的捕食是以植物为中介发生的。作者采用植物模型作为捕食环境,测试了单纯的物理因素(避难所)对七星瓢虫Coccinella septempunctata L.捕食桃蚜Myzus persicae(Sulzer)的功能反应的影响。结果表明,避难所的存在能造成七星瓢虫捕食量和捕食率极显著下降,对雄虫的影响显著比雌虫强,且在中等猎物密度时影响更为突出。Logistic回归分析发现,七星瓢虫雌虫和雄虫无论避难所是否存在,功能反应类型均为HollingⅡ型。避难所不存在的情况下,雌、雄成虫的圆盘方程分别为N a=1.0259 N0/(1+0.003078 N0)和N a=0.9246 N0/(1+0.002127 N0),避难所存在的情况下,其圆盘方程分别为N a=0.9500 N0/(1+0.00342 N0)和N a=0.6463N0/(1+0.002262 N0)。避难所的存在能导致两性成虫瞬时攻击率极显著下降,但仅雄虫处置时间极显著延长,说明雄虫在环境异质性较高时捕获猎物更困难。     

Evidence of non‐stationary relationships between climate and forest responses: Increased sensitivity to climate change in Iberian forests

Climate and forest structure are considered major drivers of forest demography and productivity. However, recent evidence suggests that the relationships between climate and tree growth are generally non‐stationary (i.e. non‐time stable), and it remains uncertain whether the relationships between climate, forest structure, demography and productivity are stationary or are being altered by recent climatic and structural changes. Here we analysed three surveys from the Spanish Forest Inventory covering c. 30 years of information and we applied mixed and structural equation models to assess temporal trends in forest structure (stand density, basal area, tree size and tree size inequality), forest demography (ingrowth, growth and mortality) and above‐ground forest productivity. We also quantified whether the interactive effects of climate and forest structure on forest demography and above‐ground forest productivity were stationary over two consecutive time periods. Since the 1980s, density, basal area and tree size increased in Iberian forests, and tree size inequality decreased. In addition, we observed reductions in ingrowth and growth, and increases in mortality. Initial forest structure and water availability mainly modulated the temporal trends in forest structure and demography. The magnitude and direction of the interactive effects of climate and forest structure on forest demography changed over the two time periods analysed indicating non‐stationary relationships between climate, forest structure and demography. Above‐ground forest productivity increased due to a positive balance between ingrowth, growth and mortality. Despite increasing productivity over time, we observed an aggravation of the negative effects of climate change and increased competition on forest demography, reducing ingrowth and growth, and increasing mortality. Interestingly, our results suggest that the negative effects of climate change on forest demography could be ameliorated through forest management, which has profound implications for forest adaptation to climate change.