On the use of partial area under the ROC curve for comparison of two diagnostic tests

Evaluation of diagnostic performance is typically based on the receiver operating characteristic (ROC) curve and the area under the curve (AUC) as its summary index. The partial area under the curve (pAUC) is an alternative index focusing on the range of practical/clinical relevance. One of the problems preventing more frequent use of the pAUC is the perceived loss of efficiency in cases of noncrossing ROC curves. In this paper, we investigated statistical properties of comparisons of two correlated pAUCs. We demonstrated that outside of the classic model there are practically reasonable ROC types for which comparisons of noncrossing concave curves would be more powerful when based on a part of the curve rather than the entire curve. We argue that this phenomenon stems in part from the exclusion of noninformative parts of the ROC curves that resemble straight‐lines. We conducted extensive simulation studies in families of binormal, straight‐line, and bigamma ROC curves. We demonstrated that comparison of pAUCs is statistically more powerful than comparison of full AUCs when ROC curves are close to a “straight line”. For less flat binormal ROC curves an increase in the integration range often leads to a disproportional increase in pAUCs’ difference, thereby contributing to an increase in statistical power. Thus, efficiency of differences in pAUCs of noncrossing ROC curves depends on the shape of the curves, and for families of ROC curves that are nearly straight‐line shaped, such as bigamma ROC curves, there are multiple practical scenarios in which comparisons of pAUCs are preferable.     

Increased abundance of native and non-native spiders with habitat fragmentation

Habitat fragmentation and invasive species often contribute to the decline of native taxa. Since the penetration of non‐native species into natural habitat may be facilitated by habitat fragmentation, it is important to examine how these two factors interact. Previous research documented that, in contrast to most other arthropod taxa, spiders increased in density and morphospecies richness with decreasing fragment area and increasing fragment age (time since insularization) in urban habitat fragments in San Diego County, California, USA. We tested whether a specific mechanism, an increase in non‐native species with fragmentation, is responsible for this pattern. We found that both native and non‐native taxa contributed to the pattern. Abundance of native spiders per pitfall trap sample increased significantly with decreasing fragment size (i.e. a negative density–area relationship) and abundance of non‐natives increased significantly with increasing fragment age. The proportion of non‐native individuals also increased significantly with age. One non‐native species, Oecobius navus, comprised the majority of non‐native individuals (82.2%) and a significant proportion of total individuals (25.1%). Richness of spider families per sample (family density) increased with fragment age due to an increase in the occurrence of non‐natives in older fragments, however, native family richness did not vary with age or area. Due to increasing dominance by non‐native and some native families, family evenness declined with decreasing fragment size and increasing fragment age. Native and non‐native abundance covaried positively arguing against strong negative interactions between the two groups. O. navus had a strong positive association with another common non‐native arthropod, the Argentine ant (Linepitheme humile), suggesting a possible direct interaction. In contrast, abundance of native spiders was negatively correlated with Argentine ant abundance. We hypothesize that fragmentation in this semiarid habitat increases productivity in smaller and older fragments enhancing the density of both native and non‐native taxa.     

Spectral composition of shade light in coastal-zone oak forests in SE Bulgaria,and relationships with leaf area index: a first overview

Major knowledge gaps exist with respect to light-quality regimes in the coastal-zone Strandzha Quercus frainetto (Q.f.) forest region adjoining the southern Bulgarian Black Sea. This paper presents preliminary results that help narrow these gaps. In conjunction with leaf area index (LAI) field campaigns we undertook measurements with an array of 7 broad-band (ca 40 nm) sensors covering the range 0.40–0.94 μm, plus 1 sensor for UVB (0.297 μm peak) and 1 for photosynthetically active radiation (PAR). Measurements focused on inside-forest shade conditions at sites 0 to ca 15 km from the Black Sea and at altitudes up to ca 120 m above sea level. Some of the sites were also studied using a high-resolution spectroradiometer. A sequential measuring strategy was necessary. This involves potentially large uncertainties, here addressed through estimations of the variability around the sinusoidal course of daylight. Light-quality regimes were found to be in general support of earlier studies of deciduous forests. Our data from the broad-band sensors and from the spectroradiometer are mutually supportive. They indicate a stronger red-shift below Q.f. canopies than below canopies in enclaves dominated by Fagus orientalis and Pinus sylvestris. Transmission in the range 0.50–0.55 μm increases beneath the three types of canopies, most pronounced in the Q.f. case. Analysis of relationships between the inside-forest to open-field irradiance ratio and LAI supports the use of Beer’s Law. We found a fairly strong relationship between the red (0.66 μm) to far-red (0.73 μm) irradiance ratios (R/FR) and LAI for the Q.f. forest. In quantitative terms, the result is new for this Q.f. region, and suggests further research to explore whether a two-sensor approach (0.66 and 0.73 μm) might offer possibilities for further low-cost mapping of the spatio-temporal patterns of R/FR and LAI in Strandzha. Such mapping would assist in further studies of the region’s forest biogeochemistry and vitality.     

Photosynthesis and root growth in Spartina alterniflora in relation to root zone aeration

Spartina alterniflora Lois. is a dominant species growing in intermediate and saline marshes of the US Gulf coast and Atlantic coastal marshes. S. alterniflora plants were subjected to a range of soil redox potential (Eh) conditions representing a well aerated to reduced conditions in a rhizotron system under controlled environmental conditions. The low soil Eh resulted in inhibition of root elongation shortly after treatment initiation. Root elongation was reduced as soil Eh approached values below ca. +350 mV. Substantial decrease in root elongation was noted when soil Eh fell below +200 mV. Generally, net photosynthetic rate (PN) decreased as soil Eh was reduced, with substantial reductions in PN found when Eh approached negative values. Average PN was reduced to 87, 64, and 44% of control under +340, +245, and -180 mV treatments, respectively. The reductions in root elongation and PN in response to low soil Eh indicated the adverse effects of low soil Eh on plant functioning and the need for periods of soil aeration that allow plants to resume normal functioning. Thus periods of drainage allowing soil aeration during the growing season appear to be critical to S. alterniflora by providing favorable conditions for root growth and gas exchange with important implications for plant carbon fixation. This revised version was published online in June 2006 with corrections to the Cover Date.     

Relative efficiency of unequal versus equal cluster sizes in cluster randomized trials using generalized estimating equation models

There is growing interest in conducting cluster randomized trials (CRTs). For simplicity in sample size calculation, the cluster sizes are assumed to be identical across all clusters. However, equal cluster sizes are not guaranteed in practice. Therefore, the relative efficiency (RE) of unequal versus equal cluster sizes has been investigated when testing the treatment effect. One of the most important approaches to analyze a set of correlated data is the generalized estimating equation (GEE) proposed by Liang and Zeger, in which the “working correlation structure” is introduced and the association pattern depends on a vector of association parameters denoted by ρ. In this paper, we utilize GEE models to test the treatment effect in a two‐group comparison for continuous, binary, or count data in CRTs. The variances of the estimator of the treatment effect are derived for the different types of outcome. RE is defined as the ratio of variance of the estimator of the treatment effect for equal to unequal cluster sizes. We discuss a commonly used structure in CRTs—exchangeable, and derive the simpler formula of RE with continuous, binary, and count outcomes. Finally, REs are investigated for several scenarios of cluster size distributions through simulation studies. We propose an adjusted sample size due to efficiency loss. Additionally, we also propose an optimal sample size estimation based on the GEE models under a fixed budget for known and unknown association parameter (ρ) in the working correlation structure within the cluster.     

What is the optimal number of leaves when measuring leaf area of tree species in a forest community?

植物形态性状叶面积简单易测, 能够反映植物对环境的适应与响应, 指示生态系统的功能与过程。在野外测定叶面积时, 叶片取样数量往往采用约定俗成的10-20片, 但到底采集多少叶片才是最优和最具代表性, 却少有探究。该研究以浙江金华山常绿落叶阔叶混交林的优势树种木荷(Schima superba)与枫香树(Liquidambar formosana)为研究对象, 通过对5个胸径等级植株和每个植株6个方位开展大批量叶片取样(>2 500个), 分析两个树种的叶面积变异特征, 探讨叶片取样数量为多少才能最代表该森林类型的叶片大小性状规律。结果表明, 常绿乔木木荷平均叶面积与变幅均小于落叶乔木枫香树。木荷叶面积与胸径无显著相关性, 而枫香树叶面积与胸径有较显著相关性, 但两个树种均在中胸径等级(15-20 cm)差异不显著; 两个树种的叶面积与采样方位无显著相关性, 但在东、西和底部的差异不显著。因此, 综合考虑代表性与野外可操作性, 叶片采集首选中胸径成树的底部叶片。随机抽样统计可知, 树木叶面积测定的最适叶片采集数量因物种而异, 木荷的最适叶片采集数量为40, 而枫香树最少为170片。因此, 在叶面积测定时, 叶片采集的数量应该不能只局限在10-20片, 在人力、物力和时间等条件允许的情况下, 应该尽可能多地测定较多叶片的叶面积。